cp10_3.m

离散控制系统设计的MATLAB 代码

%%%%%%%%%%% Comprehensive Problem 10.3 %%%%%%%%%%
%   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                 %
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% Electric Power Generation System

clear all, close all
disp('Comprehensive Problem CP10.3')

dpower2          % load power system model with extra damping
disp('*****>'), pause

disp('Power system model state matrices, with Vterminal, ')
disp('  w(speed), and P(power) as output')
disp('Continuous-time model')
Gs
disp('*****>'), pause

disp('discretized model with a sampling period of 0.01 s')
Ts = 0.01
Gz = c2d(Gs,Ts) 
disp('Note that most of the zero entries of the A & B matrices')
disp('  of the continuous time model have become nonzero in the')
disp('  discrete time models. The C & D matrcies are unchanged.')
disp('*****>'), pause

disp('System model with Vterminal as the only output')
Gv = Gz(1,1)
disp('*****>'), pause

% extract system matrices
[Ad,Bd,Cd,Dd] = ssdata(Gv);

% find eigenvalues
disp('Open-loop system poles')
lam = eig(Ad);
xy2p(lam);
disp('*****>'), pause

% assign full state feedback eigenvalues
lams = lam;
lams(7) = 0.98;   % shift 0.9989 mode to 0.98

disp('assign full-state-feedback eigenvalues at ')
xy2p(lams);
disp('*****>'), pause

disp('full-state-feedback gain') 
K = place(Ad,Bd,lams)
disp('*****>'), pause

% assign observer eigenvalues
lamo = lam;
lamo(7) = 0.96;

disp('assign observer eigenvalues at ')
xy2p(lamo);
disp('*****>'), pause

disp('observer gain')
L = place(Ad',Cd',lamo);
L = L'

disp('*****>');pause
A_f = Ad-Bd*K-L*Cd;                  % controller system matrix
f_poles = eig(A_f);                  % controller poles
disp('Controller poles')
xy2p(f_poles);
disp('Controller zeros')
f_zeros = tzero(A_f,-L,-K,0);        % controller zeros
xy2p(f_zeros);

disp('*****>');pause
Gc = ss(A_f,-L,-K,0,Ts);
ww = logspace(-1,2,100);
figure, bode(Gc,ww), grid            % frequency response plot
title('CP10.3: Frequency response of controller') 
disp('Plotting controller frequency response')
disp('*****>');pause
%
GK = Gv*Gc;
figure, margin(GK)
disp('Plotting gain and phase margins of the compensated system')
disp('*****>');pause
%
Gcl = feedback(GK,1);                % closed-loop system
disp('closed-loop system poles')
xy2p(pole(Gcl));                     % closed-loop system poles
disp('*****>');pause
figure, [y,t] = step(Gcl,6);
plot(t,0.05*y,'o')
xlabel('Time (s)')
ylabel('Amplitude')
grid;title('CP10.3: Step response of closed loop system')
%
disp('end of Comprehensive Example 10.3')
%%%%%%%%%%