Compute steady-state value of MPC controller plant model state for given inputs and outputs
Use the Model Predictive Control Toolbox™
trim function to calculate steady state values of LTI discrete-time
plants controlled by an MPC controller (see
mpc for background).
Here, A,B, C, and
D are the state space realization matrices of the discrete-time plant
model used within
yoff are the nominal values of the extended
state x, input u, and output y
Create a plant, a corresponding MPC object, and calculate the steady state value of the plant model state.
mpcverbosity off; % turn off mpc messaging plant=c2d(ss(zpk(,[-1 -10],20)),1); % create plant (note the steady state gain) mpcobj=mpc(plant,1); % create mpc object x=trim(mpcobj,2,1) % caclulate trim point MPCSTATE object with fields Plant: [0.4000 0.4000] Disturbance: 0 Noise: [1×0 double] LastMove: 1 Covariance: [3×3 double] % check whether the calculated value is actually an equilibrium point mpcobj.Model.Plant.A*x.Plant+mpcobj.Model.Plant.B*1-x.Plant ans = 1.0e-15 * 0.1110 0.0555 mpcobj.Model.Plant.C*x.Plant+mpcobj.Model.Plant.D*1-2 ans = -2.2204e-16
The resulting state value is an equilibrium point because for the given output and input values, the state at the next time step is equal to the current state (except some numerical errors).
y— steady state plant output
MPCobj.Model.Nominal.Y(default) | column vector | scalar
This is the plant output (including both measured and unmeasured signals) for which
you want to find a stationary value of the extended plant state. If the plant has a
finite steady state gain matrix
y is equal
G0*u then the plant has a stationary state with output
y and input
u— steady state plant input
MPCobj.Model.Nominal.U(default) | column vector | scalar
This is the plant input (including manipulated variables, measured disturbances, and
unmeasured disturbances) for which you want to find a stationary value of the extended
plant state. If unmeasured input disturbance variables exist, their value must be
x— steady state extended plant state
This is the best approximation, in a least squares sense, of the steady-state value for the plant state corresponding to the given input and output values.