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Project Title - Pointing Error Engineering Tool (PEET)

1. Block mask parameters P Gains Vector A vector containing the proportional gains for each axis I Gains Vector A vector containing the integral gains for each axis D Gains Vector A vector containing the differential gains for each axis Note that per definition of this block only a single 3D input signal can be fed to the PID controller However more complex inputs e g feeding an attitude signal to the proportional part and a rate signal to the differential one can be realized by proper modification of the desired closed loop structure An example for such realization is given in section 6 2 8 3 of RD1 Astos Solutions GmbH All Rights Reserved Copyright 2013 per ISO 16016 Grund 1 78089 Unterkirnach Germany Copying and distribution is prohibited without express authority Doc No ASTOS PEET SUM 001 Astos PEET Issue 17 Date 2013 07 26 Solutions Page 39 of 60 7 13 Static System Block The static system block is used to model all kind of static systems The static system block is using a 3x3 static gain matrix as the system model The elements of the system transfer matrix are double values 7 13 1 Block Parameters The block mask parameters for the static system block are listed below Block mask parameters System matrix Matrix A 3x3 matrix of double values describing the system transfer 7 14 Summation Block The summation block is used to sum up sever
2. 7 7 Mapping Block The Mapping block is used to map a 1D signal to a spatially distributed 3D signal i e mapping thruster noise from the axis of each thruster to the reference frame of the pointing error The user input consists of the number of devices n that are mapped by this block and the nx3 mapping matrix The mapping block extends the 1D signal to an nxn signal and transfers the nxn signal through the nx3 mapping matrix which serves as a static system Finally it produces a three dimensional signal Astos Solutions GmbH All Rights Reserved Copyright 2013 per ISO 16016 Grund 1 78089 Unterkirnach Germany Copying and distribution is prohibited without express authority Doc No ASTOS PEET SUM 001 Astos PEET Issue 17 Date 2013 07 26 Solutions Page 22 of 60 7 7 1 Block Parameters The next table explains the block mask parameters for the Mapping block Block mask parameters Number of devices Selection The number of devices which will be mapped by this block Possible values are in the range from 1 to 99 Mapping matrix Matrix The nx3 mapping matrix with as many rows as devices are defined The columns contain the mappings for the x y and z axis 7 8 PEC Blocks The pointing error contributor block represents the endpoint of each PEET system model at which the resulting total error contribution shall be evaluated The evaluation is realized according to AST 4 of AD2 and the results ar
3. It is also possible to define correlations between error sources This is done by selecting Setup Edit PES Correlations from the menu This will open the correlation manager dialog shown in Figure 10 8 Correlation Matrix First source PESi1 we Second source DES 3 wv Correlation between PES Correlation Uncorrelated ze Figure 10 8 Correlation manager dialog Using this dialog the correlation between two error sources can be defined The correlation can be set to either Uncorrelated or Fully correlated In this example the correlation between PES 1 and PES 2 is set to Uncorrelated Simply click Cancel to close the dialog 10 2 Computing pointing errors After the pointing system has been defined the error computations can be performed To perform the error computations some error indices must be created Afterwards the computation can be performed from the tree view window and the results can be inspected in the information section of the tree view window 10 2 1 Creating error indices Before running any computation one or more error indices must be created To create an error index the error index manager must be opened This is done by selecting Setup Edit Error Indices from the menu bar of the system view window The error index manager is shown in Figure 10 9 stos PEET Issue 1 7 Date 2013 07 26 Astos Solutions GmbH Grund 1 78089 Unterkirnach Germany All Rights Reserved
4. The location of the blocks can be changed by selecting a block and dragging it to the desired location It is also possible to zoom the system view by pressing the right mouse button and moving the mouse to the left zoom out or right zoom in For editing a connection between blocks the user has some possibilities Figure 6 2 shows a selected connection which now can be edited by the user PEET W sources PEET examples SimpleDemo peet DER Fie Setup Database Windows xKA Static System 1 eg AN Dynamic System 2 gt Dynamic System 1 Static System 2 Figure 6 2 Editing connections To edit the location of the connection the user has to click on one of the red spots of the line Afterwards the spot can be moved to the desired location In this way connections are completely adjustable by the user Astos Solutions GmbH All Rights Reserved Copyright 2013 per ISO 16016 Grund 1 78089 Unterkirnach Germany Copying and distribution is prohibited without express authority Doc No ASTOS PEET SUM 001 Astos PEET Issue 1 7 Date 2013 07 26 f J Solutions Page 13 of 60 6 2 The Tree View The tree view window can be used to analyse pointing errors Figure 6 3 gives an example of the tree view window Error Budgeting Block ID Dynamic System 2 Blocktype Dynamic System Out
5. Copyright 2013 per ISO 16016 Copying and distribution is prohibited without express authority Astos Solutions Doc No ASTOS PEET SUM 001 PEET Issue Page 1 7 57 Date 2013 07 26 of 60 Index Manager Choose Error Index Type Choose error index type Absolute Knowledge Error Absolute Knowledge Error Absolute Performance Error Mean Knowledge Error Mean Performance Error Relative Knowledge Error Relative Performance Error Knowledge Drift Error Performance Drift Error Figure 10 9 Error index manager At the beginning no error indices are defined To add an error index click on the green plus sign This will open a small dialog in which the type of the error index must be selected Select Absolute Performance Error and press the OK button This will add a new error index to the index manager The list of all defined error indices is located on the left side of the error index manager Figure 10 10 shows the error index manager after the new error index was created If the newly created error index is not selected in the index list select it Selecting an error index will show its parameters in the index manager These parameters may vary depending on the error index type For this example set the ID to APE ensemble the statistical interpretation to 1 to 3 0 Then confirm the index settings by pressing the OK button Ensemble and the confidence coefficient Ast
6. The number of flexible modes Inertia Matrix A 3x3 matrix containing the inertia tensor Coupling coefficients Matrix A 3xn matrix containing the coupling coefficients for each axis and for each mode Cantilever frequency Matrix Annx1 vector containing the diagonal elements of the cantilever frequency matrix for the n modes of the flexible plant Damping ratio Matrix Annx1 vector containing the diagonal elements of damping ratio matrix for the n modes of the flexible plant 7 5 Gyro Rate Noise Block This block implements a special kind of pointing error source which combines typical gyro rate noise contributors in one source The resulting noise shape is fitted to a transfer function with user specified parameters and mapped to all axes x y and z assuming no correlation between the axes Astos Solutions GmbH All Rights Reserved Copyright 2013 per ISO 16016 Grund 1 78089 Unterkirnach Germany Copying and distribution is prohibited without express authority Doc No ASTOS PEET SUM 001 Astos PEET Issue 17 Date 2013 07 26 Solutions Page 20 of 60 7 5 1 Block Parameters The GUI parameters for the gyro rate noise block are shown in the table below Block mask parameters Min pole order Double Minimum pole order for rational fit of PSD Max pole order Double Maximum pole order for rational fit of PSD Number of frequency Double Frequency point used for rational fitting
7. 16016 Grund 1 78089 Unterkirnach Germany Copying and distribution is prohibited without express authority Doc No ASTOS PEET SUM 001 J Astos P E ET Issue 1 7 Date 2013 07 26 Solutions Page 43 of 60 8 1 Global settings Before computing the error budget some global settings can be adapted by the user This is done by selecting Settings from the Setup menu Here the evaluation bandwidth for the determination of equivalent random process variances can be specified by providing the upper and lower frequency bounds the number of frequency points evaluated between these bounds In addition the line of sight axis for the pointing error evaluation can be selected 8 2 Configuring blocks After a block was added to the pointing system its parameters must be set This is done by double clicking on the block This will bring up the block mask associated with the block type Figure 8 2 gives an example for such a block mask PEET W sources PEET examples SimpleDemo peet Fie Setup Database Windows Y KA ccc Static System 1 PES 3 Settings Signal dimension E v v Use time constant part V Use time random part LN Time constant Time random Dynamic System 1 Distribution type Discrete x 3 0 Mean value Static System 2 Figure 8 2 Block mask for a pointing error source The content of th
8. 5 Rayleigh Distribution Parameter The Rayleigh distribution is a continuous probability distribution with the probability density function 2 pdf x e Ze x20 0 gt 0 o in which o is called the Rayleigh parameter The parameters provided by the block mask are listed in the next table Block mask parameters Rayleigh parameter Double Vector The Rayleigh parameter of the Rayleigh distribution In case of a three dimensional PES this is a vector containing the Rayleigh Astos Solutions GmbH All Rights Reserved Copyright 2013 per ISO 16016 Grund 1 78089 Unterkirnach Germany Copying and distribution is prohibited without express authority Doc No ASTOS PEET SUM 001 Astos PEET Issue 17 Date 2013 07 26 Solutions Page 27 of 60 parameter for the x y and z axis For a one dimensional PES the parameter is a single double value Axes correlation String The correlation between the axes Possible values are Uncorrelated and Full correlated Only available in case of a three dimensional PES 7 9 2 Time Random Block Parameters The time random part of the pointing error source can either be defined as a random variable or as a random process If the time random part is defined as a random variable the user has to choose from a list of probability distributions Possible values are Uniform Gaussian and Drift For the Uniform distribution the parameters are the same as for th
9. 78089 Unterkirnach Germany Copying and distribution is prohibited without express authority Doc No ASTOS PEET SUM 001 Astos PEET Issue 17 Date 2013 07 26 Solutions Page 19 of 60 7 4 Flexible Plant Block This block implements flexible satellite dynamics It takes multiple n flexible modes defined by the user with their corresponding parameters and the inertia tensor of the plant Afterwards it constructs an n termed dynamic system transfers the input signal through each term of the dynamic system each flexible mode and sums up the transferred signals as the final response of this block type The underlying model is given by the following set of equations Oa s5a N Eq 7 1 amp 26244 0 a 5 Q Eq 7 2 with spacecraft inertia matrix 3x3 vector of spacecraft angular rates 3x1 a matrix of coupling coefficients describing the coupling of flexible modes into the spacecraft body rotation 3xn N vector of torques acting on the spacecraft body 3x1 a vector containing the amplitudes of n flexible modes nx1 diagonal matrix containing the damping ratio of the flexible modes nxn Q diagonal matrix containing the cantilever frequencies of the flexible modes nxn Note that this model ignores the coupling between the flexure and the spacecraft linear acceleration force 7 4 1 Block Parameters The block mask parameters for the flexible block are listed in the next table Block mask parameters Mode Integer
10. A1 will link the first cell in the first row of an Excel sheet 2 The row and column is defined by an index starting at 1 The column index comes first and is preceded by the lower letter c The row index is preceded by the lower letter r Example Setting range to c1r1 will link the first cell in the first row of an Excel sheet Matrix and table data Matrix and table data values can be defined similar to scalar values In this case the upper left and the lower right cell of the data range must be defined 1 The upper left and the lower right cell are defined using upper case letters for the columns and indices for the rows The row index of the first row is 1 The cells are separated by Example Setting range to A1 C3 will link a 3x3 matrix starting at the first cell of the first row of an Excel sheet 2 The upper left and the lower right cell are defined using row and column indices starting at 1 The column index comes first and is preceded by the lower letter c The row index is preceded by the lower letter r The cells are separated by Example Setting the range to c1r1 c3r3 will link a 3x3 matrix starting at the first cell of the first row of an Excel sheet 8 2 1 2 Linking to MATLAB workspace variables Linking parameter values to MATLAB variables is similar to the linking of Excel data In order to link data from the MATLAB workspace a MATLAB variable must be created before parameter values can be linked to it Af
11. Astos Solutions GmbH Grund 1 78089 Unterkirnach Germany All Rights Reserved Copyright 2013 per ISO 16016 Copying and distribution is prohibited without express authority Doc No ASTOS PEET SUM 001 Astos PEET Issue 17 Date 2013 07 26 Solutions Page 32 of 60 k Oj x o r SC NN Eq 7 9 with m flywheel mass F the x y excitation forces for the radial translation mode damping of the radial translation mode f frequency of the radial translation mode F sc resulting x y disturbance forces at the spacecraft interface F 7 10 1 2 Axial Force Model The axial wheel z axis disturbance forces acting on the spacecraft interface are modelled using the set of equations described below mz c z k z F Eq 7 10 c 4n Im Eq 7 11 k m 2zf Eq 7 12 F sc k z Eq 7 13 with m flywheel mass F the excitation forces for the axial translation mode damping of the axial translation mode f frequency of the axial translation mode F sc resulting z disturbance force at the spacecraft interface a 7 10 1 3 Excitation Force Model According to RD8 the overall excitation force comprises broadband noise and tonal disturbances which can be defined individually for the radial and axial modes F r r tond r noise F F F tonal ee Eq 7 14 j F E tia a F noise Astos Solutions GmbH All Rights Reserved Copyright 2013 per ISO 16016 Grund 1 78089 Unterkirnach Germany Copying and d
12. Date 2013 07 26 Doc No ASTOS PEET SUM 001 J Solutions Page 21 of 60 R 1 K s Ka nge S Dgo Bayro eave B s K s K Kgs mg Kg Myo S K Baro 7 6 1 Block Parameters The GUI parameters for the gyro stellar estimator block are listed in the next table Kalman gain Kp Vector A three dimensional vector containing the Kalman gains Kp for the x y and z axis The elements of the vector are of type double Kalman gain Kd _ Vector A three dimensional vector containing the Kalman gains Kd for the x y and z axis The elements of the vector are of type double 7 6 2 Block inputs and outputs The gyro stellar estimator block offers the user three input and two output ports All of these ports are optional and can be left unconnected An explanation of these ports is provided by the tables below n_str The star tracker measurement noise n_gyro The gyro rate measurement noise b_gyro The gyro drift bias noise Rate random walk _est The attitude estimation error B est The gyro bias estimation error Note the gyro noise contributions can be realized in different ways Either as individual signals using both n_gyro and b_gyro or by combining the gyro drift bias and rate noise to a total noise using the Gyro Rate Noise block presented in section 7 5 only and feeding it to the n_gyro input only see also definition of PES 7 in the PointingSat example for further details
13. PEET SUM 001 Astos PEET Issue 17 Date 2013 07 26 Solutions Page 37 of 60 7 10 2 3 Block Parameters The following tables summarize the parameters to be defined by the user Wheel properties Block mask parameters Inertia about spin Double Wheel inertia about spin axis kg m axis Inertia perpendicular Double Wheel inertia perpendicular to spin axis kg m to spin axis Wheel speed Double Rotational speed of the reaction wheel rpm Rocking mode Block mask parameters Rocking mode Double Rocking mode frequency Hz frequency Rocking mode Double Rocking mode damping damping Broadband noise Selection Type of noise model for torque Standard deviation Band limited or PSD Noise standard Double Torque noise standard deviation case Standard deviation deviation or Band limited Nm Noise bandwidth Double Upper frequency limit for torque noise content case Band limited Hz PSD representation Dependent See section 7 9 2 4 N VHz case PSD Tonal disturbance Selection Type of noise model for disturbance torque by imbalance or by harmonics Dynamic imbalance Double Dynamic imbalance coefficient case by imbalance coefficient cm g Number of Double Overall number N of harmonics to be considered for harmonics the rocking mode case by harmonics Amplitude Vector Nx1 vector of amplitude coefficients case by coefficients harmonic
14. field B is the angle between the sensor boresight and the spacecraft rotation axis and a is the angle between the star image direction of motion on the detector matrix and the reference axis The PSD of the field of view noise can be modelled using a 2nd order filter as 2 D dg PSD E 4 r Eq 7 33 1 1 pixe 52 2 amp oS S pixe q where the characteristic frequency ou is given by 46 Eq 7 34 pixel The correlation time TI is again assumed to be proportional to the inverse of the velocity Vga star N pixels T pixel v Eq 7 35 star where N pixels is the size of the centroiding window 7 15 1 Block Parameters The block mask parameters for the star tracker noise are listed in the next table subdivided into general parameters field of view noise parameters and pixel noise parameters General parameters Block mask parameters Detector size Double Number of detector pixels Sensor field of view Double Field of view of the sensor camera head Spacecraft angular Double Average spacecraft angular velocity velocity Average number of Double Average number of stars tracked by the sensor tracked stars Alpha Double The angle between the star image direction of motion on the detector matrix and the reference axis Beta Double The angle between the sensor boresight and the spacecraft rotation axis Note For a worst case set Alpha to 0 and Beta to 2 2 Field of vi
15. gives a detailed explanation about performing and analysing error computations Astos Solutions GmbH All Rights Reserved Copyright 2013 per ISO 16016 Grund 1 78089 Unterkirnach Germany Copying and distribution is prohibited without express authority Doc No ASTOS PEET SUM 001 Astos PEET Issue 17 Date 2013 07 26 Solutions Page 9 of 60 4 Prerequisites The following items are mandatory to install PEET Standard Desktop PC Windows XP or higher MATLAB 201 1b or higher MATLAB Control System Toolbox Astos Solutions GmbH All Rights Reserved Copyright 2013 per ISO 16016 Grund 1 78089 Unterkirnach Germany Copying and distribution is prohibited without express authority Doc No ASTOS PEET SUM 001 ssue ate 07 J Astos PEET 1 7 Date 2013 07 26 Solutions Page 10 of 60 5 Installing and running PEET 5 1 Installation PEET can be installed to any location by simply placing the PEET folder at the desired location The PEET folder must be writeable for all users PEET is completely running inside the MATLAB environment As already mentioned in the introduction the graphical user interface is written in Java All the java classes required by PEET are stored in the following jar files peet jar graphical user interface of PEET jxl jar Java classes used for import and export of Excel data piccolo2d core 1 3 1 jar graphical framework used by the GUI piccolo2d extras 1 3 1 jar graphical framework us
16. next table Astos Solutions GmbH All Rights Reserved Copyright 2013 per ISO 16016 Grund 1 78089 Unterkirnach Germany Copying and distribution is prohibited without express authority Doc No ASTOS PEET SUM 001 Astos PEET Issue 17 Date 2013 07 26 Solutions Page 25 of 60 Block mask parameters Mean value Double Vector The mean value of the discrete distribution In case of a three dimensional PES this is a vector containing the mean values for the x y and z axis For a one dimensional PES the mean value is a single double value 7 9 1 2 Uniform Distribution Parameters The uniform distribution is a continuous probability distribution with the probability density function 1 pdf x b a 0 x gt a or x gt b a lt x lt b in which a is called the minimum value and b is called the maximum value The parameters for the Uniform probability distribution are listed below Block mask parameters Minimum Double The minimum value of the uniform distribution In Vector case of a three dimensional PES this is a vector containing the minimum values for the x y and z axis For a one dimensional PES the minimum value is a single double value Maximum Double The maximum value of the uniform distribution In Vector case of a three dimensional PES this is a vector containing the maximum values for the x y and z axis For a one dimensional PES the maximum value is a single double value
17. oV2n in which u is called mean value o is called standard deviation and o is called variance The block mask parameters offered by the PES block are listed below Block mask parameters Mean value Double Vector The mean value for the Gaussian distribution In case of a three dimensional PES this is a vector containing the mean values for the x y and z axis For a one dimensional PES the mean value is a single double value Standard Double Vector The standard deviation for the Gaussian deviation distribution In case of a three dimensional PES this is a vector containing the standard deviation for the x y and z axis For a one dimensional PES the standard deviation is a single double value Axes correlation String The correlation between the axes Possible values are Uncorrelatedand Full correlated Only available in case of a three dimensional PES In case of a three dimensional PES a 3x3 covariance matrix is always used in addition to the mean value To simplify the user input the user can specify the correlation between the axes For an uncorrelated or a fully correlated PES it is required to only define the standard deviations for the x y and z axis These standard deviations are used to compute the diagonal elements of the covariance matrix Internally all other elements of the covariance matrix are set automatically to 0 for an uncorrelated PES and 1 for a fully correlated PES 7 9 1
18. of broadband noise case noise Standard deviation Band limited or PSD Radial mode Block mask parameters Translation mode Double Radial translation mode frequency Hz frequency Translation mode Double Radial translation mode damping damping Noise standard Double Force noise standard deviation case Standard deviation deviation or Band limited N Noise bandwidth Double Upper frequency limit for force noise content case Band limited Hz PSD representation Dependent See section 7 9 2 4 N VHz case PSD Tonal disturbance Selection Type of noise model for radial force by imbalance or by harmonics Static imbalance Double Static imbalance coefficient case by imbalance coefficient cm g Number of Double Overall number N of harmonics to be considered for harmonics the radial mode case by harmonics Amplitude Vector Nx1 vector of amplitude coefficients case by coefficients harmonics N rpm Harmonic numbers Vector Harmonic numbers i e ratios of frequency of harmonic with respect to wheel speed case by harmonics Axial mode fully optional via checkbox Block mask parameters Axial mode Double Axial translation mode frequency Hz frequency Axial mode damping Double Axial translation mode damping Noise standard Double Force noise standard deviation case Standard deviation deviation or Band limited N Noise bandwidth Double Upper frequency limit for force noise conten
19. points Angle random walk N Double The magnitude of the angle random walk 9 Vh Rate random walk K Double The magnitude of the angle random walk Ian Bias instability B Double The magnitude of the bias instability Yh Quantization noise Q Double The magnitude of the quantization noise arcsec Time window T Double The time window s Using the parameters defined the Gyro Rate Noise block realizes a PSD type error source with a spectral behaviour as shown in Figure 7 2 For further information about the involved parameters see appendix B of RD2 G f h Hz 0 001 0 0000001 0 000001 0 00001 0 0001 0 001 0 01 f Hz Figure 7 2 Gyro noise PSD derived from typical specifications RD2 7 6 Gyro Stellar Estimator Block This block implements the gyro stellar estimator in PEET It is the only block type which has more than one output port The parameters required by this block type are the two Kalman gains Kp and Kd In general the Kalman estimator is realized as a dynamic system which takes 3 inputs and 2 outputs It computes the signal transfer according to the fixed Kalman estimator structure using user input gains from the model given below individually for each axis Astos Solutions GmbH All Rights Reserved Copyright 2013 per ISO 16016 Grund 1 78089 Unterkirnach Germany Copying and distribution is prohibited without express authority Astos P E ET Issue 17
20. the results Astos Solutions GmbH All Rights Reserved Copyright 2013 per ISO 16016 Grund 1 78089 Unterkirnach Germany Copying and distribution is prohibited without express authority Doc No ASTOS PEET SUM 001 Astos P E ET Issue 17 Date 2013 07 26 Solutions Page 55 of 60 FS PEET W sources PEET examples PointingSat peet File Setup Database Windows x RW Figure 10 6 PES 1 block port selected PEET W sources PEET examples PointingSat peet File Setup Database Windows e NA Figure 10 7 The final pointing system Astos Solutions GmbH All Rights Reserved Copyright 2013 per ISO 16016 Grund 1 78089 Unterkirnach Germany Copying and distribution is prohibited without express authority Doc No ASTOS PEET SUM 001 AAA Solutions Page 56 of 60 10 1 2 Defining correlations between error sources
21. 07 26 Solutions Page 54 of 60 Fa PEET W sources PEET examples PointingSat peet File Setup Database Windows x y System matrix 431566 D y 0 0 Figure 10 5 Setting block parameters for the static system 10 1 1 Connecting blocks Connecting blocks is straight forward All that has to be done is to select the source port and the destination port The source port must always be a block output port and the destination port must always be an input port No loops are allowed Input block ports are always on the left site of the block symbol and output ports are always on the right site The order in which the ports are selected does not matter In this case the output port of the PES 1 block is selected first Move the mouse cursor near the output port of PES 1 The cursor will change to a plus sign Select the port by clicking the left mouse button A selected port is visualized with a red colour like shown in Figure 10 6 Now move the mouse cursor to the input port of the SUM 1 block until it changes to a plus sign Click again on the left mouse button and a connection will be created between PES 1 and SUM 1 Proceed with adding connections until all blocks are connected like in Figure 10 7 Now the pointing system is built up completely The next step is to run the error computation and to analyse
22. 29 of 60 dimensional PES this is a vector containing the maximum drift rates for the x y and z axis For a one dimensional PES the parameter is a single double value Gaussian Rate Distribution The parameters provided by the block mask for the Gaussian rate distribution are listed below Block mask parameters Mean rate Double Vector The mean drift rate In case of a three dimensional PES this is a vector containing the mean drift rates for the x y and z axis For a one dimensional PES the parameter is a single double value Standard deviation Double Matrix The standard deviation of the drift rate In case of a three dimensional PES 3x1 vector containing the standard deviations and the standard deviations For a one dimensional PES the variance is a single double value Bimodal Rate Distribution Only one single parameter is required for the bimodal rate distribution This parameter is explained below Block mask parameters Amplitude Double Vector The amplitude for a bimodal drift distribution In case of a three dimensional PES this is a vector containing the amplitudes for the x y and z axis For a one dimensional PES the parameter is a single double value 7 9 2 3 Random Process Time Series Parameters In case the time random part is defined as a random process of type Time series the block mask provides a single table con
23. Astos Solutions PEET Doc No ASTOS PEET SUM 001 Issue 1 7 Page 1 Date 2013 07 26 of 60 Pointing Error Engineering Tool PEET Software User Manual IFR Cesa Document Number ASTOS PEET SUM 001 Date Issue 1 7 2013 07 26 Name Function Organization Signature Prepared by J Eggert Astos Solutions d Gy 2013 07 26 M Hirth Astos Solutions Zeg 2013 07 26 H Su iFR b 2013 07 26 T Ott iFR De OL 2013 07 26 Checked by S Weikert Astos Solutions _S LEAR 2013 07 26 Product Assurance A Wiegand Astos Solutions Vers 2013 07 26 Project Management S Weikert Astos Solutions Ba LLG 2013 07 26 Astos Solutions GmbH Grund 1 78089 Unterkirnach Germany All Rights Reserved Copyright 2013 per ISO 16016 Copying and distribution is prohibited without express authority Doc No ASTOS PEET SUM 001 Astos PEET Issue 17 Date 2013 07 26 Solutions Page 2 of 60 Document Change Record f Reason for Change Issue Date Affected Chapter Section Page Brief Description of Change Draft 2012 10 15 All Draft issue 1 1 2012 10 16 7 10 Added chapters 1 2 2012 10 18 110 Added references to the PointingSat example 1 3 2012 10 30 12 1 7 8 9 10 1 1 Customer Review 1 4 2012 11 23 All Customer Review 15 2012 12 19 1 2 3 Added references added paragraph 1 6 2013 07 08 7 9 Added PEC position and reaction wheel m
24. Axes correlation String The correlation between the axes Possible values are Uncorrelatedand Full correlated Only available in case of a three dimensional PES 7 9 1 3 Bimodal Distribution Parameters The bimodal distribution is a continuous probability distribution with two modes The modes appear as two distinct peaks local maxima in the probability density function In the context of PEET it is sufficient to only specify the amplitude of the local maxima All parameters required by the block mask are shown in the next table Block mask parameters Amplitude Double Vector The amplitude of the bimodal distribution In case of a three dimensional PES this is a vector containing the amplitudes for the x y and z axis For a one dimensional PES the amplitude is a single double value Axes String The correlation between the axes Possible values are correlation Uncorrelated and Full correlated Only available in case of a three dimensional PES Astos Solutions GmbH All Rights Reserved Copyright 2013 per ISO 16016 Grund 1 78089 Unterkirnach Germany Copying and distribution is prohibited without express authority Doc No ASTOS PEET SUM 001 Astos PEET Issue 17 Date 2013 07 26 Solutions Page 26 of 60 7 9 1 4 Gaussian Distribution Parameters The Gaussian distribution is a continuous probability distribution with the probability density function x pdf x ote
25. Optical Metrology Alignment and Impact on the Measurement Performance of the LISA Technology Package Journal of Physics Conference Series 7th International LISA Symposium Barcelona Spain 2008 NPD 5022 TD TR 001 v1 r1 m0 Error Budgets for Formation Flying Missions Harwood A March 2008 PFF MEMO MC 001 Reaction Wheel Microvibration Model Memo Casasco M April 2013 Masterson R A Development and Validation of Empirical and Analytical Reaction Wheel Disturbance Models Master Thesis Massachussetts Institute of Technology June 1999 P3 EST TN 7001 RD10 Masterson R A Miller D W Grogan R L Development of Empirical and Analytical Reaction Wheel Disturbance Models AIAA 99 1204 AIAA Structural Dynamics and Materials Conference St Louis USA 1999 Astos Solutions GmbH All Rights Reserved Copyright 2013 per ISO 16016 Grund 1 78089 Unterkirnach Germany Copying and distribution is prohibited without express authority Doc No ASTOS PEET SUM 001 estes P E ET Issue 1 7 Date 2013 07 26 Solutions Page 7 of 60 2 2 1 Terms Definitions and Abbreviated Terms Acronyms The following abbreviations are used throughout this document PEET Pointing error engineering tool CDF ESA ESTEC Concurrent Design Facility GUI Graphical user interface PEC Pointing Performance error contributor PES Pointing error source PSD Power spectral density CRV Constant r
26. Rights Reserved Copyright 2013 per ISO 16016 Grund 1 78089 Unterkirnach Germany Copying and distribution is prohibited without express authority Doc No ASTOS PEET SUM 001 Nestos PEET Issue 1 7 Date 2013 07 26 Solutions Page 16 of 60 Representation Selection The type of the matrix elements Possible values are Transfer function Frequency Response Zero Pole Gain and State space Matrix element Selection A drop down menu providing the user the possibility to choose the element of the system transfer matrix for editing This parameter is only used by the block mask and has no effect on the error calculations In general always the whole 3x3 transfer matrix will be used for the system transfer Possible values are x x x y x z y x y y y z z x z yand z z Only available if the representation is not set to State space In this case the state space model defines the entire 3x3 system 7 2 1 1 Transfer Function Parameters A transfer function is described by the coefficients for its numerator and its denominator The parameters provided by the block mask are listed below Numerator List A list of coefficients defining the numerator of the transfer function Each coefficient is of type double Denominator List A list of coefficients defining the denominator of the transfer function Each coefficient is of type double 7 2 1 2 Zero Pole Gain Parameters The zero pole gain model is desc
27. There will be always on output port tab The number of input port tabs is related to the number of input ports of the currently selected block Compared to the system view window the blocks and connections cannot be moved inside the tree view window The tree view window automatically organizes all blocks and connections in a tree like structure starting with the error sources on the upper most level and ending with the PEC block on the lowest level Astos Solutions GmbH All Rights Reserved Copyright 2013 per ISO 16016 Grund 1 78089 Unterkirnach Germany Copying and distribution is prohibited without express authority Doc No ASTOS PEET SUM 001 Aesios PEET Issue 1 7 Date 2013 07 26 Solutions Page 14 of 60 6 3 The Database Browser The database browser provides access to the block database It organizes all available block types in categories For each block category a tab is shown in the database browser Block Database Container Coordinate Transformation Dynamic System Feedback System gt n_str gt n_gyro gt b_gyro Flexible Plant Gyro Rate Noise Input Port Gyro Stellar Estimator Position Attitude 1 Mapping Block Output Port PEC Pointing PEC Position Gest b_est PID Controller Reaction Wheel Force Reaction Wheel Torque Rigid Plant Star Tracker Noise Static System Figure 6 4 Database Browser The first tab contains all block types used by PEET All other tabs represent a catego
28. ain to transfer the input signal 7 1 1 Block Parameters The coordinate transformation parameters offered by the block mask are listed in the following table Block mask parameters Rotation sequence Selection The rotation sequence used for the Euler transformation Possible values are 1 2 3 1 3 2 2 1 3 2 3 1 37122 34251 ta241 ie3 L 2 12 24342 3 1 3 and 3 2 3 Phi Double The angle describing the rotation around the first axis of the rotation sequence Theta Double The angle describing the rotation around the second axis of the rotation sequence Psi Double The angle describing the rotation around the third axis of the rotation sequence 7 2 Dynamic System Block The dynamic system block is used to model any kind of dynamic systems In general the system transfer is described by a 3x3 matrix The elements of the system transfer matrix can be transfer functions frequency response models or zero pole gain models Alternatively a state space model can be provided which defines the dynamic system Internally all inputs are transformed to a state space model which will be used for the system transfer 7 2 1 Block Parameters Depending on the matrix element type different parameters are provided by the block mask as described in the next subchapters The two parameters which are always available independent of the matrix element type are listed in the next table Astos Solutions GmbH All
29. al error signals to one single signal It offers the user a single block mask parameter This parameter defines the number of input ports of the summation block and is listed below Block mask parameters Number of input ports Selection The number of block input ports The number of input ports is in the range from 1 to 99 7 15 Star Tracker Noise Block This special error source block implements a parametric model for the pixel and field of view noise of a typical star tracker temporal noise is not included and has to be defined in a separate pointing error source block e g as standard random process of type desired by the user The underlying model is briefly described below starting with the spectrum of the field of view noise T PSDyoy F N fov Eq 7 30 l1 s o The correlation time 7 5 is assumed to be proportional to the inverse of the velocity v pixels sec with which the star image moves on the sensor pixel matrix star 1024 Top Eq 7 31 V star y Naas The star velocity itself can be linked to the average spacecraft angular velocity o 1024 0 FO sinB cos a Eq 7 32 7 B q star Astos Solutions GmbH All Rights Reserved Copyright 2013 per ISO 16016 Grund 1 78089 Unterkirnach Germany Copying and distribution is prohibited without express authority Doc No ASTOS PEET SUM 001 Astos PEET Issue 17 Date 2013 07 26 Solutions Page 40 of 60 where FOVis the sensor
30. andom variable RV Random variable RP Random process 2 2 Definitions The following definitions are used throughout this document Signal The information about the pointing error which will be exchanged between adjacent blocks Block mask The input dialog provided by the blocks for parameter input Astos Solutions GmbH All Rights Reserved Copyright 2013 per ISO 16016 Grund 1 78089 Unterkirnach Germany Copying and distribution is prohibited without express authority Doc No ASTOS PEET SUM 001 Astos PEET Issue 17 Date 2013 07 26 Solutions Page 8 of 60 3 Introduction The ECSS Control Performance Standard E ST 60 10C AD1 published in November 2008 provides solid and exact mathematical elements to build up a performance error budget However an additional document that provides guidelines and summation rules based on the top level clauses gathered in this ECSS E ST 60 10C standard was considered necessary by ESA to provide ESA projects with a clear pointing error engineering methodology This methodology is the basis for a step by step process with guidelines recommendations and examples consistent with and complementing the ECSS standard The answer to this necessity is the ESA Pointing Error Engineering PEE Handbook AD2 that was published in 2011 as ESA applicable document with the reference ESSB HB E 003 According to the methodology defined in the Control Performance Standard AD1 and in the P
31. ards the total pointing error for the unperturbed parameter element Param is computed The parameter element is perturbed using the equations below Param 2 2e78 Param lt 1 0 p araMpert Param 1 0 2 2e 8 Param gt 1 0 Sensitivity Analysis 0 0 0 0 Select element 6 497106 Dn Analysis result x 0 36151881 11 9455992 0 14442361 Figure 8 4 Sensitivity Analysis Manager Finally for each axis the difference quotient is computed using the equation Total pointing errorayis pert Total pointing error lt Sensitivity ia ParaMpert Param After the sensitivity analysis has finished the sensitivity for each axis can be seen in the sensitivity analysis manager The unit of the sensitivity depends on the unit of the parameter In general the unit is rad parameter unit Example Let s consider the sensitivity analysis shown in Figure 8 4 was performed for a parameter which has the unit rad kelvin In this case we can observe several things 1 Perturbing the first element of the first row will have an effect on all three axes 2 Comparing all three axes the y axis is very sensitive to changes on the selected parameter element 3 The unit of the sensitivity will be aa kelvin rad kelvin Astos Solutions GmbH All Rights Reserved Copyright 2013 per ISO 16016 Grund 1 78089 Unterkirnach Germany Copying and distribution is prohibited without express au
32. atrix of the state space model Each matrix element is a scalar value of type double 7 3 Feedback System Block Feedback systems are the only block type which allows the user to integrate loops into the pointing system The fixed structure of the feedback system implemented by this block type is shown in Figure 7 1 d O DE Ee fi G F Figure 7 1 Feedback system structure Each of the blocks labelled 1 to 6 can either be turned on or off If turned on the user has to specify the block type and the block parameters The available block types are a subset of the blocks available in the database and are explained in chapter 7 3 1 By turning internal blocks on and off the user can build up any kind of feedback system structure required for the pointing error calculations of PEET The nodes labelled A to G serves as input or output ports It is possible to define more than one input port The number of output ports is restricted to one In addition to this restriction it is not possible to use one of the nodes as input and output port All block parameters are converted internally to state space models Using this state space models an equivalent dynamic system is build up which will be used for the system transfer 7 3 1 Block Parameters The parameters for the feedback system can be divided into two groups The first set of parameters deals with the definition of the input and output ports These parameters are
33. blocks the user must first select either the port of the source block or the port of the destination block To select a block port the mouse must be moved near the block port until the mouse cursor changes to a cross Clicking on the port will select it A selected block port is visualized with a red color see Figure 8 1 Note that each pointing system requires at least one PEC block position or pointing to which the final error signals are routed E PEET W sources PEET examples SimpleDemo peet Fie Setup Database Windows yxa A Static System 1 Dynamic System 2 A Dynamic System 1 LN Static System 2 Figure 8 1 Connecting Static System 2 and SUM After one of the two required block ports is selected the mouse must be moved to the second block port Again the mouse cursor changes to a cross as soon as the cursor is near the block port Clicking on the second block port now creates the connection between the blocks The shape of the newly created connection can be adjusted by first selecting the connection As soon as the connection is selected it changes its colour to red It also owns some nodes visualized as small circles An example of a selected connection is given in Figure 6 2 By dragging the nodes of the connection the shape can be freely adjusted Astos Solutions GmbH All Rights Reserved Copyright 2013 per ISO
34. bol must be selected in the tree The signals can be analysed in the information section on the right site Figure 10 12 gives an example for the signal data of the summation block SUM BlockID SUM Block type SUM Output Port Input Port 1 Input Port 2 Signal dimension 3 Constant random variable Mean value x y 1 0000 10 4 1 9999 10 8 0001 10 n x standard deviation V 0 Random variable NIA Drift Mean value x ae gt 3 s 0853 10 8 4945 10 1 8927 10 n x standard deviation Z hi 0 0 pn 0 0 Random process Mean value x y z 1 s095 10 1 3386 10 1 4730 _ 10 Figure 10 12 Inspect signals Each signal consists of several signal components Each signal component is listed in the information section Most of the time the signal components are vectors but for the random process component a PSD plot is shown This plot is only a preview plot It can be enlarged by double clicking on the preview Data of all incoming and outgoing signals can be examined by selecting the appropriate tab in the information section The PEC block provides an information section which is slightly different from the other block types see Figure 10 13 Astos Solutions GmbH Grund 1 78089 Unterkirnach Germany stos PEET Issue 1 7 Date 2013 07 26 All Rights Reserved Copyright 2013 per ISO 16016 Copying and distribution is prohibited without ex
35. crete amplitude distribution the frequency amplitude data contains the frequency and a single amplitude For a uniform amplitude distribution the frequency amplitude data contains the frequency a minimum amplitude and a maximum amplitude In case of a three dimensional PES the same data must be provided but for all three axis x y and z 7 10 Reaction Wheel Model PEET provides two special pointing error source blocks for setting up disturbance forces and torques on the spacecraft interface which are generated by a single reaction wheel The output disturbance is always provided with respect to the wheel frame defined by wheel spin around z axis The orientation of the wheel in the spacecraft reference frame can be realized with the Coordinate Transformation PEET block multiple wheels by repeated usage of this block The implemented models are based on RD8 which are further based on RD9 and RD10 and briefly explained in the following subsections 7 10 1 Reaction Wheel Force The disturbance force model includes models for the radial and axial translation mode of the wheel and covers different kinds of parameter sets for the excitation force inputs The definition of axial force parameters is optional 7 10 1 1 Radial Force Model The radial wheel x y plane disturbance forces acting on the spacecraft interface are modelled using the set of equations described below HEH Eq 7 6 c 4n fm Eq 7 7 k m 21f Eq 7 8
36. dynamic system block For an explanation of the parameters see chapter 7 2 1 In addition to these PSD representations the user can also select Spectrum magnitude as PSD representation In this case the following parameters are available Spectrum magnitude parameters Frequency Magnitude List A list specifying frequency magnitude data In case of a three dimensional PES a magnitude for all three axes must be provided for all frequency points For a 1D signal only one magnitude at each frequency point is required Axes correlation Selection The correlation between the axes Possible values are Uncorrelated an Fully correlated 7 9 2 5 Random Process Covariance Parameters For a random process of type Covariance the following parameters are available in the block mask Block mask parameters Sampling time Double The sampling time Axes correlation Selection Only available for a three dimensional PES This parameter defines the correlation between the x y and z axis Possible values are Uncorrelated and Fully correlated Variance Double Vector In case of a three dimensional PES this is a vector containing the desired variance for the x y and z axis For a one dimensional PES the variance is a single double value and always available In case of a three dimensional PES a 3x3 covariance matrix is always used in addition to the sampling time To simplify the user input the
37. e block mask is different for every block type A detailed description of the block parameters is given in chapter 7 8 2 1 Linking to external data It is possible to link parameter values to data provided in an Excel file or data defined in the MATLAB workspace 8 2 1 1 Linking to Excel data To link parameter values to data in an Excel file right click on the parameter input field and select Import from Excel This will open a new dialog which supports the user in defining the cells containing the parameter values This dialog is shown in Figure 8 3 First of all the user has to provide the name of the Excel file Astos Solutions GmbH All Rights Reserved Copyright 2013 per ISO 16016 Grund 1 78089 Unterkirnach Germany Copying and distribution is prohibited without express authority Doc No ASTOS PEET SUM 001 j A stos PEET Issue 13 Date 2013 07 26 Solutions Page 44 of 60 Excel Import Excel File intingSat peet input PES3_data xls EA Sheet name freq_mag Range ALC Figure 8 3 The Excel Import dialog The next step is to select the Excel sheet from the dropdown list Finally the data range must be defined In case of vector data the data range can either be defined as a row or column vector Scalar values Scalar values can be defined in two ways 1 The column is defined by upper case letters the row is defined by an index The row index of the first row is 1 Example Setting range to
38. e grouped into time constant time random and total error contribution The usage of a PEC block is mandatory for each PEET system and only one PEC block can be used in a system Two kinds of blocks are available in the block database 7 8 1 PEC Pointing The PEC Pointing block is the standard block for the overall error evaluation It has no parameters and only one single input which corresponds to the total error signal of the system under consideration The content of the different parts of the input signal CRV RV drift periodic signal and random process part is summed according to AST 4 of AD2 after the equivalent variance of a potential random process signal is computed within the user defined global evaluation bandwidth The overall error is computed per axis x y z and with respect to the user defined LOS axis Note that the latter is the only special feature that links the block really to pointing Disregarding the LOS error this block and PEET could be used to compute any kind of 3 axis budget i e PEET could generally be understood as Performance Error Engineering Tool rather than a Pointing Error Engineering Tool only 7 8 2 PEC Position The PEC Position realizes a special case for the overall error evaluation It allows the computation of a position displacement error budget which is the result of pure 3 axis position errors and 3 axis attitude errors which couple into equivalent position errors due to dedicat
39. e time constant part The remaining parameters for random variable options are described in chapters 7 9 2 1 and 7 9 2 2 Note that whenever a non zero mean of a Gaussian RV is defined PEET automatically maps this mean to a CRV with discrete distribution and removes it from the RV as it essentially represents a time constant part The same is true for a uniform RV e g in case of a lower bound 0 and upper bound 3 a CRV with a mean of 1 5 is automatically created If the time random part is defined as a random process the user has to set the type of the random process Possible types are Time series PSD Covariance and Periodic The parameters for these types are explained in the chapters 7 9 2 3 to 7 9 2 6 7 9 2 1 Random Variable Gaussian Distribution Parameters The parameters for the Gaussian distribution of the time random part are listed in the table below Block mask parameters Mean value Double In case of a three dimensional PES this is a Vector vector containing the mean values for the x y and z axis For a one dimensional PES the parameter is a single double value Distribution of standard Selection The ensemble distribution of the standard deviation deviation Possible values are Discrete and Uniform Standard deviation Double A 3x1 vector defining the standard deviation for all Matrix axes In case of a one dimensional error source the standard deviation is a scalar value Only available if the distr
40. ed lever arms e g as it is the case for formation flying missions such as PROBA 3 The implemented model is based on Eq 5 in RD7 N att Natt Be 2 _ 2 22 22 Has H pos x Sly Hai T Zi ul Data O oos t Shy Das Zi ei i l i l Natt Naw a 8 eg a ape Hoty WW H pos y a gt Zi Haan Xi Hanzi Story O pos y gt Zi Daat T Xi Datz Eq 7 4 i i l Nat 2 2 att LS 2 2 22 Hotz H oe z Yh Hai Yi Maa Dias O posz x Oatty i F yi ei i l i l with axis index omitted Astos Solutions GmbH Grund 1 78089 Unterkirnach Germany All Rights Reserved Copyright 2013 per ISO 16016 Copying and distribution is prohibited without express authority Doc No ASTOS PEET SUM 001 Astos PEET Issue 17 Date 2013 07 26 Solutions Page 23 of 60 Wot total mean of resulting displacement error O iot total standard deviation of resulting displacement error H pos overall mean of pure position error contributors O pos overall standard deviation of pure position error contributors Nott number of attitude error coupling to position Marti mean of i th attitude error Oatti standard deviation of i th attitude error Xi Yi Zi components of coupling vector of i th attitude error Different to Eq 5 in RD7 there is no summation over different position error contributors The summation of these contributors has to be realized using standard Sum blocks in the PEET system this allows the usage of one single position error
41. ed by the GUI In order that MATLAB can find the Java classes the absolute paths to all the jar files must be added to the static class path of MATLAB This is done by adding the absolute paths to the classpath txt file located in the toolbox local folder of your MATLAB installation If this file cannot be edited or should be kept in its original state it is also possible to create a local classpath txt file for each user Simply copy the content of the original classpath txt file to a new classpath txt file located in the Documents MATLAB folder or My Documents MATLAB on Windows platforms other than Windows Vista This local classpath txt file will be used at start up The required jar files can now be added to the new classpath txt file 5 2 Running PEET PEET is started by entering int_ esa peet gui Peet main installation_path on the MATLAB command line For installation_path use the absolute path to the PEET folder Figure 5 1 shows an example assuming that the PEET folder was placed in c Program Files MATLAB R2012a File Edit Debug Desktop Window Help WE HR o nr E ei current Folder s matias ye Shortcuts al Howto Add 2 What s New Current Folder mn Da x Eg b s Workspace gt Sr gt MATLAB gt 2 New to MATLAB Watch this Video see Demos or read Getting Started x Zei Name f gt gt int_ esa peet gui Peet main c Program Files PEET Name E classpath txt lt Comma
42. efined error indices is shown Selecting one of the list entries allows the user to edit the parameters for the error index Error indices can be added or removed by the elements of the tool bar If a new index will be added the user has to choose the type of the error index The absolute knowledge error and the absolute performance error can be only defined once All other index types can be defined several times To remove an error index select the error index and click on the cross in the tool bar All defined error indices are available in the dropdown menu of the tree view window After one or more error indices are defined the computation can be triggered inside the tree view window The computation is either triggered by changing the error index in the dropdown menu or by pressing the green arrow in the tool bar of the tree view Every time a block parameter was changed the computation must be performed again by clicking on the green arrow or by changing the error index The results of the pointing error computation can be analysed in the information section of the tree view window Each signal consists of several signal parts These parts are constant random variable random variable drift random process and periodic see Figure 6 3 Not all signal parts are always available If a signal part is not available it is marked as N A in the information section of the tree view window Astos Solutions GmbH All Rights Reserved Copyrigh
43. ew noise parameters Astos Solutions GmbH All Rights Reserved Copyright 2013 per ISO 16016 Grund 1 78089 Unterkirnach Germany Copying and distribution is prohibited without express authority Astos Solutions Doc No ASTOS PEET SUM 001 B E ET Issue 1 7 Date 2013 07 26 Page 41 of 60 Noise level Double The low frequency noise level for all axes Pixel noise parameters damping coefficient Size of centroiding Double The size of the centroiding window in pixels window Noise level Double The low frequency noise level for the sensor boresight boresight axis Noise level cross Double The low frequency noise level for the cross boresight axes axes 2nd order filter filter Double The damping coefficient used for the pixel noise transfer function Astos Solutions GmbH Grund 1 78089 Unterkirnach Germany All Rights Reserved Copyright 2013 per ISO 16016 Copying and distribution is prohibited without express authority Doc No ASTOS PEET SUM 001 j Astos PEET Issue 1 7 Date 2013 07 26 Solutions Page 42 of 60 8 Building Pointing Systems Using PEET Building pointing systems using PEET is similar to Simulink Blocks are added to the pointing system by dragging the required block type from the database browser to the system view window After the block was added it must be connected with other blocks of the pointing system To create a connection between two
44. ght 2013 per ISO 16016 Grund 1 78089 Unterkirnach Germany Copying and distribution is prohibited without express authority Doc No ASTOS PEET SUM 001 Astos PEET Issue 17 Date 2013 07 26 Solutions Page 24 of 60 the total mean and standard deviation of the resulting displacement error time constant time random and overall contribution the mean and standard deviation of the pure position error contributor only time constant time random and overall contribution the mean and standard deviation of the position error due to all the attitude contributors only time constant time random and overall contribution 7 9 PES Block The pointing error source block is used to model all kind of error sources applicable to pointing error calculations Each pointing error source consists of a time constant part and a time random part The time constant part is defined by a probability distribution function The time random part is either defined as a random variable or as a random process Internally the time constant part and the time random part of type random variable are converted to an equivalent Gaussian distribution If the time random part is described as a random process it is converted to a state space representation The signal generated by a pointing error source block can either be one dimensional or three dimensional The dimension of the signal is set by the parameter listed in the table below The dimension applies to the
45. he time constant check box To configure the time random part select the time random tab Now set the representation to Random process the type to Periodic and the amplitude distribution to Uniform Set the correlation to Uncorrelated Insert the values 1 1574e 5 2 424e 5 7 272e 5 1 939e 5 4 848e 5 4 85e 6 2 424e 5 into the first row of the table PEET W sources PEET examples PointingSat peet File Setup Database Windows PES 9 Settings Use time constant part Time constant Time random Representation Type Amplitude distribution Unifor Correlation Bn Bn p Frequ Minimu Maxim Minimu Maxim Minimu Maxim 1 1 1574E 5 2 4246 5 s 1 9996 5 4 848E 5 4 85E 6 Games D T jj Ce e Figure 10 3 Setting time random parameters In this case the table contains only one row It is also possible to add or remove rows by using the three icons to the upper left of the table Now all pointing error sources are added to the pointing system But there are still missing some system transfers In the next step add a coordinate transformation by dragging the coordinate transformation block from the block database to the system view window Rename itto STR to Body Frame Astos Solutions GmbH All Rights Reserved Cop
46. ibution of the standard deviation is set to Discrete Minimum Double A 3x1 vector defining the minimum standard Matrix deviation for all axes In case of a one dimensional error source the minimum standard deviation is a scalar value Only available if the distribution of Astos Solutions GmbH All Rights Reserved Copyright 2013 per ISO 16016 Grund 1 78089 Unterkirnach Germany Copying and distribution is prohibited without express authority Doc No ASTOS PEET SUM 001 Astos PEET Issue 17 Date 2013 07 26 Solutions Page 28 of 60 the standard deviation is set to Uniform Maximum Double A 3x1 vector defining the maximum standard Matrix deviation for all axes In case of a one dimensional error source the maximum standard deviation is a scalar value Only available if the distribution of the standard deviation is set to Uniform Axes correlation String The correlation between the axes Possible values are Uncorrelatedand Full correlated Only available in case of a three dimensional PES 7 9 2 2 Random Variable Drift Distribution Parameters The drift distribution is only available for the time random part The parameters provided by the block mask are listed in the table below Block mask parameters Reset time Double The time after which the drift will be reset Rate distribution Selection A probability distribution used for the drift rate Possible values are Discrete U
47. ile Setup Database Windows yA Figure 10 1 PointingSat with some missing blocks The PointingSat example and all pointing systems in general must always contain a PEC block which serves as the final end block of the pointing system The signal going into the PEC block is the final signal containing all the pointing error data of the whole pointing system Building up a pointing system requires the user to add blocks from the database to the pointing system This is done similar to Simulink by simply dragging the required block type from the database window to the system window The database window can be opened either by using the first button in the system view tool bar or by selecting Database Show Block Database from the menu bar Astos Solutions GmbH All Rights Reserved Copyright 2013 per ISO 16016 Grund 1 78089 Unterkirnach Germany Copying and distribution is prohibited without express authority Doc No ASTOS PEET SUM 001 Astos P E ET Issue 1 7 Date 2013 07 26 J Solutions Page 51 of 60 After the database window was opened simply drag the PES block from the database window to the system window A new PES block is now available in the system view window Blocks inside the system view can be dragged in order to define the location of the blocks Move the new block to the same location like
48. input for the PEC Position block Above realization corresponds to the option Exact in the block s Summation rule drop down menu In case the directions sign relations of individual contributors are not exactly known a priori PEET alternatively offers of a more conservative approach using the Worst case option Here the total mean is computed using absolute values according to the following equation Natt Hiot x ee aly X lan Zaya Na Hoty T KA E E Hanzi Eq 7 5 a Hotz e hn ER Zlatan cs i The number of additional block inputs for attitude errors depends on the settings of the parameters which are listed in the table below Block mask parameters Summation rule Selection Desired summation for the means in the equation above see Eq 5 in RD7 possible selections are Worst case and Exact Number of attitude Selection The number of attitude contributors Nay that couple contributors with different lever arms to position errors determines the number of additional block input ports Attitude coupling Matrix Nax3 Mapping matrix with as many rows as attitude vector contributors are defined The columns contain the x y and z components of the i th coupling vector The tree view of the block finally provides the following information signal content of each attitude and position error signals Astos Solutions GmbH All Rights Reserved Copyri
49. inting system It also contains the menu entry used to create the reports for the currently loaded pointing system The setup menu contains all menu entries used for configuring the current pointing system Using the setup menu the user can define the correlations between the pointing error sources define the error indices he is interested in and define the global parameters applicable for the pointing system Astos Solutions GmbH All Rights Reserved Copyright 2013 per ISO 16016 Grund 1 78089 Unterkirnach Germany Copying and distribution is prohibited without express authority Doc No ASTOS PEET SUM 001 ssue ate 07 J Astos P E ET l 1 7 Date 2013 07 26 Solutions Page 12 of 60 The Database menu contains all actions related to the block database It provides the user the possibility to open the database browser and to manage user defined block types Finally the Windows menu gives the user access to all window types and to actions related to the system view e g fit the current system view in order to show the whole pointing system The tool bar contains some short cuts to menu entries Starting on the left the user can open the database browser open the tree view delete the selected element or fit the system view to show the whole pointing system The main part of the system view window shows the currently loaded pointing system Each pointing system consists of a number of blocks and connection between the blocks
50. istribution is prohibited without express authority Doc No ASTOS PEET SUM 001 Astos PEET Issue 17 Date 2013 07 26 Solutions Page 33 of 60 Noise The noise contribution to both the axial and translational force can be defined in different ways which correspond to selected options also available from the standard PES block section 7 9 2 by definition of a standard deviation only RV definition by definition noise bandwidth upper frequency together with a standard deviation which is converted to a PSD random process definition by direct definition of a PSD random process definition Tonal disturbance The tonal force contributions to both the axial and translational force are realized as one periodic 3D signal with amplitudes at frequencies of the corresponding harmonics The amplitude A of the k th harmonic k 1 N index for radial and axial mode omitted and the corresponding frequency f are obtained from A C Q Eq 7 15 f 20h Q Eq 7 16 where Q is the spin speed of the wheel C is the amplitude coefficient of the k th harmonic and D the harmonic number i e the ratio of frequency of k th harmonic to spin frequency of the wheel Alternatively the radial disturbance can also be defined by the static imbalance coefficient U i e considering only the first harmonic resulting in an amplitude frequency set A U Q Eq 7 17 f 20Q Eq 7 18 The wheel speed itself is assumed to be constant withi
51. king translation mode frequency of the rocking mode resulting x y disturbance torques at the spacecraft interface Excitation Torque Model According to RD8 the overall excitation torque comprises broadband noise and tonal disturbances for the rocking mode and negligible disturbance torques around the z axis y Astos Solutions GmbH Grund 1 78089 Unterkirnach Germany All Rights Reserved Copyright 2013 per ISO 16016 Copying and distribution is prohibited without express authority Doc No ASTOS PEET SUM 001 Astos PEET Issue 17 Date 2013 07 26 Solutions Page 36 of 60 T rock Tea CR LE rock T 0 Tock gie F Fees Eq 7 23 0 0 Noise The noise contribution to the torque can be defined in different ways which correspond to selected options also available from the standard PES block section 7 9 2 by definition of a standard deviation only RV definition by definition noise bandwidth upper frequency together with a standard deviation which is converted to a PSD random process definition by direct definition of a PSD random process definition Tonal disturbance The tonal torque contribution from the rocking mode is realized as one periodic 3D signal with amplitudes at frequencies of the corresponding harmonics The amplitude A of the k th harmonic k 1 N index for rocking mode omitted and the corresponding frequency f are obtained from A C Eq 7 24 f 20h Q Eq 7 25 where Q is
52. l can pass this block without any modifications to it If a block type different than Unused is selected additional parameters are available These parameters are described in the next chapters 7 3 1 1 Internal Block Type Coordinate Transformation The parameters for the coordinate transformation type are the same as for the Coordinate Transformation block These parameters are explained in detail in chapter 7 1 7 3 1 2 Internal Block Type Dynamic System The parameters for the dynamic system type are the same as for the Dynamic System block These parameters are explained in detail in chapter 7 2 7 3 1 3 Internal Block Type Flexible Plant The parameters for the flexible plant type are the same as for the Flexible Plant block These parameters are explained in detail in chapter 7 4 7 3 1 4 Internal Block Type Rigid Plant The parameters for the rigid plant type are the same as for the Rigid Plant block These parameters are explained in detail in chapter 7 11 7 3 1 5 Internal Block Type Static System The parameters for the static system type are the same as for the Static System block These parameters are explained in detail in chapter 7 13 7 3 1 6 Internal Block Type PID Controller The parameters for the PID controller system type are the same as for the PID Controller block These parameters are explained in detail in chapter 7 12 Astos Solutions GmbH All Rights Reserved Copyright 2013 per ISO 16016 Grund 1
53. listed in the next table Block mask parameters Input ports Selection The user can choose one or more input ports Possible values are A B C D E FandG The node which is currently set as output port cannot be selected as input port Astos Solutions GmbH All Rights Reserved Copyright 2013 per ISO 16016 Grund 1 78089 Unterkirnach Germany Copying and distribution is prohibited without express authority Doc No ASTOS PEET SUM 001 Astos PEET Issue 17 Date 2013 07 26 Solutions Page 18 of 60 Output port Selection The user can select the output port Only one node can be set as output port Possible values are A B C D E F and G If the user selects a node which is currently used as input port this port is removed from the list of input ports and set as the one and only output port The second set of parameters deals with the parameter settings for the blocks Each of the blocks provides the same parameters which are listed below In general any system transfer block from the database can be selected with the only restriction of one single 3D input and one single 3D output Block mask parameters Block type Selection The type of the block Possible values are Unused Coordinate Transformation Dynamic System Flexible Plant RigidPlant Static System and PID Controller Using the block type Unused turns off the block By turning off a block the signa
54. lock Parameters wicc1 cack ahs tie a en ee es 21 7 6 2 Block inputs ANd OUTPUTS siarsio aiaa a a 21 7 7 Mapping BlOCK EE 21 7 7 1 Block Parameters ssrtariniasis nnan AAEE AA RS RAAN 22 Astos Solutions GmbH All Rights Reserved Copyright 2013 per ISO 16016 Grund 1 78089 Unterkirnach Germany Copying and distribution is prohibited without express authority Doc No ASTOS PEET SUM 001 Astos PEET Issue 17 Date 2013 07 26 Solutions Page 4 of 60 7 8 el GE 22 7 8 1 PEG POIMUAG EE 22 7 8 2 PEG E Le EE 22 7 9 PES BIOK iiinn n He eee eee een 24 7 9 1 Time Constant Block Parameters sessesseseeerssresrssresrresrresriesrrssre 24 7 9 2 Time Random Block Parameterg AA 27 7 10 Reaction Wheel Modell cccccescccceceecceeeeeeeceeeenseceeeeneeaeeesneeeeesneeeeeeseeeaeeeenees 31 7 10 1 Reaction Wheel Force ccccccescccceceeecceeeneeceeeeneeaeeeseeeeeeesnseaeenseeeeeenenees 31 7 10 2 Reaction Wheel Torque essssessssesssrresssrnessnnesnnnnentenneennnnnntnnneennnnnnnennee 35 7 11 Rigid TEE 37 7 11 1 Block Parameters ei etitsdegesbege det e arni ii ea Aa ara NE 38 OH IR Ree 38 7 12 1 Block Parameters eege codec eet eee eect ee eek 38 7 13 Static System Block 0 0 cece cece ananin aena aaraa aai aeaa 39 7 13 1 Block Parameters 224 fesse eeesee i eetsecttep shed inser ee ete ndetaecaeeyesea EEN eg 39 LAA Summation NEE 39 7 15 Star Tracker Noise Block eeccesesseeseceeeecceeeeeceeeaeeeeaeeeeeae
55. n a single observation period This can be understood as a linearization around a certain working point during the observation In addition it has to be noted that there is no distinction between the radial axes amplitudes x and y although the time based model in RD8 accounts for the 90 phase shift between the axes for each harmonic This is however no restriction of the model as from a performance point of view only the overall magnitude or temporal mean is of interest when applying the statistical interpretation Furthermore it has to be noted that the arbitrary phase angle between different harmonics cannot be directly accounted for as in the time domain model from RD8 As a full correlation between the different harmonics and axes might be too pessimistic an uncorrelated set is realized in the PEET model Astos Solutions GmbH All Rights Reserved Copyright 2013 per ISO 16016 Grund 1 78089 Unterkirnach Germany Copying and distribution is prohibited without express authority Doc No ASTOS PEET SUM 001 PEET Issue 1 7 Date 2013 07 26 Astos Solutions Page 34 of 60 7 10 1 4 Block Parameters The following tables summarize the parameters to be defined by the user Wheel properties Block mask parameters Wheel mass Double mass of the flywheel kg Wheel speed Double Rotational speed of the reaction wheel rpm Broadband force Selection Representation type
56. nd Figure 5 1 Running PEET from the MATLAB command line Astos Solutions GmbH All Rights Reserved Copyright 2013 per ISO 16016 Grund 1 78089 Unterkirnach Germany Copying and distribution is prohibited without express authority Doc No ASTOS PEET SUM 001 ssue ate 07 J Astos PEET 1 7 Date 2013 07 26 Solutions Page 11 of 60 6 Graphical User Interface This chapter will provide the user an introduction to the graphical user interface and to the various window types he will face while building up pointing systems and analysing pointing errors 6 1 The System View The system view is the main window of PEET It will be the first window after PEET has been started It is mainly used to build up the pointing system in a way similar to Simulink A detailed description on how a pointing system can be build is given in chapter 8 PEET W sources PEET examples SimpleDemo peet File Setup Database Windows Static System 1 _ p Dynamic System 2 gt Dynamic System 1 Static System 2 Figure 6 1 The System View window Figure 6 1 shows the system view window This window contains a menu bar a tool bar and the system view covering most of the window The file menu contains all actions related to file handling e g opening an existing pointing system creating an empty pointing system or saving the current po
57. niform Gaussian and Bimodal Axes correlation String The correlation between the axes Possible values are Uncorrelated and Full correlated Only available in case of a three dimensional PES Depending on the rate distribution additional parameters are available in the block mask These additional parameters are explained below Discrete Rate Distribution The parameters for the discrete rate distribution are shown in the next table Block mask parameters Rate Double Vector The drift rate In case of a three dimensional PES this is a vector containing the drift rates for the x y and z axis For a one dimensional PES the parameter is a single double value Uniform Rate Distribution The table below list all parameters available for the uniform rate distribution Block mask parameters Minimum rate Double Vector The minimum drift rate In case of a three dimensional PES this is a vector containing the minimum drift rates for the x y and z axis Fora one dimensional PES the parameter is a single double value Maximum rate Double Vector The maximum drift rate In case of a three Astos Solutions GmbH All Rights Reserved Copyright 2013 per ISO 16016 Grund 1 78089 Unterkirnach Germany Copying and distribution is prohibited without express authority Astos Solutions E ET Issue 1 7 Date 2013 07 26 Doc No ASTOS PEET SUM 001 Page
58. odels 1 7 2013 07 26 7 PEC position updated Astos Solutions GmbH All Rights Reserved Copyright 2013 per ISO 16016 Grund 1 78089 Unterkirnach Germany Copying and distribution is prohibited without express authority Doc No ASTOS PEET SUM 001 Astos PEET Issue 17 Date 2013 07 26 Solutions Page 3 of 60 Table of Contents 1 Applicable and Reference Documents 6 1 1 Applicable Documents sorssisosinn ni na TEAN 6 1 2 Reference Documents ccccescceceeeeceeeeeeeceeeeneeceeeeseceeesnseeeeesneeeeeeeneeaeeneneeaes 6 2 Terms Definitions and Abbreviated Temms 7 2 1 e te EE 7 2 2 Nuit 7 3 te TEE 8 e EE E TE 9 5 Installing and running PEET WEE 10 5 1 ET Le 10 5 2 ROANING d E 10 6 Graphical gun 11 6 1 The Systemi View sissisota daia aeia a aaa aE aaa a i a 11 6 2 CAN 13 6 3 The Database Browser iie cecccecesevecgesssanetesvecedencacetesascctendvatitenssiciteedeancteeseieene 14 7 Blok TYPOS eemgebegeru ieeg nedd 15 7 1 Coordinate Transformation Block 15 7 1 1 Block Parameters anisa aa a E Eege Eegen 15 7 2 Dynamic System BIOCK eamsrnrma iinan a aaa 15 7 2 1 Block Paramete insni SE detec a cdulewstoetaaespedetcentde lee atteis 15 7 3 Feedback System Bock 17 7 3 1 Block Parameters sorsia aan Ranen an aa S RAAE 17 7 4 SEN Ee 19 7 4 1 Block Parameters cribau a T S a 19 7 5 Gyro Rate Noise Bock 19 7 5 1 Block Parameters merridiani ideda aiaiai diia 20 7 6 Gyro Stellar Estimator Block 20 7 6 1 B
59. ointing Error Engineering Handbook AD2 a software tool called PEET Pointing Error Engineering Tool was developed to support system engineers and control engineers working in CDF and in Phase A studies in performing preliminary pointing error engineering tasks PEET was designed as an extension to MATLAB It uses the computational power provided by MATLAB and provides the user a graphical user interface suitable for building pointing systems and analysing pointing errors The graphical user interface is implemented in Java The core of the PEET software containing the mathematical algorithms for error computation is implemented using MATLAB classes PEET runs completely inside the MATLAB environment The MATLAB classes are based on the iFR Precision Analysis and Control Toolbox in MATLAB This toolbox provides algorithms in MATLAB for the research results published in RD3 RD6 but also to not yet published results In order to integrate the toolbox in the PEET framework it has been extended and adapted by the subcontractor iFR This software user manual explains how pointing systems can be build up in PEET and how pointing error computations can be performed Chapter 6 will introduce the reader to the graphical user interface in general and to the various window types the user is faced with while building up pointing systems and analysing pointing errors How to build up pointing systems is explained in detail in chapter 8 while chapter 9
60. ort the settings of the error index and the total pointing error The other sheets contain the output signal data For each signal part CRV RV Drift Periodic and RP a separate sheet is available containing for each block the block ID the block type and the equivalent mean and variance values of the signal part for each axis Not all signal parts must be available for each block Signal parts which are not available inside an output signal are marked with N A Astos Solutions GmbH All Rights Reserved Copyright 2013 per ISO 16016 Grund 1 78089 Unterkirnach Germany Copying and distribution is prohibited without express authority Doc No ASTOS PEET SUM 001 Astos PEET Issue 1 7 Date 2013 07 26 Solutions Page 50 of 60 10 PointingSat Example In this chapter a step by step example is given on how a pointing system is built up and how the pointing error computations are performed The pointing system used in this example is the PointingSat example defined in RD1 10 1 Building the pointing system Before the error computations can be performed the pointing system must be defined by adding blocks from the database to the pointing system setting up the block parameters and by connecting the blocks Adding blocks to the pointing system Figure 10 1 shows the structure of PointingSat Some blocks marked by green rectangles are missing and will be added step by step PEET W sources PEET examples PointingSat peet F
61. os Solutions GmbH Grund 1 78089 Unterkirnach Germany All Rights Reserved Copyright 2013 per ISO 16016 Copying and distribution is prohibited without express authority Doc No ASTOS PEET SUM 001 Astos P E ET Issue 1 7 Date 2013 07 26 Solutions Page 58 of 60 Index Manager X Absolute Performance Error ID APE_ensemble rror Index Statistical interpretation Ensemble v Confidence coefficient n Figure 10 10 Error index settings 10 2 2 Perform error computation After error indices are defined they can be accessed in the tree view window see Figure 10 11 using the drop down menu in the tool bar E Error Budgeting Figure 10 11 The tree view window Astos Solutions GmbH All Rights Reserved Copyright 2013 per ISO 16016 Grund 1 78089 Unterkirnach Germany Copying and distribution is prohibited without express authority Doc No ASTOS PEET SUM 001 JNA Solutions Page 59 of 60 To run the computation press the green arrow The computation must be performed every time the pointing system was modified It will be performed automatically if the error index has changed using the drop down menu Because only one error index is defined in this example only the green arrow can trigger the computation 10 2 3 Analyse pointing errors After the error computation has been performed the results can be inspected To inspect the input and output signals of a block the associated block sym
62. pen a dialog in which the name of the block type and the category can be defined It is also possible to create a new category Container Fie Setup Database Windows y KA Input Port Static System Output Port Input Port 1 Figure 8 5 System View window for a container block Astos Solutions GmbH All Rights Reserved Copyright 2013 per ISO 16016 Grund 1 78089 Unterkirnach Germany Copying and distribution is prohibited without express authority Doc No ASTOS PEET SUM 001 J Astos PEET Issue 1 7 Date 2013 07 26 Solutions Page 47 of 60 9 Computing Pointing Errors Using PEET After the pointing system has been built the error computation can be performed To perform the error computation one or more error indices must be defined This is done by selecting Edit Error Indices from the Setup menu This will open the Error Index Manager shown in Figure 9 1 __ Index Manager X Absolute Knowledge Error ID art Absolute Performance Error Statistical interpretation Ensemble v Confidence coefficient 3 0 APE Choose Error Index Type Choose error index type Absolute Knowledge Error Absolute Knowledge Error Absolute Performance Error Mean Knowledge Error Mean Performance Error Relative Knowledge Error Relative Performance Error Knowledge Drift Error Performance Drift Error Figure 9 1 Error Index Manager On the left side of the Error Index Manager a list of all currently d
63. press authority Doc No ASTOS PEET SUM 001 Astos PEET Issue 1 7 Date 2013 07 26 Solutions Page 60 of 60 E Error Budgeting Block ID PEC Block type PEC Pointing error Input Port 1 Final pointing error x y z s 1685 10 3 2596 10 2 7277 10 4 Time constant pointing error 2 3 4309 10 4 2 6210 10 2 2330 10 4 Time random pointing error E 2 2 0395 10 4 8 4391 10 6 5710 105 Line of sight error 4 2505419649708825E 4 Figure 10 13 Final pointing error In addition to the input signal data first tab summarizes the total pointing error together with its time random and time constant contributions together with the line of sight error around the user selected axis Astos Solutions GmbH All Rights Reserved Copyright 2013 per ISO 16016 Grund 1 78089 Unterkirnach Germany Copying and distribution is prohibited without express authority
64. put Port Input Port 1 Constant random variable x Y z Mean value 6 73469936 6 73469936 6 73469936 State System 2 State System 1 Dynamic System 1 x y z 5 13911070 5 13911070 5 13911070 Variance Random variable Nia Drift NjA Random process Dynamic System 2 Magnitude arcsec Sqrt Hz RRR R Be RR RRR RRB g G OE5 106 4 0000 aot o 10 100 1000 10000 Frequenzy Hz Periodic x y z Mean value 1 53168813 1 53168813 1 53168813 Y z Variance 2 18004026 2 18004026 2 18004026 n Figure 6 3 The Tree View window The tree view window consists of a tool bar a tree like representation of the pointing system and an information section Using the drop down menu in the tool bar the user can select the error index he wants to analyse The information shown in the information section on the right of the window shows the current signal data for the selected error index and the selected block To select a block the user simply clicks on the block of interest If no block is selected no data is available in the information section A detailed description of the information section is provided in chapter 9 The user can switch between the data of input and output ports of a block by selecting the associated tab in the information panel
65. ribed by a list of coefficients describing the zeros of the transfer function a list of coefficients describing the poles of the transfer function and a gain value The block mask provides the following parameters Zeros List A list of coefficients defining the zeros of the transfer function Each coefficient is of type double Poles List A list of coefficients defining the poles of the transfer function Each coefficient is of type double Gain Double A single double value describing the gain of the transfer function 7 2 1 3 State Space Parameters The state space model is described by the number of state variables n and by four matrices A B C and D State variables Selection The number of state variables Possible values are in the range from 1 to 99 A nxn Matrix The state matrix of the state space model Each matrix element is a scalar value of type double Astos Solutions GmbH All Rights Reserved Copyright 2013 per ISO 16016 Grund 1 78089 Unterkirnach Germany Copying and distribution is prohibited without express authority Doc No ASTOS PEET SUM 001 Astos PEET Issue 17 Date 2013 07 26 Solutions Page 17 of 60 B Nx3 Matrix The input matrix of the state space model Each matrix element is a scalar value of type double C 3xn Matrix The output matrix of the state space model Each matrix element is a scalar value of type double D 3x3 Matrix The feedthrough m
66. ry containing a subset of the block types available on the first tab To add blocks from the database to the pointing system the desired block must be dragged from the database browser to the system view window A detailed description on how a pointing system will be created is given in chapter 8 Astos Solutions GmbH All Rights Reserved Copyright 2013 per ISO 16016 Grund 1 78089 Unterkirnach Germany Copying and distribution is prohibited without express authority Doc No ASTOS PEET SUM 001 Astos PEET Issue 17 Date 2013 07 26 Solutions Page 15 of 60 7 Block Types This chapter explains the various block types and their required parameters For each block type the meaning of the block parameters will be explained in detail If not otherwise stated in the software user manual or in the block masks all parameters must be provided in SI units e g angles must be defined in radian It is up to the user to ensure that the numbers are consistent across the pointing system If a block mask forces the user to provide parameters in Non SI units these parameters will be converted to SI units internally 7 1 Coordinate Transformation Block The coordinate transformation block is used to transform signal data from one coordinate system to another coordinate system The coordinate system transformation is defined by an Euler transformation using three angles and a rotation sequence The resulting matrix is used as static system g
67. s Nm rpm Harmonic numbers Vector Harmonic numbers i e ratios of frequency of harmonic with respect to wheel speed case by harmonics 7 11 Rigid Plant This block can be used to add rigid plants to the pointing system It realizes the following ideal plant model Ow N Eq 7 28 with Astos Solutions GmbH All Rights Reserved Copyright 2013 per ISO 16016 Grund 1 78089 Unterkirnach Germany Copying and distribution is prohibited without express authority Doc No ASTOS PEET SUM 001 Astos PEET Issue 17 Date 2013 07 26 Solutions Page 38 of 60 spacecraft inertia matrix 3x3 vector of spacecraft angular rates 3x1 N vector of torques acting on the spacecraft body 3x1 7 11 1 Block Parameters The block mask parameters are listed in the next table Block mask parameters Inertia Matrix A 3x3 matrix of containing the inertia 7 12 PID Controller This block represents a system transfer via a set of ideal single input single output Proportional Integral Derivative PID controllers It is represented in transfer function notation by the following model individually for each axis K K K Eq 7 29 S with K _ total controller transfer function K proportional gain of the controller K integral gain of the controller K differential gain of the controller s Laplace variable 7 12 1 Block Parameters The block mask parameters are listed in the next table
68. saeeeeaaesteeaeeeeeaeen 39 7 15 1 Block Parameters cccesseccecesseeeeeeeeeeeeseeeeeeeseeeeeeeseeaaeeeseeeeeeeseeeeeeeees 40 8 Building Pointing Systems Using DEET 42 8 1 Global Settings EE 43 8 2 Configuring DIOCKS ireira orainne aei aaaea aa aaa ai aaa aa atant 43 8 2 1 Linking to external data saassseeeesrneessrnesesrnesssnnesrnnnennnnnnntnnnnnnnnnnnnnnnnannna 43 8 2 2 Sensitivity E EE 45 8 3 Container DIOCKS asit sifistecsieivihitnie na dandieeid a ainda 46 9 Computing Pointing Errors Using PEET ssnsmiviciccsincessssteerccetveersieaneencreteeotes 47 9 1 Pointing pudget ee 49 10 PointingSat Example as seastes cape ee die a tsiaede pines eee 50 10 1 Building the Pointing system e ec cece eeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeseeeeeeeeeeeaeens 50 10 1 1 Connecting BIOCKS E 54 10 1 2 Defining correlations between error Sources 56 10 2 Computing pointing errorg nenn nenn nnt 56 10 2 1 Creating error indices cceecceceeeceeeneceeeeeeeeeeeceaeeeeaaeseeeeeseaeestaeseeneeeeaes 56 10 2 2 Perform error Computatlon 58 Astos Solutions GmbH All Rights Reserved Copyright 2013 per ISO 16016 Grund 1 78089 Unterkirnach Germany Copying and distribution is prohibited without express authority Doc No ASTOS PEET SUM 001 Astos B E ET Issue 1 7 Date 2013 07 26 J Solutions Page 5 of 60 10 2 3 Analyse pointing errors ssseessssssssrresssnnessnnnesrennesnnnnnntennennnnnntnnnennnnnnnennnee 59 As
69. t case Band limited Hz PSD representation Dependent See section 7 9 2 4 N VHz case PSD Astos Solutions GmbH Grund 1 78089 Unterkirnach Germany All Rights Reserved Copyright 2013 per ISO 16016 Copying and distribution is prohibited without express authority Doc No ASTOS PEET SUM 001 E ET Issue 1 7 Date 2013 07 26 stos Page 35 of 60 Number of Double Overall number N of harmonics to be considered for harmonics the axial mode Amplitude Vector Nx1 vector of amplitude coefficients N rpm coefficients Harmonic numbers Vector Harmonic numbers i e ratios of frequency of harmonic with respect to wheel speed 7 10 2 Reaction Wheel Torque The disturbance torque model includes a model for the rocking mode in the x y plane only as according to RD8 axial disturbance are negligible 7 10 2 1 Rocking Mode Model The disturbance torques due to the rocking mode wheel x y plane which act on the spacecraft interface are modelled using the set of equations described below with I lz T rock g rock Frock T rock SC 7 10 2 2 a Hol Crock QL 0 D Kach 0 d T QL Crock 6 0 Kock 0 Ed E Crock Ang rockfrocklrr Eq 7 20 K ock K 2m f Eq 7 21 Koc 0 d Thockse 0 k IH Eq 7 22 rock flywheel inertia perpendicular to spin axis flywheel inertia about spin axis x y excitation torques for the rocking mode damping of the roc
70. t 2013 per ISO 16016 Grund 1 78089 Unterkirnach Germany Copying and distribution is prohibited without express authority Doc No ASTOS PEET SUM 001 J Astos PEET Issue 1 7 Date 2013 07 26 Solutions Page 48 of 60 The random process signal part is represented by a PSD plot In the information section a preview of the plot is shown This preview can be enlarged by double clicking on the plot This will open a new plot window shown in Figure 9 2 Dynamic System 2 Output 0 DAR Si z Ei a H D 3 LI o bal ki D 3 3 E ja D Lol 0 1 Frequenzy Hz Figure 9 2 Plot window In this plot window the plot can be examined in detail It is possible to click on one of the lines to get a detailed description of the current value at this position To do this the data picker must be first selected in the tool bar right most icon It is also possible to zoom into the plot in order to enlarge certain regions This is done by using the right mouse button and dragging a rectangle to define the region of interest To analyse the final pointing error the PEC block must be selected in the tree view window In this case the final pointing error is shown on the first tab of the information section see Figure 9 3 The total error on all axes individually The error contribution from all time constant signals The error contribution from all time random signals In addi
71. taining time value data For each time step a new row must be added to this table which contains the time and the data values for the x y and z axis at this time point The time series are then converted to equivalent spectrum magnitudes auto and cross spectra first This frequency magnitude data is fitted to a rational transfer function in a subsequent step Block mask parameters Min pole order Double The minimum order used for the rational fit of the retrieved PSD optional Max pole order Double The maximum order used for the rational fit of the retrieved PSD optional Time series List A list of time value pairs containing the time and the data values for the x y and z axis In case of a 1D signal only a single data value must be Astos Solutions GmbH Grund 1 78089 Unterkirnach Germany All Rights Reserved Copyright 2013 per ISO 16016 Copying and distribution is prohibited without express authority Doc No ASTOS PEET SUM 001 Astos PEET Issue 17 Date 2013 07 26 Solutions Page 30 of 60 provided 7 9 2 4 Random Process PSD Parameters For the random process of type PSD the user has to specify a either a 3x3 matrix in which the elements can either be transfer functions frequency response models or zero pole gain models or he has to specify a state space model The parameters for the PSD type are similar to the parameters of the
72. terwards right click on the parameter input field which will be linked and select Import from MATLAB A new dialog will be shown providing a dropdown list of all available MATLAB variables It is up to the user to select a Astos Solutions GmbH All Rights Reserved Copyright 2013 per ISO 16016 Grund 1 78089 Unterkirnach Germany Copying and distribution is prohibited without express authority Doc No ASTOS PEET SUM 001 ssue ate 07 J Astos PEET 17 Date 2013 07 26 Solutions Page 45 of 60 variable which fits to the dimension of the linked block parameter In case of tabular data the linked data must have the same number of columns but can have as many rows as desired 8 2 2 Sensitivity analysis PEET provides the possibility of a sensitivity analysis This feature can be accessed by the same popup menu used to link parameters to external data sources see chapter 8 2 1 After selecting sensitivity analysis the sensitivity analysis manager shown in Figure 8 4 will be opened The sensitivity analysis uses difference quotients for each axis to compute the sensitivity Therefore the user first selects the parameter element he wants to examine In case of a scalar value nothing has to be selected Pressing the Analyse button will now compute the difference quotients During the analysis the total pointing error is computed twice First the total pointing error for the perturbed parameter element Parampe is computed Afterw
73. the red block shown in Figure 10 2 FI PEET W sources PEET examples PointingSat peet File Setup Database Windows sm N L j Dee 1 i mo n PES 1 Settings CO Stu Dteate pare SSES imension Use time random part wo Uniform ov x Y z o o on 0 0 l x H z 1454E 4 1 212E 4 1 309E 4 Uncorrelated i Kales Figure 10 2 Setting block parameters for the first PES Blocks can also be renamed To rename a block double click on the block name below the block A small dialog will open into which the new block name can be entered Block names must be unique inside a system view window but they can have the same name if they are in two different system views More than one system view window is only available if container blocks are used see chapter 8 3 for details In this example the PES block is renamed to PES 1 Double click on the name below the PES block and enter PES 1 into the rename dialog After pressing the OK button the new name is used in the pointing system Most of the blocks must be configured with some parameters For this reason every configurable block type owns a block mask This block mask can be opened by double clicking the block symbol inside the system
74. the spin speed of the wheel C is the amplitude coefficient of the k th harmonic and D the harmonic number i e the ratio of frequency of k th harmonic to spin frequency of the wheel Alternatively the rocking mode can also be defined by the dynamic imbalance coefficient Ua i e considering only the first harmonic resulting in an amplitude frequency set A U Eq 7 26 L Art Eq 7 27 The wheel speed is assumed to be constant within a single observation period This can be understood as a linearization around a certain working point during the observation In addition it has to be noted that there is no distinction between the radial axes amplitudes and 0 although the time based model in RD8 accounts for the 90 phase shift between the axes for each harmonic This is however no restriction of the model as from a performance point of view only the overall magnitude or temporal mean is of interest when applying the statistical interpretation Furthermore it has to be noted that the arbitrary phase angle between different harmonics cannot be directly accounted for as in the time domain model from RD8 As a full correlation between the different harmonics and axes might be too pessimistic an uncorrelated set is realized in the PEET model Astos Solutions GmbH All Rights Reserved Copyright 2013 per ISO 16016 Grund 1 78089 Unterkirnach Germany Copying and distribution is prohibited without express authority Doc No ASTOS
75. thority Doc No ASTOS PEET SUM 001 ssue ate 07 J Astos PEET 1 7 Date 2013 07 26 Solutions Page 46 of 60 4 Increasing the selected parameter element by 1 rad kelvin will decrease the total pointing error on the x axis by 0 36151881 rad 5 Increasing the selected parameter element by 1 rad kelvin will increase the total pointing error on the y axis by 11 9455992 rad 6 Increasing the selected parameter element by 1 rad kelvin will decrease the total pointing error on the z axis by 0 14442361 rad 8 3 Container blocks Container blocks are a special kind of block type They can be used to abstract a complex block structure into a single block symbol They do not have a block mask Double clicking a container block will open a new system view window Figure 8 5 shows an example for a container block The content of a container block is added to the system view of the container in the same way as for the pointing system All the blocks added to a container must be configured separately Container blocks can have as many input and output ports as required Input and output ports are defined by adding Input Port and Output Port blocks from the database browser to the system view of the container block Container blocks can also be exported to the block database as user defined block types This is done by selecting the container block which should be exported and selecting the menu Database Export selected block This will o
76. time constant part as well as to the time random part Block mask parameters Signal dimension Selection The dimension of the output signal of the PES block Possible values are 1D and 3D Use time constant Checkbox A flag indicating if the pointing error source provides a part time constant part or not Use time random Checkbox A flag indicating if the pointing error source provides a part time random part or not 7 9 1 Time Constant Block Parameters The time constant part of the pointing error source block is defined by using a probability distribution function The parameter responsible for the type of the probability distribution function is given in the next table Block mask parameters Distribution type Selection The probability distribution function used to specify the time constant part of the pointing error source block Possible values are Discrete Uniform Bimodal Gaussian and Rayleigh Depending on the distribution additional block mask parameters are available to the user The next subchapters will list the parameters for each probability distribution function applicable for the time constant part 7 9 1 1 Discrete Distribution Parameters A discrete distribution is a probability distribution whose variables can only take discrete values In the context of PEET only the mean value must be given by the user The parameters provided by the block mask are shown in the
77. tion the PEC Pointing block provides the line of sight error around the user selected axis while the PEC Position additionally displays the contribution from pure position errors and attitude error couplings on separate tabs Astos Solutions GmbH All Rights Reserved Copyright 2013 per ISO 16016 Grund 1 78089 Unterkirnach Germany Copying and distribution is prohibited without express authority Doc No ASTOS PEET SUM 001 Astos P E ET Issue 1 7 Date 2013 07 26 f Solutions Page 49 of 60 B Error Budgeting Block ID PEC Block type PEC Pointing error Input Port 1 x Y 2 39 1472647 41 8633375 38 9407646 Final pointing error Figure 9 3 Final pointing error 9 1 Pointing budget reports PEET offers the possibility to export the output signals of the budgeting computation in a tabular format to an Excel report file At least one error index must be defined in order to access this feature using File Create Report For each defined error index a new report will be created in the output folder of the currently loaded pointing systems peet folder Each Excel report file contains six sheets One sheet containing some general information and five sheets for the various signal parts The general information sheet contains some general data like the creation date of the rep
78. tos Solutions GmbH All Rights Reserved Copyright 2013 per ISO 16016 Grund 1 78089 Unterkirnach Germany Copying and distribution is prohibited without express authority Doc No ASTOS PEET SUM 001 Astos PEET Issue 17 Date 2013 07 26 Solutions Page 6 of 60 1 1 AD1 AD2 1 2 RD1 RD2 RD3 RD4 RD5 RD6 RD7 RD8 RD9 Applicable and Reference Documents Applicable Documents ECSS E ST 60 10C Control Performance Standard ECSS E ST 60 10C ESA ESTEC Requirements amp Standards Division 2008 ESSB HB E 003 ESA Pointing Error Engineering Handbook Issue 1 19 July 2011 Reference Documents ASTOS PEET TN 001_Iss1 0 PointingSat Definition IEEE STD 952 1997 R2003 IEEE Standard Specification Format Guide and Test Procedure for Single Axis Interferometric Fiber Optic Gyros Ott T Benoit A Van den Braembussche P Fichter W ESA Pointing Error Engineering Handbook 8th International ESA Conference on Guidance Navigation amp Control Systems Karlovy Vary CZ June 2011 Ott T Fichter W Bennani S Winkler S Precision Pointing H Control Design for Absolute Windowed and Stability Time Errors manuscript submitted to CEAS Space Journal Hirth M Brandt N Fichter W Inertial Sensing for Future Gravity Missions GEOTECHNOLOGIEN Science Report No 17 Observation of the System Earth from Space Bonn 2010 ISSN 1619 7399 Hirth M Fichter W et al
79. user can specify the correlation between the axes For an uncorrelated or a fully correlated PES it is required to only define the variances for the x y and z axis These variances are used for the diagonal elements of the covariance matrix Internally all other elements of the covariance matrix are set automatically to 0 for an uncorrelated PES and 1 for a fully correlated PES 7 9 2 6 Random Process Periodic Parameters In case the Periodic type is used for the random process definition the PES output signal is supposed to be a composition of sine functions In this case the required block mask parameters are listed in the next table Astos Solutions GmbH Grund 1 78089 Unterkirnach Germany All Rights Reserved Copyright 2013 per ISO 16016 Copying and distribution is prohibited without express authority Doc No ASTOS PEET SUM 001 Issue 1 7 Page 31 of 60 PEET Astos Solutions Date 2013 07 26 Block mask parameters Amplitude distribution Selection The distribution of the amplitude Possible values are Discrete and Uniform Axes correlation Selection Only available for a three dimensional PES This parameter defines the correlation between the x y and z axis Possible values are Uncorrelated and Fully correlated Frequency Amplitude List The frequency amplitude data This data depends on the PES dimension and the amplitude distribution For a one dimensional PES and a dis
80. view window Double click on the PES 1 block This will open the block mask for the PES 1 block This block mask is shown in Figure 10 2 To configure the block the user can now provide values for the parameters In this example the error source PES 1 only provides a time constant pointing error This can be defined by deselecting the check box labelled Use time random part lf the time random tab is now selected the whole content is greyed out indicating that these Astos Solutions GmbH All Rights Reserved Copyright 2013 per ISO 16016 Grund 1 78089 Unterkirnach Germany Copying and distribution is prohibited without express authority Doc No ASTOS PEET SUM 001 J Astos PEET Issue 1 7 Date 2013 07 26 Solutions Page 52 of 60 parameters are not used Switch back to the time constant tab Now set the distribution type to Uniform This will enable the user to define all parameters required for a uniform distribution In this case minimum and maximum values for all three axes must be defined For the minimum values enter 0 0 0 0 0 0 and for the maximum values use 1 454e 4 1 212e 4 1 309e 4 Set the correlation to Uncorrelated The block is now correctly set up Now insert a second error source and rename it to PES 9 Move it to the position shown in Figure 10 3 Open the block mask for the new error source by double clicking the block symbol of PES 9 In this case the error source will own a time random part Deselect t
81. yright 2013 per ISO 16016 Grund 1 78089 Unterkirnach Germany Copying and distribution is prohibited without express authority Doc No ASTOS PEET SUM 001 esis PEET Issue 1 7 Date 2013 07 26 Solutions Page 53 of 60 FA PEET W sources PEET examples PointingSat feet Figure 10 4 Setting block parameters for the coordinate transformation To configure the coordinate transformation block open the block mask and select the rotation sequence 1 2 1 from the drop down menu For the angles enter 0 0 1 5708 and 3 1416 Angles are always defined in radians The second system transfer is represented by a static system block Add a static system block from the database rename it to Temp to Focal Point and open the block mask Enter the values 4 315e 6 5 624e 6 5 769e 6 on the diagonal of the system matrix After all blocks are added to the pointing system the system should look like in Figure 10 7 Blocks can be rearranged by dragging them in the system view window The next step is to connect the blocks Astos Solutions GmbH All Rights Reserved Copyright 2013 per ISO 16016 Grund 1 78089 Unterkirnach Germany Copying and distribution is prohibited without express authority Doc No ASTOS PEET SUM 001 J Astos PEET Issue 1 7 Date 2013

Project Title - Pointing Error Engineering Tool (PEET)

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