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Getting Started with Ch Control System Toolkit

To help users to get familiar with Ch Control System Toolkit, a sample program will be used to illustrate basic features and applications of Ch Control System Toolkit.

In this example, the control system shown below

consists of a plant and a feedback controller with transfer functions 3 G(s) = ------ s(s+2) 2 H(s) = --- 3 The closed-loop transfer function of the system is G(s) T(s) = ---------- 1+G(s)H(s) 3 = -------- s^2+2s+2 The step response of the closed-loop system will be plotted in this example.
The code listed below is a Ch program using Ch Control System Toolkit for solving this problem.

#include <control.h> int main() { double num[1] = {3}; double den[3] = {1, 2, 2}; class CPlot plot; class CControl sys; sys.model("tf", num, den); sys.step(&plot, NULL, NULL, NULL); return 0; }

The first line of the program

#include <control.h> includes the header file control.h which defines the class CControl, macros, and prototypes of member functions. Like a C/C++ program, a Ch program will start to execute at the main() function after the program is parsed. The next two lines double num[1] = {3}; double den[3] = {1, 2, 2}; define two arrays num and den to store the coefficients of the numerator and denominator of the polynomials of the transfer function T(s), respectively. Line class CPlot plot; defines a class CPlot for creating and manipulating two and three dimensional plotting. The CPlot class is defined in header file chplot.h which is included in control.h header file. Line class CControl sys; instantiates a CControl class. Line sys.model("tf", num, den); constructs a transfer function model of the system. The type of models created by member function model() is specified by the first argument. For example, string "tf" indicates transfer function model. The second and third arguments specify the coefficients of the numerator and denominator polynomials of the transfer function. Ch Control System Toolkit supports transfer function (TF), zero-pole-gain (ZPK), state-space (SS), and other LTI models. The details of model types supported by Ch Control System Toolkit are described in Ch Control System Toolkit User's Guide. Like C++, the keyword class is optional in Ch. Line sys.step(&plot, NULL, NULL, NULL); computes and plots the step response of the system. Member function step() has four arguments. The first argument is a pointer to an existing object of class CPlot. The other three arguments are arrays of reference containing the output of the step response, time vector, and state trajectories. If the output data are not required, these three arguments can be set to NULL. The step response of the system, when the above program is executed, is shown in the figure below.

As another example, for a control system represted by transfer function

2s^2-3.5s+1.5 T(s) = -------------- s^2-1.5s+0.9 The following program can generate the root locus of the system modeled in discrete form as shown in the plot. #include <control.h> // Ch Control System Toolkit header file int main() { // numerator of the transfer function double num[3] = {2, -3.5, 1.5}; // denominator of the transfer function double den[3] = {1, -1.5, 0.9}; CPlot plot; // plotting class CControl sys; // control class /* build control system in transfer function in discrete model */ sys.model("tf", num, den, -1); sys.zgrid(1); // use z-grid sys.rlocus(&plot, NULL, NULL);// display root locus return 0; }

More application examples in comparison with MATLAB Control System Toolbox can be found here.