ME2142/ME2142E Feedback Control Systems

Transcription

1 ME2142/ME2142E Feedback Control Systems Installing OCTAVE in WINDOWS And Using OCTAVE for Control Systems Analysis August 2013 Department of Mechanical Engineering National University of Singapore

2 1. Introduction to GNU Octave GNU Octave ( is a high-level language mostly compatible with MATLAB ( It is primarily intended for numerical computations, for solving common numerical linear algebra problems, manipulating polynomials, and integrating ordinary differential and differential-algebraic equations. It also has facilities for displaying the results of computation in various forms of graphs which makes it really nice. The really nice thing about GNU Octave is that it is a freely redistributable software. You may redistribute it and/or modify it under the terms of the GNU General Public License (GPL as published by the Free Software Foundation ( On-line documentation on the usage of Octave can be found at 2. OCTAVE for Control Systems Study Similar to MATLAB, OCTAVE also has extensive tools for various functions including a control systems toolbox and it is these that we will primarily be interested in in this first introductory course on control systems. 3. Downloading, Installing and Using OCTAVE For those using Windows, do the following to install a copy of Octave 3.2.4: 1. Download, either from IVLE or from the module website the installer file Octave 3.2.4_i686 pc mingw32_gcc 4.4.0_setup.zip into a folder in your local disk drive. Downloading could take a few to tens of minutes depending upon your connection speed. Once downloading is completed, unzip and run the installer. 2. During installation, click next at the following two screens 2

3 3. Choose a folder for the Octave installation files and click Next in the following screen. 3

4 4. In the next screen, scroll down to, and select, the toolbox control. Then click Next. 5. Select a Start Menu Folder, or just use the default given, and click Next in the next screen shown below. Wait till installation is complete and then click Finish. 6. Test that the installation is running properly by launching OCTAVE START>All Programs>GNU Octave 3.2.4>Octave to open an Octave window. Note that you can also view Octave documentations. 4

5 7. In the Octave window, at the command line, type (underlined below) Octave exe:1> sys=tf(1,[1,2,4]); Octave exe:2> step(sys); The figure below, which was copied to clipboard and pasted here, should then appear of a step response for an underdamped 2nd-order system. 8. Congratulations, you have successfully installed Octave Version with the Control Toolbox. Note that there are many other toolboxes that you can install depending upon your needs. 9. There are a few demonstration programs for control systems study in the Octave suite. To get to these, type controldemo at the Octave prompt and the list of demonstration programs will be shown for selection: 4 Some Notes on Using Octave 4.1 Control System Specification: The control system under study can be specified in several ways. (a) By using vectors to represent the coefficients of the numerator and denominator polynomials of the closed-loop transfer function. For example, to specify the system with the closed-loop transfer function The following commands can be used: Octave exe:3> num=[1 3]; Octave exe:4> den=[1 2 4]; Octave exe:5> sys1=tf(num,den); or, alternatively, the following: Octave exe:6> sys2=tf([1 3],[1 2 4]); in which [1 3] specifies the polynomial. and [1 2 4] specifies the polynomial 5

6 To display the data structure of the system, the sysout command can be used as: Octave exe:7> sysout(sys1); Octave exe:8> sysout(sys2); (b) By using vectors to specify the zeros and poles of the closed-loop system: For example, to define the system with the closed-loop transfer function we can use the commands: octave exe:9> num=[-3]; octave exe:10> den=[0-2 -6]; octave exe:11> k=5; octave exe:12> sys3=zp(num,den,k); or,alternatively, the following: octave exe:13> sys4=zp([-3],[0-2 -6],5); To display the data structure of the system, the sysout command can be used as: octave exe:14> sysout(sys3); octave exe:15> sysout(sys4); 4.2 Transient Responses: The unit impulse response and the unit step response of a system can be easily obtained by using the impulse function and the step function respectively. These functions produce a plot of the transient response. For example: octave exe:16> impulse(sys1); octave exe:17> step(sys4); 4.3 Root Locus Plots: Root locus plots can easily be obtained using the function rlocus(sys,[inc, min_k, max_k]), or where sys is the open-loop transfer for which the root locus plot is desired, inc is the increment in the gain parameter, and min_k and max_k are the minimum and maximum values of the gain parameter for the plot. For example, if the root locus plot is desired of the system named sys4 specified in Section 4.1 above, the following command can be used: octave exe:18> rlocus(sys4); octave exe:19> rlocus(sys4,0.02,0,5); 6