How to apply step disturbance on one output at specific time in MPC?

I want to apply a step change of 70 in set point of one CV at minute 200 and a step disturbance of -70 at minute 600 on the same controlled variable (output) and use a MPC controller. I have 10 CVs (outputs) and 7 MVs (inputs). I have transfer function for each MV-CV set. I specified my transfer fucntions and converted them to state space and then used mpc functon in MATLAB and set the signals specifying the disturance as unmesured disturbance in mpc:

D = tf( 70, [1 0], 'IOdelay', (0),'TimeUnit','min');

DT = ss([D; 0; 0; 0; 0; 0;0;0;0;0;0;0]);

%from continous to discrete

SYS = c2d([sys1 DT],1);

Ts=1;

Pr = 240;

Tfinal =1000;

mpc1 = mpc(SYS, Ts);

How can I apply a step change (of 70) in set point of CV #1 in my system at minute 200 and another step disturbance(of -70) at minute 600?

Any help is apperciated!

Answer 1

[Sam Chak]

Hi @HN

I believe your algorithmic-based MPC can automatically handle the step change at 200 minutes, thanks to its built-in self-recovery prediction/correction mechanism at each time step, until the steady-state error is eliminated.

Have you attempted injecting step changes into the MPC-controlled system using the sim(mpcobj, numSimSteps, r, d) command? Here is a simple example demonstrated in minutes; you can convert it to seconds.

Ts          = 0.2;      % sampling time
Tstop       = 1000;     % minutes
numSimSteps = round(Tstop/Ts);

t = linspace(0, Tstop, numSimSteps);

rValue      = 70;       % reference value
rStartTime  = 200;      % minutes
rStartStep  = rStartTime*numSimSteps/Tstop;
r = [zeros(rStartStep, 1); rValue*ones(numSimSteps-rStartStep, 1)];

dValue      = -70;      % disturbance value
dStartTime  = 600;      % minutes
dStartStep  = dStartTime*numSimSteps/Tstop;
d = [zeros(dStartStep, 1); dValue*ones(numSimSteps-dStartStep, 1)];

subplot(211), plot(t, r), grid on, title('Reference signal')
subplot(212), plot(t, d), grid on, title('Disturbance signal'), xlabel('Time (minutes)')