PID Controller for a double integrator.

------------------------------------------------------------------------
See also @statespace/statespace.m, FResp, PIDMIMO, Series, TResp,
Plot2D
------------------------------------------------------------------------

Contents

%--------------------------------------------------------------------------
%   Copyright (c) 1994 Princeton Satellite Systems, Inc.
%   All rights reserved.
%--------------------------------------------------------------------------
%   Since version 1.
%--------------------------------------------------------------------------

The plant model-a single axis vehicle with an inertia of 1

aP = [0 1;0 0];
bP = [0;1];
cP = [1 0];
dP = 0;

The frequency range for plotting

w  = logspace(-4,2,200);

The PID controller. The rate filter is automatically set

inr  = 1;
zeta = 2;
wN   = 1;
tauI = 20;
[aC,bC,cC,dC] = PIDMIMO(inr,zeta,wN,tauI);
FResp(aC,bC,cC,dC,1,1,w);

Close the loop the plant and controller are in the forward path

[a,b,c,d] = Series(aP,bP,cP,dP,aC,bC,cC,dC);

% Closed loop plant
a = a - b*c;

The output is the angle

c = [1 0 0 0];

% Conput the eigenvalues
e = eig(a);
DispWithTitle(e,'Eigenvalues');

Eigenvalues
           -5
      -3.7321
     -0.26795
        -0.05

Double integrator

[magOL,~]	= FResp(aP,bP,cP,dP,1,1,w);
magOL     = 20*log10(magOL);

Closed loop system

[magCL,~] = FResp(a,b,c,d,1,1,w);
magCL     = 20*log10(magCL);

Plot2D(w,[magOL;magCL],'Frequency (rad/sec)','Magnitude (db)',...
  'Disturbance transmission','xlog',[],[],[],[],[],...
  {{'Open Loop' 'Closed Loop'}})

Step response

g = statespace( a, b, c, d );
TResp( g, [0;0;0;0] );


%--------------------------------------
% $Date$
% $Id: c08a706621a15dd2744004291b782a04a712a81e $

Published with MATLAB® R2021b