Model Predictive Control Toolbox™

Convert unconstrained MPC controller to state-space linear form

Syntax

• sys=ss(MPCobj)
  [sys,Br,Dr,Bv,Dv,Boff,Doff,But,Dut]=ss(MPCobj)
  [sys,Br,Dr,Bv,Dv,Boff,Doff,But,Dut]=ss(MPCobj,ref_preview,
  md_preview,name_flag)
  

Description

The ss utility returns the linear controller sys as an LTI system in ss form corresponding to the MPC controller MPCobj when the constraints are not active. The purpose is to use the linear equivalent control in Control System Toolbox™ software for sensitivity analysis and other linear analysis.

sys=ss(MPCobj) returns the linear discrete-time dynamic controller sys

where ym is the vector of measured outputs of the plant, and u is the vector of manipulated variables. The sampling time of controller sys is MPCobj.Ts.

[sys,Br,Dr,Bv,Dv,Boff,Doff,But,Dut]=ss(MPCobj) returns the linearized MPC controller in its full version, that has the following structure

Note    Vector x includes the states of the observer (plant+disturbance+noise model states) and the previous manipulated variable u(k-1).

In the general case of nonzero offsets, y_m (as well as r, v, u_target) must be interpreted as the difference between the vector and the corresponding offset. Vectors B_off, D_off are constant terms due to nonzero offsets, in particular they are nonzero if and only if MPCobj.Model.Nominal.DX is nonzero (continuous-time prediction models), or MPCobj.Model.Nominal.Dx-MPCobj.Model.Nominal.X is nonzero (discrete-time prediction models). Note that when Nominal.X is an equilibrium state, B_off, D_off are zero.

Only the following fields of MPCobj are used when computing the state-space model: Model, PredictionHorizon, ControlHorizon, Ts, Weights.

[sys,...]=ss(MPCobj,ref_preview,md_preview,name_flag) allows you to specify if the MPC controller has preview actions on the reference and measured disturbance signals. If the flag ref_preview='on', then matrices B_r and D_r multiply the whole reference sequence:

Similarly if the flag md_preview='on', then matrices B_r and D_r multiply the whole measured disturbance sequence:

The optional input argument name_flag='names' adds state, input, and output names to the created LTI object.

Examples

To get the transfer function LTIcon from (y_m,r) to u,

• [sys,Br,Dr]=ss(MPCobj);
  set(sys,'B',[sys.B,Br],'D',[sys.D,Dr]);
  

See Also

mpc, set, tf, zpk

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