cp5_4.m

离散控制系统设计的MATLAB 代码

%%%%%%%%%%% Comprehensive Problem 5.4 %%%%%%%%%%%
%   Discrete-Time Control Problems using        %
%       MATLAB and the Control System Toolbox   %
%   by J.H. Chow, D.K. Frederick, & N.W. Chbat  %
%         Brooks/Cole Publishing Company        %
%                September 2002                 %
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% Ball and Beam System              
% System has 4 states, 1 input, and 2 outputs
% 4 states : ball's position and velocity, and
%            wheel's angular position and velocity
% 1 input  : motor voltage (u)
% 2 output : ball's position (xi), and 
%            wheel's angular position (theta)

disp('CP5.4: Ball and Beam')

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% Part A : Load model
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clear; close all

% Load continuous and discrete-time systems
if ~exist('bbeam.mat'), 
    dbbeam
elseif exist('bbeam.mat') == 2,
    load bbeam 
end

disp('Continuous-time System Gs is (in dbbeam):')
Gs
disp('*******>');pause

disp('Continuous-time system poles')
pole(Gs)
disp('*******>');pause

disp('Zeros from wheel angle output')
tzero(Gs(2,1))
disp('Zeros from ball position output')
tzero(Gs(1,1))
disp('*******>');pause

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% Part B : Sampling at 50Hz
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

disp('Sampling at 50 Hz :')
fs = 50;   % sampling at 50 Hz 
Ts = 1/fs;
Gz50 = c2d(Gs,Ts,'zoh');
[Ad50,Bd50,Cd50,Dd50] = ssdata(Gz50);
disp('Matrices A and B of the DT model sampled at 50 Hz are:')
format short e
Ad50, Bd50
format
disp('Note that all the upper diagonal entries of Ad are nonzero')
disp('*******>'); pause;
disp('Poles of Gz50:'); pole(Gz50)
disp('Similar to Ad and Bd in dbbeam')
disp('Related to continuous system poles p by exp(p*Ts)')
disp('*******>'); pause;
disp('Zeros from wheel angle output')
tzero(Gz50(2,1))
disp('Zeros from ball position output')
tzero(Gz50(1,1))
disp('The relationship between the zeros of the continuous time ')
disp('and discrete time zeros is quite involved and cannot be ')
disp('obtained by inspection.')
disp('*******>');pause

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% Part C : Sampling at 25Hz
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
disp('Sampling at 25 Hz :')
fs = 25;   % sampling at 25 Hz 
Ts = 1/fs;
Gz25 = c2d(Gs,Ts,'zoh');
[Ad25,Bd25,Cd25,Dd25] = ssdata(Gz25);
disp('Matrices A and B of the DT model sampled at 25 Hz are:')
Ad25, Bd25
disp('Poles of Gz25:'); pole(Gz25)
disp('Note the poles not at z = 1 have smaller magnitude when')
disp('the system is sampled slower.')
disp('*******>');pause; 
disp('Zeros from wheel angle output')
tzero(Gz25(2,1))
disp('Zeros from ball position output')
tzero(Gz25(1,1))
disp('*******>');pause

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% Part D : Sampling at 100Hz
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
disp('Sampling at 100 Hz :')
fs = 100;   % sampling at 100 Hz 
Ts = 1/fs;
Gz100 = c2d(Gs,Ts,'zoh');
[Ad100,Bd100,Cd100,Dd100] = ssdata(Gz100);
disp('Matrices A and B of the DT model sampled at 100 Hz are:')
Ad100, Bd100
disp('Poles of Gz100:'); pole(Gz100)
disp('Note the poles not at z = 1 have larger magnitude when')
disp('the system is sampled faster.')
disp('*******>');pause; 
disp('Zeros from wheel angle output')
tzero(Gz100(2,1))
disp('Zeros from ball position output')
tzero(Gz100(1,1))
disp('*******>');pause; disp(' ');

disp('End of Comprehensive Problem CP5.4')
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