MPC for state space model with constant term

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aurochs 2021-12-17

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编辑： aurochs 2021-12-17

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I want to design an MPC for a plant with state space model that includes constant term f:

Following suggestions from other answers (Discussion 1, Discussion 2), I tried several methods:

Include unmeasured input disturbance of random step-like model with magnitude f

A = [0 1;-2.4e3 -528];
B = [0 0 0;0.0004 0 -1];
C = eye(3);
D = zeros(2,3);
f = 42.6506;
Ts = 0.2;
plant = ss(A,B,C,D,Ts);
p = 5;
m = p;
mpcobj = mpc(plant,Ts,p,m);
setindist(mpcobj,'model',tf(f,[1 0]));

2. Include an offset of f/B to the MPC's control signal before the plant

A = [0 1;-2.4e3 -528];
B = [0 0;0.0004 0];
C = eye(2);
D = zeros(2,2);
f = 42.6506;
Ts = 0.2;
Offset_time=[0:Ts:30 f/B(2,1) 0];
plant = ss(A,B,C,D,Ts);
p = 5;
m = p;
mpcobj = mpc(plant,Ts,p,m);