setestim (Model Predictive Control Toolbox™)

Model Predictive Control Toolbox™

setestim

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Modify MPC object's linear state estimator

Syntax

setestim(MPCobj,M)
setestim(MPCobj,'default')

Description

The setestim function modifies the linear estimator gain of an MPC object. The state estimator is based on the linear model (see State Estimation)

where v(k) are the measured disturbances, u(k) are the manipulated plant inputs, y_m(k) are the measured plant outputs, and x(k) is the overall state vector collecting states of plant, unmeasured disturbance, and measurement noise models. The order of the states in x is the following: plant states; disturbance models states; noise model states.

setestim(MPCobj,M), where MPCobj is an MPC object, changes the default Kalman estimator gain stored in MPCobj to that specified by matrix M.

setestim(MPCobj,'default') restores the default Kalman gain.

The estimator used in Model Predictive Control Toolbox™ software is described in State Estimation. The estimator's equations are as follows.

Predicted Output Computation:

Measurement Update:

Time Update:

By combining these three equations, the overall state observer is

where L=AM.

Note The estimator gain M has the same meaning as the gain M in function DKALMAN in Control System Toolbox™ software.

Matrices A, B_u, B_v, C_m, D_vm can be retrieved using getestim as follows:

```
[M,A,Cm,Bu,Bv,Dvm]=getestim(MPCobj)
```

As an alternative, they can be retrieved from the internal structure MPCobj.MPCData.MPCstruct under the fields A,Bu,Bv,Cm,Dvm (see getmpcdata).

Examples

To design an estimator by pole placement, you can use the commands assuming that the linear system AM=L is solvable.

[M,A,Cm]=getestim(MPCobj);
L=place(A',Cm',observer_poles)';
M=A\L;
setestim(MPCobj,M);

Note The pair (A,C_m) describing the overall state-space realization of the combination of plant and disturbance models must be observable for the state estimation design to succeed. Observability is checked in Model Predictive Control Toolbox software at two levels: (1) observability of the plant model is checked at construction of the MPC object, provided that the model of the plant is given in state-space form; (2) observability of the overall extended model is checked at initialization of the MPC object, after all models have been converted to discrete-time, delay-free, state-space form and combined together (see the note on page 2-12).

See Also

getestim, mpc, mpcstate

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