APPENDIX II User s Guide and Toolbox Example

Transcription

1 APPENDIX II User s Guide and Toolbox Example To fulfill the aims of the research presented in this thesis, a User s Guide was authored for the MATLAB Control Allocation Toolbox. The User s Guide provides basic installation and operation instructions for the toolbox. It also presents the various pages of the toolbox in vivd color to illustrate the GUI layout achieved during the design phase. The comparative value afforded by this control allocation design tool is demonstrated by applying it to F-18 HARV aerodynamic data. The User s Guide presents the process and results obtained from such an application as an example (i.e., that referred to in Chapter 5). The User s Guide was written prior to this thesis, and has only been slightly modified for inclusion here. The page numbering and page headings have been adjusted to match those of the thesis. However, the User s Guide utilizes a separate Title Page, Table of Contents, and presents redundant information insofar as the control allocation methods are concerned. 170

2 MATLAB CONTROL ALLOCATION TOOLBOX INSTALLATION AND USER S GUIDE Michelle L. Glaze October 1998 Department of Aerospace and Ocean Engineering Virginia Polytechnic Institute and State University Blacksburg, VA

3 FOREWORD This effort was supervised by John V. Foster of the NASA Langley Research Center, and funded under Grant NAG Special thanks go to Dr. Wayne Durham of Virginia Polytechnic Institute and State University for his advice, clear guidance, and patience throughout this undertaking. Thanks also go to Dr. Ken Bordignon and John G. Bolling, alumni of Virginia Polytechnic Institute, for their previous research and findings in the area of control allocation.

4 TABLE OF CONTENTS INTRODUCTION INSTALLATION AND OPERATION TOOLBOX OVERVIEW Assumptions Methods Implemented Toolbox Pages TOURING THE TOOLBOX Introduction Page Data Input Page Edit Data Page - Input Data Control Allocation Page Edit Data Page - Weighting Matrix Numerical Output Pages AMS Comparison Pages EXAMPLE -- F-18 HARV Background CAT in Action Some Conclusions GENERAL USER INFORMATION Path Definition Loading/Saving Files Edit Data Page Limitations Temporary Data Files Output Data REFERENCES...206

5 Michelle L. Glaze Appendix II: User s Guide and Example 174 INTRODUCTION This manual is intended to famaliarize you with the Control Allocation Toolbox for Matlab. It discusses the purpose behind such a computer-based tool, and provides you with a basic knowledge of the methods implemented within. It also contains in-depth descriptions about the toolbox features, and provides examples to aid in understanding. The purpose and overall functionality of the toolbox are briefly discussed below, followed by installation instructions and a complete overview of the toolbox (i.e., the methods implemented, the different user-interface pages). The Control Allocation Toolbox for Matlab is an interactive, windows-based, graphical user interface created to aid in the design of control allocation systems. This toolbox seeks to provide the designer with all of the numerical and graphical information necessary to make reliable, practical comparisons between allocation methods. To enhance its comparative value, the following methods (described in detail later) are evaluated in the toolbox: Direct Allocation Pseudo-Inverse Allocation Weighted Pseudo-Inverse Allocation General Allocation It should be noted that this toolbox, although providing accurate comparisons between allocation methods, does not seek to solve an allocation problem in itself; it does not consider all possible design parameters, e.g., control rate limiting, control prioritization. Furthermore, the Control Allocation Toolbox is just what its name implies it to be, a user-friendly design tool.

6 Michelle L. Glaze Appendix II: User s Guide and Example 175 INSTALLATION AND OPERATION Before installing and operating the Control Allocation Toolbox, you should make an effort to acquire the equipment and software listed below, as they are required for operation: PC, Macintosh PPC, or 32-bit SGI (i.e., desktop machines) Matlab version 5.0 or higher Color monitor with a resolution no less than 800x600 In desiging the toolbox, it was noted that any monitor under 15" provided insufficient viewing of the graphical user interface. To obtain optimal viewing, it is recommended that you acquire at least a 15" color monitor with a preferred resolution of 1024x768. Once you have obtained all the required equipment and the toolbox software, you need to install it. The installation procedure is a relatively simple process consisting of only three steps. The procedure differs slightly for 32-bit UNIX machines due to the way the overall Matlab path is defined on workstations. To account for this difference, there are two installation procedures presented below; one for the PC and Macintosh PPC, and one for a 32-bit UNIX workstation. Installation Procedure (PC and Mac PPC) 1) If downloaded from the web, decompress the file using WinZip, DropStuff, etc. 2) Put the GUI folder and files contained therein into the main Matlab directory 3) Edit the Matlab path (see Matlab documentation) to include this new folder; the folder should be added to the beginning of the path as opposed to the end. The new path should be similar to one of the following: PC : "... \matlab\gui" Mac : "... :matlab:gui" NOTE : The GUI folder should not be renamed as it is used internal to the toolbox for locating and saving files. Installation Procedure (32-bit UNIX) 1) If downloaded from the web, decompress the file using gunzip 2) Put the GUI folder and files contained therein into your local directory

7 Michelle L. Glaze Appendix II: User s Guide and Example 176 3) Edit the Matlab path to include this new folder. To ensure proper orientation of the toolbox, create an M-file containing the lines below. Save the M-file in your local directory, and run it prior to running the toolbox. Example M-file % M-file to edit the Matlab path prior to running CAT p1 = path; p2 =.../GUI ; % Replace...with your local directory name path(p2,p1); To eliminate the possibility of errors, the installation procedure(s) described above should be completed each time a new version of the toolbox is installed. Once installation is complete, the toolbox is ready for operation. Basic operation of the toolbox is as straightforward as the installation procedure. The four basic steps are listed below: Basic Operation 1) Run Matlab as usual 2) If using 32-bit UNIX, run the M-file you wrote to edit the Matlab path 3) To use the toolbox type "conallo" (without quotes) at the Matlab command prompt 4) Follow the on-screen help boxes to step through the different windows of the toolbox

8 Michelle L. Glaze Appendix II: User s Guide and Example 177 TOOLBOX OVERVIEW To successfully use any computer-based tool, one should have some idea of what to expect while using it. This knowledge should include a basic understanding of the algorithms implemented, insight into the underlying assumptions, an idea of what type of information will be required during operation, and an overall picture of what the computer tool is trying to accomplish. This overview seeks to provide you with the basic information needed to successfully understand and operate the Control Allocation Toolbox for Matlab ; hereafter referred to as CAT. The sections below present the assumptions made throughout the toolbox, explain the allocation methods employed in CAT, and briefly describe the various pages that you will encounter in the toolbox. Assumptions As described earlier in this documentation, the main purpose of CAT is to compare control allocation algorithms; both graphically and numerically. Generally speaking, control allocation is any method which is used to determine how the controls of a system should be positioned to achieve some desired effect. While there are many applications of control allocation, the main focus of this text is the effectiveness of multiple, redundant control effectors in generating body-axis moments for the control of an aircraft. Thus each problem considered is taken to be three-dimensional (i.e., one dimension per body-axis moment); the input is some set of desired moments (C l, C m, C n ), and the numerical output is the set of control effector positions after allocation and the associated set of attained moments. Note that you may use other input combinations, e.g., three angular accelerations, two moments and one force, but the the output will continue to reflect the previously-metioned moment notation. The allocation problems considered are assumed throughout to be linear. Thus the control effectiveness (i.e., the entries in the effectiveness matrix) referred to throughout this guide is based on the slope of the moment (or some other objective) vs. the control deflection curve. The slope may be defined in any way desired, e.g., slope at the origin, secant slope to the control deflection limits. The final assumption arises from the fact that CAT is a comparative tool. To effectively compare any two methods there needs to be some relative measure of performance similar to both. For a given linear effectiveness and control effector position limits there exists a set of maximum attainable performance from the control effectors. When considering the moment-generating capabilities of an aircraft this results in the Attainable Moment Subset (AMS); the volume of the attainable moments in

9 Michelle L. Glaze Appendix II: User s Guide and Example 178 three-dimensional moment space. Therefore, the relative measure of performance is assumed to be the volume of the AMS associated with a given allocation method. Methods Implemented As previously mentioned, there are a total of four control allocation methods evaluated by CAT. Of those four, only three are directly implemented: Direct Allocation, Pseudo-Inverse Allocation, and Weighted Pseudo-Inverse Allocation. These three methods are uniquely defined for any given control effector configuration. Thus for each of these methods, you may allocate controls for specific demands as well as determine the overall capability of the method. For other more general allocation methods, the controls allocated for specific demands must be generated off-line and provided to the toolbox for evaluation using the General Allocation option. Direct allocation uses the control effector position limits to determine the optimal (maximum) attainable moment subset at a given instant and flight condition. This approach directly solves the defining vector equation: m d = Bu (1) where m d is the set of n desired moments, B is the nxm linear control effectiveness matrix at a given instant and flight condition, and u is the associated set of m control effectors that is to be determined. Direct allocation first solves equation (1) to determine the maximum AMS, then allocates controls as a possibly scaled-down version of the unique solutions associated with the maximum. In this sense direct allocation is an "optimal" solution to the control allocation problem. Thus when evaluating direct allocation, both the maximum AMS and the controls allocated in response to specific demands are always available. Since direct allocation is taken as the optimal solution, it is used as a basis for comparison with the other three methods evaluated in the toolbox. Pseudo-inverse allocation, or minimum-norm allocation (including weighted pseudo-inverses), is a common method used for solving an underdetermined (i.e. redundant control effectors, m>n) set of linear equations. This algorithm minimizes the two-norm of a given set of control effectors and provides linear solutions of the form: u = Pm (2)

10 Michelle L. Glaze Appendix II: User s Guide and Example 179 where u is the given set of effectors, m is the set of attainable moments, and P is the mxn right pseudoinverse matrix solving the equation: BP = I n (3) where n is the number of moments. The pseudo-inverse solution, equation (2), is easily generated and may be used to allocate controls for specific demands. It is generally true that no pseudo-inverse solution can achieve the maximum AMS without violating some control constraint. In the Control Allocation Toolbox the AMS associated with the pseudo-inverse solution is calculated as the intersection of the n-dimensional column space of P with the admissible control deflections, using algorithms described in Ref. 1. Toolbox Pages Having explained the methods implemented in CAT, described its purpose, and presented the underlying assumptions, it now remains to introduce the pages that make up this toolbox. Several different types of pages form the foundation of CAT; those requiring user input, those presenting results, those requiring input to manipulate the results, and those providing help to the user. Each page is briefly described below, providing information on the types of input needed and/or the types of output displayed. Each page will be discussed in further detail in a subsequent section of this text. The first page encountered while using CAT is the Introduction Page. This particular page is nothing more than a stepping block into the toolbox; it requires no data from you, nor displays any allocation results. The basic purpose of the Introduction Page is to assure you that installation was completed successfully, and inform you that CAT is ready to use. The next page in the toolbox, the Data Input Page, is one of the most important because the data gathered on this page are required for any further use of CAT. It is here that you must provide all of the information necessary for control allocation; the number of controls, the control effectiveness matrix, and the control effector position limits. After inputing all of the required information, the Data Input Page provides a means by which you can edit and/or save the data for later use. Should you choose to edit the input data, the Edit Data Page will appear. This particular page displays the control effectiveness and min/max control position limit data that were input using the Data Input Page. Double-clicking on any numerical text box allows you to change the value displayed therein,

11 Michelle L. Glaze Appendix II: User s Guide and Example 180 effectively changing the control allocation problem and associated solution. Any changes made to the data will not take effect until the "Done" button is pressed, effectively closing the window. Having successfully entered the data using the Data Input Page, you continue to the Control Allocation Page. More than the name implies, this page is used to implement the allocation algorithms, and to display both the graphical and numerical results obtained from them. The main features of the Control Allocation Page are as follows: 1) allows for the selection and implementation of control allocation methods 2) provides direct links to each of the four AMS Comparison Pages 3) provides links to the two Numerical Results Pages 4) allows you to save a hard copy of the numerical allocation results to a file 5) allows editing of the input data at any time during the comparison. Since it provides access to all of the comparitive information, this page is essentially the backbone of the toolbox. The numerical results of each allocation method are displayed on the Numerical Results Pages; one displays the control effector positions after allocation, and the other displays the moments attained by the chosen method. Each page is in tabular form, and presents the numerical results for the three methods directly implemented in the toolbox. Both Numerical Results Pages update each time an allocation method is implemented, or the desired moments are changed from their initial values. It should be noted that controls MUST be allocated before the results to appear on the respective pages. The AMS Comparison Pages present the graphical results of the allocation methods implemented in the toolbox. There are four such comparison pages, three which plot the optimal AMS (i.e., direct allocation) in comparison to another of the previously-described methods. The fourth comparison page plots all of the methods together to provide an overall comparison; it updates each time a previously unused method is chosen. Each AMS Comparison Page is accessed from a pull-down menu of the same name on the Control Allocation Page. These pages allow you to change the viewpoint and/or size of the displayed AMS, as well as plot the attained and/or facet-defining moments inside the optimal". Unlike the Numerical Output Pages, controls DO NOT have to be allocated prior to plotting the AMS comparisons. The final pages of interest here are the Help Pages. Each of the previously described pages has a direct link to an associated Help Page under a pull-down menu labeled TOOLBOX Help. Each Help Page presents a brief description of the page in question followed by either a list of possible options, or a method by which to use the page; each also contains a "Done" button which closes the Help Page and any other related Help Pages.

12 Michelle L. Glaze Appendix II: User s Guide and Example 181 TOURING THE TOOLBOX The descriptions provided in the previous section were merely meant to highlight the features of different pages in the Control Allocation Toolbox. This section will augment those descriptions to offer you more in-depth, "how-to" knowledge about toolbox operation. The segments below take you on a "tour" of each page in the toolbox -- presenting a picture of each, and describing the characteristics associated with it. The pictures displayed are screen captures taken from the UNIX version of CAT (the Mac version will be presented in subsequent sections). The characteristics are presented in outline form, and written in a different font to distinguish them from the other text in this documentation. Introduction Page The Introduction Page, as depicted in Figure 1, is the first page you will see after typing "conallo" at the Matlab command prompt. Essentially a stepping block into the toolbox, this page serves as a welcome mat letting you know that everything is in working order and ready to go. To continue using the toolbox, you press the button labeled "Press to Begin". Purpose: Welcome to the toolbox! Inputs: None required Outputs: None Options: To continue, depress the "Press to Begin" button. Help: Not available Figure 1 -- Introduction Page

13 Michelle L. Glaze Appendix II: User s Guide and Example 182 Data Input Page The Data Input Page is the second page in the toolbox, opened immediately after the Introduction Page is closed. The main purpose of this page, shown in Figure 2, is to gather the information necessary to perform control allocation. Aside from gathering information, this page also allows you to view, edit, and/or save the data. Purpose: Gather the data necessary to perform control allocation. Inputs: 1) # of controls, m 2) Control effectiveness matrix 3) Effector position limits Outputs: None Options: 1) View/ edit data 2) Save data to file Help: Pull-down menu, Toolbox HELP Procedure: Figure 2 -- Data Input Page 1) Enter the number of controls in the box labeled "Number of controls" by double-clicking the mouse over the? and entering the appropriate number. 2) Choose one of the two input methods from the pop-up menu displaying "Choose Method" under the label "Input Methods". Text file: Prompts you to load a text file containing the control effectiveness and control effector position limits as a 5xm matrix; the first three rows are the effectiveness, the last two are the min/max limits, respectively. Random Generation: Randomly generates a 3xm matrix, and sets the minimum/maximum effector positions to -1/1, respectively. 3) To view and/or edit the data, click on the button labeled "View/Edit"; the Edit Data Page appears (see next section for details). 4) To save the data to a file, press the "Save" button; you will be prompted to enter the path and filename of the saving location. 5) After entering the required data, press "Continue" to open the Control Allocation Page.

14 Michelle L. Glaze Appendix II: User s Guide and Example 183 Edit Data Page - Input Data The Edit Data Page, used here to display the input data, is accessible only from the Data Input Page (see previous section). This page displays the data as you entered it (i.e., as a 5xm matrix), allowing you to check for and/or correct any possible errors. If changes are made to the input data, they will not take effect until the Edit Data Page, presented in Figure 3, is closed as described below: Figure 3 -- Edit Data Page w/ Input Data Purpose: Display the input data, and allow editing when deemed appropriate. Inputs: None required Outputs: None Options: 1) Check data for errors 2) Correct any errors Help: Pull-down menu, Toolbox HELP Procedure: 1) Double click on the numerical entry you want to change; the text will be highlighted. 2) Type in the new desired value; the old text will automatically be deleted. 3) Repeat for every entry you want to change. 4) Depress the "Done" button for changes to take place

15 Michelle L. Glaze Appendix II: User s Guide and Example 184 Control Allocation Page The appearance of the Control Allocation Page, shown in Figure 4, indicates that you have correctly entered the required input data. You can now begin the process of comparing allocation methods. This page implements the allocation methods, and provides direct links to the graphical AMS comparisons and numerical output pages (allocation is required prior to viewing the numerical results). The other features of this page are presented below along with several procedures that you may find helpful: Purpose: Implement allocation routines and provide links to all comparative results. Inputs: 1)Desired moments C l, C m, C n prior to allocation. 2) Weighting matrix where appropriate. Output: 1) AMS comparisons 2) Control positions 3) Moments attained Options: 1)View AMS comparisons 2) Select method & allocate 3) View numerical results 4) Print numerical results 5) Print PI matrices 6) Edit input data 7) Edit weighting matrix 8) Start over or quit Help: Pull-down menu, Toolbox HELP Figure 4 -- Control Allocation Page Procedure #1 - Allocating Controls 1) Choose one of the three methods from the pop-up menu labeled "Choose Method" under the heading "Control Allocation Methods". 2) A box labeled "Desired Moment Data" should appear; enter the desired moments (or other defined parameters) in the text boxes provided. 3) If you use Weighted Pseudo-Inverse Allocation, and have not previously entered a weighting matrix, press the button labeled "ENTER WEIGHTING MATRIX"; the Edit Data Page opens displaying an mxm weighting matrix (see subsequent segment for details). 4) To allocate controls, click on the button labeled "ALLOCATE CONTROLS". 5) If desired, repeat steps 1-4 for the remaining methods. 6) To display numerical results choose "Display Numerical Results" from the"options" pull-down menu.

16 Michelle L. Glaze Appendix II: User s Guide and Example 185 Procedure #2 - Displaying/Printing Numerical Results 1) Click on the pull-down menu labeled "Options". 2) Click on either Display Numerical Results or "Print Numerical Results" 3) If you chose "Display Numerical Results", the two numerical output pages appear; one displaying the control effector positions after allocation, and one displaying the moments attained. Note: Results are presented for allocation methods applied prior to display. The output pages update when a new method is used, or when one of the desired moments is changed from its previous value. 4) If you chose "Print Numerical Results", you must then select the results you want to print, e.g., Scaled Pseudo-Inverse, Truncated Pseudo-Inverse, from the submenus. 5) When prompted, enter the path and name of the file to save. 6) Repeat steps 1, 4-5 to print the numerical results of the other methods. Procedure # 3 - Displaying Graphical AMS Results 1) Click on the pull-down menu labeled "AMS Comparisons". 2) Choose one of the four comparisons available, e.g., "Direct/Pseudo-Inverse", "All Methods". 3) If you chose the "Direct/Weighted Pseudo" comparison, and have not previously entered a weighting matrix, you are prompted to do so before the AMS results are plotted; the Edit DataPage opens displaying the default weighting matrix. 4) If you chose the "Direct/General Allocation" comparison, you are prompted to load a data file containing a kx3 array of points, where k is the number of points to be fitted with a convex hull. Note: As the user, you are responsible for ensuring that the data have physical significance to the current control effectiveness and position limit data. If a file is not loaded (i.e., you click "Cancel"), Matlab generates a random 100x3 matrix for evaluation; there is no comparative value with other methods. 5) If you chose "All Methods", methods that do not require user input (i.e., direct allocation and pseudo-inverse) are plotted automatically. The other methods will only be plotted if they are already displayed on their respective AMS Comparison Page. 6) See the subsequent section on Graphical Comparison Pages for details on manipulating the size and viewpoint of the AMS comparison plots. Procedure #4 - Printing the PI Matrices 1) Click on the pull-down menu labeled "Options". 2) Select either "Pseudo" or "Weighted Pseudo" from the submenu. 3) In each instance, the matrix used in calculating the corresponding solution will be written to the Matlab Command Window. 4) To print the matrices from the command window, you can do one of two things: 1 st option: Highlight the matrices using the mouse, choose "Print Selection" from the Matlab "File" menu (if avaiable). 2 nd option: Cut and paste the matrices into a text editor, print from the editor.

17 Michelle L. Glaze Appendix II: User s Guide and Example 186 Procedure #5 - Editing Input Data 1) Click on the pull-down menu labeled "Edit" on the Control Allocation Page, and select "Input Data". 2) This action automatically closes all CAT windows, and re-opens the Edit Data Page with the previous input data displayed. 3) Edit the data as appropriate (described in a previous section of the "tour"), and click "Done" when finished. 4) The Data Input Page will appear already displaying the number of controls, and method of input. 5) To continue to the Allocation Page using the new input data, click "Continue". 6) To edit the data once more click "View/Edit" and proceed accordingly. Procedure #6 - Editing Weighting Matrix 1) Click on the pull-down menu labeled "Edit" on the Control Allocation Page, and select Weighting Matrix. 2) This closes any AMS Comparison Pages displaying the Weighted Pseudo-Inverse AMS, causes the numerical results on the Numerical Output Pages (if displayed) to "grey" out, and opens the Edit Data Page displaying the previous weighting matrix. 3) Edit the entries as appropriate (description is in a forthcoming section of the "tour"), and click the "Done" button when finished. 4) The AMS Comparison Pages closed in step 2 will re-open displaying the new Weighted Pseudo-Inverse AMS. 5) For the numerical results to reappear, you must allocate controls using the Weighted Pseudo-Inverse method following the steps in Procedure #1. Procedure #7 - Starting Over or Quitting 1) Click on the "File" pull-down menu of the Control Allocation Page. 2) Select either "Start Over" or "Quit". 3) If "Start Over" was chosen all CAT windows are closed, all variables in the workspace are cleared, and the Data Input Page reappears. 4) If you chose Quit all CAT windows are closed, all variables in the workspace are cleared, and you are returned to the Matlab command prompt. Note: Errors will result if the toolbox is quit by simply closing the Control Allocation Page. The toolbox MUST be Quit using the File pull-down menu.

18 Michelle L. Glaze Appendix II: User s Guide and Example 187 Edit Data Page - Weighting Matrix The Edit Data Page, presented in Figure 5, is used here to display the weighting matrix required for weighted pseudo-inverse allocation. Thus, you will see this page the first time you attempt to use (i.e., plot the AMS or allocate controls) the weighted pseudo-inverse method. The default matrix is a diagonal matrix, N, (i.e., off diagonal terms are zero) with entries described by: N(i,i) = 1 ui max - ui min (4) where u i_max and u i_min are the maximum and minimum position limits, respectively, for the i th control effector. Although the default matrix is diagonal, you may edit any displayed entry as described below: Figure 5 -- Edit Data Page w/ Weighting Matrix Purpose: Display the weighting matrix, and allow editing when deemed appropriate. Inputs: None required Outputs: None Options: Change matrix entries Help: Pull-down menu, Toolbox HELP Procedure: 1) Double click on the numerical entry you want to change and type in the new value. 2) Repeat for each entry you want to change, and press "Done" for the changes to take effect.

19 Michelle L. Glaze Appendix II: User s Guide and Example 188 Numerical Output Pages When you choose "Display Numerical Results" from the "Options" pull-down menu on the Control Allocation Page, you should see two pages similar to those in Figure 6 and Figure 7 (they may differ slightly if you have not allocated using all the methods presened). These pages are CAT s Numerical Output Pages. The one shown in Figure 6 displays the control effector positions after allocation, while the one in Figure 7 displays the moments attained by the chosen method(s). As you can see from the figures, the results are presented in tabular form for the three methods directly implemented in the toolbox. Be aware that only the results of methods used prior to selecting "Display Numerical Results" will appear on the output pages. However, both Numerical Output Pages update when a new allocation method is chosen, or one of the desired moments is changed from its original value. Purpose: Display the control effector positions after allocation. Inputs: None Outputs: None Options: 1) View scaled or truncated PI and weighted PI solutions. Help: Pull-down menu, Toolbox HELP Figure 6 -- Numerical Output Page w/ Control Effector Positions Purpose: Display the moments attained. Inputs: None Outputs: None Options: None Help: Pull-down menu, Toolbox HELP Figure 7 -- Numerical Output Page w/ Moments Attained Procedure: 1) To switch between the "scaled" and "truncated" solutions of the Pseudo and Weighted Pseudo methods, use the pop-up menu located under the method name on the page in Figure 6.

20 Michelle L. Glaze Appendix II: User s Guide and Example 189 AMS Comparison Pages When you choose to plot the various AMS comparisons, you will see pages similar to the one presented in Figure 8. As discussed earlier in this documentation, there are a total of four comparison pages; three plot the direct allocation solution (i.e., the wireframe AMS) with the solution of one of the other methods evaluated (i.e., pseudo, weighted pseudo, or general allocation), and the fourth plots all evaluated methods together. The first three pages provide ways to change the size and viewpoint of the AMS, and allow you to plot either the desired/attained moments or the facet-defining moments inside the optimal AMS. Each of these pages is directly linked to the fourth comparison page, the "All Methods" page, such that any changes in viewpoint and/or size affect both plots. The AMS Comparison Page below appears when "Direct/Pseudo" is selected from the AMS Comparison pull-down menu: Figure 8 -- Direct/Weighted Pseudo Comparison Page Purpose: To display AMS comparisons, and allow manipulation of resulting plot. Inputs: Viewpoint coordinates when appropriate. Outputs: Moments plotted in AMS depending on method. Options: 1) Change size 2) Change view 3) Plot moments Help: Toolbox HELP menu Procedure #1 - Changing the Viewpoint Using X,Y,Z Components 1) Select "Change Viewpoint" from the pull-down menu Options on the desired comparison page. 2) From the submenu displayed, choose "X,Y,Z Components". 3) Enter the desired viewpoint coordinates in the appropriate text boxes, and click OK. 4) The AMS plot rotates to the desired viewpoint, and a button labeled Refresh Plot appears in the upper right-hand corner of the page. NOTE: This action also changes the viewpoint on the "All Methods" comparison. This IS supposed to happen. 5) To return to the default viewpoint, click Refresh.

21 Michelle L. Glaze Appendix II: User s Guide and Example 190 Procedure #2 - Changing the Viewpoint Using Angles 1) Select "Change Viewpoint" from the pull-down menu Options on the desired comparison page. 2) From the submenu displayed, choose "Azimuth/Elevation". 3) Double click on the default values displayed, and enter the new angles. 4) When finished, click OK. 5) The AMS plot rotates to the desired viewpoint, and a button labeled Refresh Plot appears in the upper right-hand corner of the page. NOTE: This action also changes the viewpoint on the "All Methods" comparison. This IS supposed to happen. 6) To return to the default viewpoint, click Refresh. Procedure #3 - Changing the Viewpoint Using the Mouse 1) Position the mouse pointer over the plot at the desired viewpoint location, and click the left mouse button. 2) The AMS plot rotates to the desired viewpoint, and a button labeled Refresh Plot appears in the upper right-hand corner of the page. NOTE: This action also changes the viewpoint on the "All Methods" comparison. This IS supposed to happen. 3) To return to the default viewpoint, click Refresh. Procedure #4 - Plotting Desired/Attained Moments 1) Allocate controls for the desired method prior to plotting the attained moments. 2) Select "Plot Moments" from the Options pull-down menu on the desired comparison page. 3) From the submenu displayed, choose "Desired/Attained", and select the allocation method. 4) The optimal AMS is redrawn with the desired and attained moments for the chosen method displayed inside (originating from the AMS origin), and a Revert Plot button appears in the upper corner. NOTE: For each comparison page, the desired moments are plotted in magenta. The attained moments are plotted in different colors by method; red = direct, black = pseudo, blue = weighted pseudo. 5) To return the AMS plot to its original form, click on Revert Plot. Procedure #5 - Plotting Facet-Defining Moments 1) Select "Plot Moments" from the Options pull-down menu on the desired comparison page. 2) From the submenu displayed, choose "Facet-defining", and select the allocation method. 3) The optimal AMS is redrawn with the facet-defining moments for the chosen method displayed inside (originating from the AMS origin), and a Revert Plot button appears in the upper corner. 4) To return the AMS plot to its original form, click on Revert Plot.

22 Michelle L. Glaze Appendix II: User s Guide and Example 191 Procedure #6 - Resizing the AMS 1) From the Options pull-down menu, select "Zoom". 2) Enter the desired scale-factor in the box that appears over the plotbox, and click OK. 3) To return to the original size, repeat steps 1-3 using the inverse of the previous scale-factor. The fourth comparison page is presented in Figure 9. Since this page plots up to four methods on one set of axes, it includes a legend to help differentiate between them. It also provides the azimuth and elevation angles to help with visualization when changing the viewpoint. Unlike the three other comparison pages, this page does not permit you to resize the AMS or to plot moments inside the optimal AMS. However, it does provide one method by which you may change the viewpoint; see Procedure #3 above. Figure 9 -- All Methods Comparison Page Purpose: Display the AMS of all evaluated methods Inputs: None required Outputs: None Options: Change viewpoint using the mouse Help: Toolbox HELP pull-down menu

23 Michelle L. Glaze Appendix II: User s Guide and Example 192 This concludes the CAT tour. Each page you will encounter while using CAT was discussed in detail (with the exception of the Help Pages as they are self-explanatory), and procedures were provided to give guidance if needed. The next section in this guide will take you through an example, highlighting some of the features metioned in the previous pages.

24 Michelle L. Glaze Appendix II: User s Guide and Example 193 EXAMPLE -- F-18 HARV Having successfully completed the tour of the toolbox, you are ready to apply the knowledge you have gained. This example is presented to help step through the process of using CAT. Thus it is recommended that you work this example in its entirety to prior to experimenting on your own. Each CAT window displayed in subsequent sections are screen captures from the Macintosh version. Each time the toolbox requires input from the keyboard or mouse, the command will be in bold-faced print. Background The aircraft under scrutiny is the F-18 HARV, i.e. High Angle Research Vehicle. The configuration examined has 10 independent control effectors consisting of left/right horizontal tails, left/right ailerons, rudder (left and right treated as one control), left/right trailing edge flaps, and threeaxis thrust-vectoring. The model was linearized about a flight condition of 10,000 ft, Mach 0.3, at a 12.5 angle-of-attack. The effectiveness matrix, B, and the position limits are given by: T B = e e e e e e e e e e e e e e e e e e e e e e e Table 1 -- Control Effector Position Limits Control Control Effector Minimum Value Maximum Value (rad) (rad) u 1 Right horizontal tail u 2 Left horizontal tail u 3 Right aileron u 4 Left aileron u 5 Combined rudders u 6 Right trailing-edge flap u 7 Left trailing-edge flap u 8 Roll thrust vectoring control u 9 Pitch thrust vectoring control u 10 Yaw thrust vectoring control The set of desired moments used in this example are taken as (1, 1, 1) for roll, pitch, and yaw, respectively. This set is not representative of any particular aircraft maneuver, but is for demonstration purposes only. CAT in Action Before launching CAT, you need to decide how to enter the data given above. The first option is to make a text file out of the effectiveness matrix and effector positions such that the first three rows are B, and the last two are u min and u max, respectively. All that remains then is to load the text file when prompted as described during the tour. The second option, though somewhat more tedious, is to enter the

25 Michelle L. Glaze Appendix II: User s Guide and Example 194 data by hand after Matlab has generated a random 5xm set of data. For ease of illustration, a 5x10 text file was created; it is located in "...\GUI\Data\cont10.dat" as represented on a PC.. Once you have a suitable text file, launch CAT by typing conallo at the Matlab command prompt. Executing this command, the Introduction Page appears: Figure Introduction to F-18 Example letting you know that CAT is ready to use. To continue click "Press to Begin". This effectively closes the Introduction Page and opens the Data Input Page. As established, the Data Input Page requires the number of controls, and the desired input method. Enter the number of controls by typing "10" in the appropriate box. Select the input method; in the case being considered here we choose "Text File" from the pop-up menu. Select "cont10.dat" from the files displayed in the box that appears. The Data Input Page should now resemble: Figure Data Input Page, F-18 Example

26 Michelle L. Glaze Appendix II: User s Guide and Example 195 To make sure there were no errors made when entering the data file, we click on "View/Edit" which opens the Edit Data Page. This page displays the effectiveness data and control effector position limits provided to you at the beginning of this example. You should notice that the data has a total of 5 rows, and a total of 10 columns; a 5xm matrix with m = 10. After checking the entries displayed, and correcting any errors (in our case there were none) click the "Done" button. Figure Input Data Page, F-18 Example This action closes the Edit Data Page, returning you to the Data Input Page. We want to continue to the Control Allocation Page, so click "Continue". The Control Allocation Page provides several different options for comparing control allocation algorithms. Be aware that the procedure followed here is only one of many possible scenarios. There are two options available to us at this point; we can allocate controls or examine the AMS Comparisons. We decide to allocate controls using direct allocation; select "Direct Allocation" from the pop-up menu displaying "Choose Method". This action opens a window displaying three empty text boxes, one for each desired momnt. Enter the desired moment values in the appropriate text boxes; our set of desired moments was chosen to be (1,1,1), so enter "1" (without quotes) next to each labeled moment box. Performing these actions results in the following representation of the Control Allocation Page:

27 Michelle L. Glaze Appendix II: User s Guide and Example 196 Figure Control Allocation Page, F-18 Example Click on "ALLOCATE CONTROLS" to complete allocation. We repeat the procedure to allocate controls using the pseudo-inverse method. To view the numerical results of the allocation performed, click on the "Options" menu, and select Display Numerical Results. This opens the two Numerical Output Pages; one displaying allocated control effector positions, one displaying the attained moments: Figure Control Positions After Allocation, F-18 Example

28 Michelle L. Glaze Appendix II: User s Guide and Example 197 Figure Moments Attained, F-18 Example To complete the numerical comparison, we want to allocate controls using the pseudo-inverse method. Select "Weighted Pseudo-Inverse" from the pop-up menu. The desired moments do not change, but the "ALLOCATE CONTROLS" button now says "ENTER WEIGHTING MATRIX" as illustrated below: Figure Control Allocation Page w/ Weighting Matrix Option Click on this button to open the Edit Data Page; it displays the default weighting matrix as described in the toolbox tour. It is not necessary to change any entries in the matrix, so click "Done" to close the window and return to the Control Allocation Page. Once there, click "ALLOCATE CONTROLS". Executing this command effectively allocates controls and updates the Numerical Output Pages with the results obtained:

29 Michelle L. Glaze Appendix II: User s Guide and Example 198 Figure Final Comparison of Control Positions Figure Final Comparison of Attained Moments Having obtained all the numerical comparison data, it now remains to examine the AMS Comparison Pages. Only three of the four comparisons will be presented here in the interest of saving trees. The first comparison of interest is direct allocation vs. pseudo-inverse allocation; select "Direct/Pseudo" from the "AMS Comparisons" menu. The comparison that appears is similar to that presented by Figure 19.

30 Michelle L. Glaze Appendix II: User s Guide and Example 199 Figure Direct/Pseudo Comparison Page To illustrate the moment plotting capability of the toolbox, Figure 20 shows the facet-defining moments (i.e., those that define the facets) of the pseudo-inverse AMS plotted inside the "optimal" AMS. To obtain this figure, select "Plot Moments" from the "Options" pull-down menu. From the resulting submenus, choose "Facet-defining","Pseudo-Inverse". Figure Direct/Pseudo Comparison Page w/ Moments Plotted

31 Michelle L. Glaze Appendix II: User s Guide and Example 200 A similar comparison can be plotted for the direct/weighted pseudo case by repeating the procedure just outlined. We next want to view the overall comparison of the three methods evaluated thus far: direct allocation, pseudo-inverse allocation, and weighted pseudo-inverse allocation. To accomplish this, select "All Methods" from the "AMS Comparisons" menu. A window resembling Figure 21 should appear on you screen: Figure 21-- All Methods Comparison Page for F-18 Example The final AMS comparison of interest in this example is that comparing direct allocation with some general method. The general method of choice in this instance is a daisy chaining allocation algorithm. This particular method allows partitioning of the controls (and the B matrix) into two groups; u 1 consists of controls that may used at all times during a maneuver, u 2 contains controls which are only used when those in u 1 fail to generate the desired moments. In an offline implementation of this algorithm the controls were divided such that u 1 contained the more conventional controls (i.e., horizontal tails, ailerons, and rudders), and u 2 contained the remaining controls (i.e., trailing edge flaps and thrust vectoring vanes). Auger input was applied to the F-18 HARV aircraft under the prescribed

32 Michelle L. Glaze Appendix II: User s Guide and Example 201 conditions, providing a set of 502 points (i.e. moments). This information was saved as a 502x3 text file ("...\GUI\Data\daisy1.dat") as described in the toolbox tour. Having obtained a valid text file from an offline implementation, we proceed to plot the direct vs. general method comparison. Select "Direct/General" from the "AMS Comparisons" menu. When prompted select the data file presented above in italics. After computing the convex hull of the set of points, the results are plotted as: Figure 22-- Direct/General Comparison Page for F-18 Example Similar to the other comparison pages, the viewpoint of the resulting plot can be changed. The main difference rests in the fact that only the facet-defining moments can be plotted for the general solution. The toolbox does not directly implement the method, and as a result cannot compute the attained moments. Some Conclusions From the results presented, both graphical and numerical, you should be able to make an educated decision about which method is "best". From the graphical standpoint, daisy chaining produced an AMS with a significantly larger volume than either pseudo- or weighted pseudo-inverse allocation, although direct allocation provided the "optimal" solution. Looking at the numerical results, direct

33 Michelle L. Glaze Appendix II: User s Guide and Example 202 allocation once again appears to be the "best" allocation method available since it attains the largest moment with absolutely no effector saturation. But is direct allocation really the "best" solution? If not, which method is? These are two very important questions that need to be addressed during your evaluation of the CAT results. There are many other factors that contribute to the overall design of a control allocation system, e.g., computational time in highly aggrevated maneuvers, overall expense of the system, other design parameters (i.e., control prioritization, control rate limiting). These factors need to be weighed against the results otained using CAT since each provides a piece of the overall puzzle. REMEMBER!! CAT is simply a design tool that seeks to provide the designer with the numerical information necessary to compare allocation algorithms; hence allowing the designer to make his/her own decision as to which allocation method is best.

34 Michelle L. Glaze Appendix II: User s Guide and Example 203 GENERAL USER INFORMATION This section provides details about certain aspects of the toolbox that you, as the user, are not generally aware of. In doing so, it seeks to provide helpful hints to the user who actually reads this section of the documentation. Path Definition The instant you "Press to Begin" on the Introduction Page, CAT determines the base Matlab path for your particular environment. The search methods vary slightly depending on the platform being used, but the basic descriptions presented below should be sufficient. For the PC and Macintosh PPC, CAT determines the overall Matlab path and from it searches for the first instance of any of the following strings: "matlab", "matlab5", "Matlab", "Matlab5", "MATLAB", or "MATLAB5". When it finds a match, it sets the base Matlab path for the toolbox equal to the string that ends with one of the above. For example, on a PC the base path may be dscribed by "c:\matlab5 or "c:\matlab", etc. On UNIX workstations, things are a little less complicated as long as the path has been appended as described in the Installation section of this guide. In this case, CAT determines the overall Matlab path and searches for the first instance of the string "GUI" (the folder downloaded from the web). When it finds a match, it sets the base path to the string prior to, but excluding the "GUI". For example, say you appended the path as described during installation such that the first entry in the overall Matlab path is similar to "/usr/people/yourname/gui". CAT sets "usr/people/yourname" as the base path. Should you have problems running CAT, you may want to consider re-installing the software as described in the Introduction section. If that does not solve the problem, make sure that the folder containing your Matlab software is labeled with one of the strings above, and that the folder downloaded from the web is still named GUI. If that test fails, you may want to consider editting the M- file that performs the searches described above, directry.m, although you may cause more problems by doing so. Loading/Saving Files The default path for any input data (i.e., effectiveness/position limits, general allocation vertex list) is "...GUI/Data" as represented in UNIX. The default path for any printed output (i.e., printed