PFC controller for stable system

Question

0 个投票

I wrote code for the PFC controller to control a stable system to track to the desired value (in this one) but the system became unstable and I can not understand why the PFC controller was designed to make a stable system unstable. Code I wrote as follows

t0 = 0 ;
tf = 40;
ts = 0.01;
t = t0:ts:tf ;
Am = [0,0,0,0,0,1,0,0,0,0;0,0,0,0,0,0,1,0,0,0;0,0,0,0,0,0,0,1,0,0;0,0,0,0,0,0,0,0,1,0;0,0,0,0,0,0,0,0,0,1;-1967.63005780347,983.815028901734,0,0,0,-16.9768786127168,8.48843930635838,0,0,0;983.815028901734,-1967.63005780347,983.815028901734,0,0,8.48843930635838,-16.9768786127168,8.48843930635838,0,0;0,983.815028901734,-1967.63005780347,983.815028901734,0,0,8.48843930635838,-16.9768786127168,8.48843930635838,0;0,0,983.815028901734,-1967.63005780347,983.815028901734,0,0,8.48843930635838,-16.9768786127168,8.48843930635838;0,0,0,983.815028901734,-983.815028901734,0,0,0,8.48843930635838,-8.48843930635838];
Bm = [0,0,0,0,0;0,0,0,0,0;0,0,0,0,0;0,0,0,0,0;0,0,0,0,0;-0.00289017341040462,0,0,0,0;0,-0.00289017341040462,0,0,0;0,0,-0.00289017341040462,0,0;0,0,0,-0.00289017341040462,0;0,0,0,0,-0.00289017341040462];
Cm = [1,0,0,0,0,0,0,0,0,0;0,1,0,0,0,0,0,0,0,0;0,0,1,0,0,0,0,0,0,0;0,0,0,1,0,0,0,0,0,0;0,0,0,0,1,0,0,0,0,0;0,0,0,0,0,1,0,0,0,0;0,0,0,0,0,0,1,0,0,0;0,0,0,0,0,0,0,1,0,0;0,0,0,0,0,0,0,0,1,0;0,0,0,0,0,0,0,0,0,1]; ;
n = size(Am ,1)  ;  % number of eigenvalues
q = size(Cm , 1) ;  % number of outputs
m = size(Bm , 2) ;  % number of inputs
Np =15 ; % Prediction Horizon
Nc = 10; % Control Horizon
F = zeros(q*Np , size(Am , 1)) ;
for i = 1:Np
    F(q*i-q+1:q*i , :) = Cm * Am^i ;
end
PHI = zeros(q * Np , m*Nc);
for i = 1:Np
    for j = 1:i
        PHI(q*i-q+1:q*i , m*j-m+1:m*j) = Cm * Am^(i-j) * Bm ;
    end
end
PHI = PHI( : , 1:Nc*m) ;
%%  Main Loop
Nt = numel(t) ;
y = zeros(q , Nt)  ;
du = zeros(m , Nt) ;
x = zeros(size(Am , 1) , Nt) ;
R = 1 ;
Fval = zeros(Nt , 1 ) ;
for  i = 1:Nt-1
    FreeResponse = F * x(: , i);
    dU = (PHI'*PHI + R * size(PHI , 2))\(PHI' * (1 - FreeResponse)) ;
    du(: , i) = dU(1:m) ;
    x(: , i+1) = Am * x(: , i) + Bm * du(: ,i) ;
    y(: , i+1) = Cm * x(: , i+1) ;
end

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Sam Chak 2024-6-27

在 MATLAB Online 中打开

If discrete-time system, then the system is unstable to begin with, because all its eigenvalues should stay in the unit circle of the complex-plane.

Am = [0,0,0,0,0,1,0,0,0,0;0,0,0,0,0,0,1,0,0,0;0,0,0,0,0,0,0,1,0,0;0,0,0,0,0,0,0,0,1,0;0,0,0,0,0,0,0,0,0,1;-1967.63005780347,983.815028901734,0,0,0,-16.9768786127168,8.48843930635838,0,0,0;983.815028901734,-1967.63005780347,983.815028901734,0,0,8.48843930635838,-16.9768786127168,8.48843930635838,0,0;0,983.815028901734,-1967.63005780347,983.815028901734,0,0,8.48843930635838,-16.9768786127168,8.48843930635838,0;0,0,983.815028901734,-1967.63005780347,983.815028901734,0,0,8.48843930635838,-16.9768786127168,8.48843930635838;0,0,0,983.815028901734,-983.815028901734,0,0,0,8.48843930635838,-8.48843930635838];
eig(Am)
ans = 
 -15.6294 +58.1260i
 -15.6294 -58.1260i
 -12.0147 +51.3874i
 -12.0147 -51.3874i
  -7.2804 +40.4302i
  -7.2804 -40.4302i
  -2.9297 +25.8945i
  -2.9297 -25.8945i
  -0.3438 + 8.9210i
  -0.3438 - 8.9210i