cp8_1.m

离散控制系统设计的MATLAB 代码

%%%%%%%%%%% Comprehensive Problem 8.1 %%%%%%%%%%%
%   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('CP8.1:Ball and Beam')

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% Part A : Load model
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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) Closed_Loop - Response to
% 0.1(rad) Step Input 
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% Response to step input of magnitude 0.1 rad
disp('Design of servo control loop using root-locus technique')
disp('and closed-loop system response to unit step input of ')
disp('wheel angle command.')
disp('Select a gain for 0.9 damping ratio using the root-locus plot.')
disp(' ')

figure, ucircle, hold on
rlocus(Gz(2,1)), hold off
zgrid
axis([-1 1 -1 1])
[Kp1,ppm] = rlocfind(Gz(2,1));
disp(['Kp1 = ', num2str(Kp1)])
xy2p(ppm);

disp('For a damping ratio of 0.9, Kp1 is found to be about 5.')
disp('*******>'), pause

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% Part C : Inner (motor) Closed_Loop - Response to
% 0.1(m) Step Input - Kpm = 5 with outer loop closed
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% Response to step input of magnitude 0.1 m
disp('Design of ball position control loop using gain sweep')
disp('and closed-loop response to step position command 0.1m.')
disp('Select Kp using root-locus plots for 0.5 damping ratio')
disp('for values of Kd from 0.8 to 2.')
disp(' ')

Kp1 = 5;
Gm_OL = Gz*Kp1;                     % Open Loop (servo motor)
Gm_CL = feedback(Gm_OL,1,1,2);

Kd = [0.8:0.2:2]';
lenKd = length(Kd);
trb_vec = []; Mob_vec = []; ang_vec = []; Kp2 = [];
figure
for i = 1:lenKd
  Kb = tf([(1+Kd(i)/Ts) -Kd(i)/Ts],[1 0],Ts);
  Gb_OL = Gm_CL*Kb;                 % Open Outer Loop
  rlocus(Gb_OL(1,1))
  zgrid
  axis([0.951 1.01 -0.025 0.025])
  disp('Select Kp using root-locus plots for 0.5 damping ratio')
  [Kp,ppb] = rlocfind(Gb_OL(1,1));
  disp(['Kp = ', num2str(Kp)])
  xy2p(ppb);
  Kp2(i) = Kp;
  Gb_CL = feedback(Gb_OL*Kp,1,1,1); % CLoop
  [yb,dtime] = step(Gb_CL);
  [Mob,tpb,trb,tsb,essb] = kstats(dtime,0.1*yb(:,1),0.1);
  trb_vec(i) = trb;                 % Rise Time of outer (b&b) CL
  Mob_vec(i) = Mob;                 % Max % Overshoot of outer CL
  ang_vec(i) = max(0.1*yb(:,2));
  plot(dtime,0.1*yb(:,1),'o'); grid  
  xlabel('Time (sec)')
  ylabel('Response (m)')
  title(['Kp2=',num2str(Kp2(i)),' Kd=',num2str(Kd(i))])
  drawnow
  disp('Step response for selected poles')
  disp('******>'), pause
  
end
  
disp('     Kd         Kp   rise time (s) wheel angle (rad)')
disp([Kd Kp2' trb_vec' ang_vec'])

% Done
disp('End of Comprehensive Problem CP8.1')
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