getestim :: Functions (Model Predictive Control Toolbox™)

getestim

Purpose

Model and gain for observer design

Syntax

M=getestim(MPCobj)
[M,A,Cm]=getestim(MPCobj)
[M,A,Cm,Bu,Bv,Dvm]=getestim(MPCobj)
[M,model,Index]=getestim(MPCobj,'sys')

Description

M=getestim(MPCobj) extracts the estimator gain M used by the MPC controller MPCobj for observer design. The observer is based on the models specified in MPCobj.Model.Plant, in MPCobj.Model.Disturbance, by the output disturbance model (default is integrated white noise, see Output Disturbance Model), and by MPCobj.Model.Noise.

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

Predicted Output Computation:

Measurement Update:

Time Update:

By combining these three equations, the overall state observer is

where L=AM.

[M,A,Cm]=getestim(MPCobj) also returns matrices A,C_m used for observer design. This includes plant model, disturbance model, noise model, offsets. The extended state is

plant states; disturbance models states; noise model states]

[M,A,Cm,Bu,Bv,Dvm]=getestim(MPCobj) retrieves the whole linear system used for observer design.

[M,model,Index]=getestim(MPCobj,'sys') retrieves the overall model used for observer design (specified in the Model field of the MPC object) as an LTI state-space object, and optionally a structure Index summarizing I/O signal types.

The extended input vector of model model is

Model model has an extra measured disturbance input v=1 used for handling possible nonequilibrium nominal values (see Offsets).

Input, output, and state names and input/output groups are defined for model model.

The structure Index has the fields detailed in the following table

Field Name
Description

ManipulatedVariables
Indices of manipulated variables within input vector

MeasuredDisturbances
Indices of measured disturbances within input vector (not including offset=1)

Offset
Index of offset=1

WhiteNoise
Indices of white noise signals within input vector

MeasuredOutputs
Indices of measured outputs within output vector

UnmeasuredOutputs
Indices of unmeasured outputs within output vector

.

Field Name	Description
`ManipulatedVariables`	Indices of manipulated variables within input vector
`MeasuredDisturbances`	Indices of measured disturbances within input vector (not including offset=1)
`Offset`	Index of offset=1
`WhiteNoise`	Indices of white noise signals within input vector
`MeasuredOutputs`	Indices of measured outputs within output vector
`UnmeasuredOutputs`	Indices of unmeasured outputs within output vector

The model returned by getestim does not include the additional white noise added on manipulated variables and measured disturbances to ease the solvability of the Kalman filter design, as described in Equation 2-6 on page 2-11.

Purpose

Syntax

Description

See Also

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