Modify unmeasured input disturbance model

`setindist(`

sets
the input disturbance model to its default value. Use this syntax
if you previously set a custom input disturbance model and you want
to change back to the default model. For more information on the default
input disturbance model, see MPC Modeling.`MPCobj`

,'integrators')

Define a plant model with no direct feedthrough.

plant = rss(3,4,4); plant.d = 0;

Set the first input signal as a manipulated variable and the remaining inputs as input disturbances.

plant = setmpcsignals(plant,'MV',1,'UD',[2 3 4]);

Create an MPC controller for the defined plant.

MPCobj = mpc(plant,0.1);

-->The "PredictionHorizon" property of "mpc" object is empty. Trying PredictionHorizon = 10. -->The "ControlHorizon" property of the "mpc" object is empty. Assuming 2. -->The "Weights.ManipulatedVariables" property of "mpc" object is empty. Assuming default 0.00000. -->The "Weights.ManipulatedVariablesRate" property of "mpc" object is empty. Assuming default 0.10000. -->The "Weights.OutputVariables" property of "mpc" object is empty. Assuming default 1.00000. for output(s) y1 and zero weight for output(s) y2 y3 y4

Define disturbance models such that:

Input disturbance 1 is random white noise with a magnitude of

`2`

.Input disturbance 2 is random step-like noise with a magnitude of

`0.5`

.Input disturbance 3 is random ramp-like noise with a magnitude of

`1`

.

mod1 = tf(2,1); mod2 = tf(0.5,[1 0]); mod3 = tf(1,[1 0 0]);

Construct the input disturbance model using the above transfer functions. Use a separate noise input for each input disturbance.

indist = [mod1 0 0; 0 mod2 0; 0 0 mod3];

Set the input disturbance model in the MPC controller.

```
setindist(MPCobj,'model',indist)
```

View the conroller output disturbance model.

getindist(MPCobj)

ans = a = x1 x2 x3 x1 1 0 0 x2 0 1 0 x3 0 0.1 1 b = Noise#1 Noise#2 Noise#3 x1 0 0.05 0 x2 0 0 0.1 x3 0 0 0.005 c = x1 x2 x3 UD1 0 0 0 UD2 1 0 0 UD3 0 0 1 d = Noise#1 Noise#2 Noise#3 UD1 2 0 0 UD2 0 0 0 UD3 0 0 0 Sample time: 0.1 seconds Discrete-time state-space model.

The controller converts the continuous-time transfer function model, `indist`

, into a discrete-time state-space model.

Define a plant model with no direct feedthrough.

plant = rss(3,4,4); plant.d = 0;

Set the first input signal as a manipulated variable and the remaining inputs as input disturbances.

plant = setmpcsignals(plant,'MV',1,'UD',[2 3 4]);

Create an MPC controller for the defined plant.

MPCobj = mpc(plant,0.1);

-->The "PredictionHorizon" property of "mpc" object is empty. Trying PredictionHorizon = 10. -->The "ControlHorizon" property of the "mpc" object is empty. Assuming 2. -->The "Weights.ManipulatedVariables" property of "mpc" object is empty. Assuming default 0.00000. -->The "Weights.ManipulatedVariablesRate" property of "mpc" object is empty. Assuming default 0.10000. -->The "Weights.OutputVariables" property of "mpc" object is empty. Assuming default 1.00000. for output(s) y1 and zero weight for output(s) y2 y3 y4

Retrieve the default input disturbance model from the controller.

distMod = getindist(MPCobj);

-->Converting model to discrete time. -->The "Model.Disturbance" property of "mpc" object is empty: Assuming unmeasured input disturbance #2 is integrated white noise. Assuming unmeasured input disturbance #3 is integrated white noise. Assuming unmeasured input disturbance #4 is integrated white noise. -->Assuming output disturbance added to measured output channel #1 is integrated white noise. Assuming no disturbance added to measured output channel #2. Assuming no disturbance added to measured output channel #3. Assuming no disturbance added to measured output channel #4. -->The "Model.Noise" property of the "mpc" object is empty. Assuming white noise on each measured output channel.

Remove the integrator from the second input disturbance. Construct the new input disturbance model by removing the second input channel and setting the effect on the second output by the other two inputs to zero.

```
distMod = sminreal([distMod(1,1) distMod(1,3); 0 0; distMod(3,1) distMod(3,3)]);
setindist(MPCobj,'model',distMod)
```

When removing an integrator from the input disturbance model in this way, use `sminreal`

to make the custom model structurally minimal.

View the input disturbance model.

tf(getindist(MPCobj))

ans = From input "UD1-wn" to output... 0.1 UD1: ----- z - 1 UD2: 0 UD3: 0 From input "UD3-wn" to output... UD1: 0 UD2: 0 0.1 UD3: ----- z - 1 Sample time: 0.1 seconds Discrete-time transfer function.

The integrator has been removed from the second channel. The first and third channels of the input disturbance model remain at their default values as discrete-time integrators.

Define a plant model with no direct feedthrough.

plant = rss(2,2,3); plant.d = 0;

Set the second and third input signals as input disturbances.

plant = setmpcsignals(plant,'MV',1,'UD',[2 3]);

Create an MPC controller for the defined plant.

MPCobj = mpc(plant,0.1);

-->The "PredictionHorizon" property of "mpc" object is empty. Trying PredictionHorizon = 10. -->The "ControlHorizon" property of the "mpc" object is empty. Assuming 2. -->The "Weights.ManipulatedVariables" property of "mpc" object is empty. Assuming default 0.00000. -->The "Weights.ManipulatedVariablesRate" property of "mpc" object is empty. Assuming default 0.10000. -->The "Weights.OutputVariables" property of "mpc" object is empty. Assuming default 1.00000. for output(s) y1 and zero weight for output(s) y2

Set the input disturbance model to unity gain for both channels.

```
setindist(MPCobj,'model',tf(eye(2)))
```

Restore the default input disturbance model.

```
setindist(MPCobj,'integrators')
```

`MPCobj`

— Model predictive controllerMPC controller objectModel predictive controller, specified as an MPC controller
object. To create an MPC controller, use the `mpc`

command.

`model`

— Custom input disturbance model`[]`

(default) | `ss`

object | `tf`

object | `zpk`

objectCustom input disturbance model, specified as a state-space (`ss`

), transfer function (`tf`

), or zero-pole-gain (`zpk`

) model. The MPC controller converts
the model to a discrete-time, delay-free, state-space model. Omitting `model`

or
specifying `model`

as `[]`

is
equivalent to using `setindist(MPCobj,'integrators')`

.

The input disturbance model has:

Unit-variance white noise input signals. For custom input disturbance models, the number of inputs is your choice.

*n*outputs, where_{d}*n*is the number of unmeasured disturbance inputs defined in_{d}`MPCobj.Model.Plant`

. Each disturbance model output is sent to the corresponding plant unmeasured disturbance input.

This model, in combination with the output disturbance model (if any), governs how well the controller compensates for unmeasured disturbances and prediction errors. For more information on the disturbance modeling in MPC and about the model used during state estimation, see MPC Modeling and Controller State Estimation.

`setindist`

does not check custom input disturbance
models for violations of state observability. This check is performed
later in the MPC design process when the internal state estimator
is constructed using commands such as `sim`

or `mpcmove`

. If the controller states are not
fully observable, these commands generate an error.

This syntax is equivalent to ```
MPCobj.Model.Disturbance
= model
```

.

`getEstimator`

| `getoutdist`

| `mpc`

| `setEstimator`

| `setindist`

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