cp9_1.m

离散控制系统设计的MATLAB 代码

%%%%%%%%%%% Comprehensive Problem 9.1 %%%%%%%%%%%
%   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('CP9.1: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

Ts = 0.02;                    % (50Hz) in dbbeam already
disp('Loaded dbbeam')
disp('*******>'); pause; disp(' ')

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% Part B : Inner (motor) loop - Close Loop using 
%          proportional gain controller
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% Response to step input of magnitude 0.1 rad
disp('Design of servo control loop using lag controller')
disp('and closed-loop system response to unit step input of ')
disp('wheel angle command.')
disp(' ')

Kp1 = 5;
Gm_OL = Gz*Kp1;               % Open Loop (servo motor)
Gm_CL = feedback(Gm_OL,1,1,2);
Gbw = d2c(Gm_CL,'tustin')     % bilinear transform
disp('*****>'), pause
figure, bode(Gbw(1,1)),grid        % phase goes below -180 deg because of the bilinear transform
title('Bode plot of Ball position with servo control loop closed')
disp('Plotting frequency response of ball position')
disp('*****>'), pause

figure, margin(Gbw(1,1))
title('Margin plot of Ball position with servo control loop closed')
disp('Plotting margins of ball position loop')
disp('*****>'), pause

% unity gain feedback system
Gbw_CL = feedback(Gbw(1,1),1,1,1);
figure, step(Gbw_CL,'o'),grid
title('Step response of ball position with unity feedback')
disp('Plotting step response of ball position with unity feedback')
disp('*****>'), pause

% find gain and phase of Gbw_CL at 1 rad/s
[mag1,ph1] = bode(Gbw(1,1),1)

des_pm = 55;
del_pm = des_pm - (180 + ph1);
Alead = (1+sin(del_pm*pi/180))/(1-sin(del_pm*pi/180)) % Eq (9.21)
wwc = 1;                      % desired gain crossover frequency
Zlead = -wwc/sqrt(Alead)      % compute zero
Kbw1 = tf(Alead*[1  -Zlead],[1  -Alead*Zlead])  % 1 section of lead
[magKbw1,phKbw1] = bode(Kbw1,1)
Kbw = (1/mag1)/magKbw1*Kbw1;
figure, bode(Gbw_CL*Kbw),grid
title('bode plot of ball position with lead controller')
disp('Plotting frequency response of ball position with lead controller')
disp('*****>'), pause

figure, margin(Gbw_CL*Kbw),grid
title('Margin plot of ball position with lead controller')
disp('Plotting margins of ball position with lead controller')
disp('*****>'), pause

Gbw_CL_final = feedback(Gbw*Kbw,1,1,1)
figure, step(Gbw_CL_final,'o'),grid
title('Step response of ball position with lead controller')
disp('Plotting step response of ball position with lead controller')

% Done
disp('End of Comprehensive Problem CP9.1')
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