A system with one feedback input and one measurement:

The feedback input and measurement are inputs to the estimator-regulator:

A system with one noisy input as well:

Noisy inputs are not inputs to the estimator-regulator:

A system with one feedback and one exogenous input:

The exogenous input is an input to the estimator-regulator:

A system where only some of the outputs are measured:

Only the feedback input and measured output are fed to the estimator-regulator:

Compute the gains using pole placement:

Assemble the estimator-regulator:

Compute the gains optimally:

Assemble the estimator-regulator:

Compute the feedback gains optimally:

Use pole placement to compute the estimator gains:

Assemble the estimator-regulator:

A continuous-time StateSpaceModel:

The controller for a set of gains:

The closed-loop system:

Compute it automatically:

The poles of the closed-loop system:

A discrete-time StateSpaceModel:

The controller for a set of gains:

Its closed-loop system:

And poles:

A descriptor StateSpaceModel:

The controller has the same descriptor matrix:

Its closed-loop system:

And poles:

An AffineStateSpaceModel with a set of gains:

Its controller:

The closed-loop system:

Its poles are that of the Taylor linearized model:

A NonlinearStateSpaceModel with a set or gains:

Its controller:

The closed-loop system:

Its poles are that of the Taylor linearized system:

By default, EstimatorRegulator returns the controller comprising the estimator and regulator:

The controller can also be obtained as a property:

The estimator model:

The feedback gains model:

The closed-loop system:

The closed-loop poles:

The estimator-regulator feedback model:

In this model, the feedback input is fed back directly:

Assemble the estimator and regulator with feedback to get the same result as before:

The closed-loop system differs from the computed one only in the input matrix:

The design method:

Properties related to the input model and gains:

Get the controller data object:

The list of available properties:

The value of a specific property:

Design a tracking controller:

First design a state feedback controller and estimator:

Assemble the tracking controller:

The closed-loop system tracks the reference signal :

Design a tracking controller for a discrete-time system:

First design a state feedback controller and estimator:

Assemble the tracking controller:

The closed-loop system tracks the reference signal :

Track multiple outputs:

Design an optimal state feedback controller:

And an estimator using pole placement:

Assemble the tracking controller:

The closed-loop system tracks two different reference signals:

Compute the controller effort:

Design an optimal state feedback controller:

And an estimator:

Assemble the tracking controller:

The controller model:

The controller inputs:

The controller effort:

Track a desired reference signal:

The reference signal is of order 2:

And sinusoidal:

Set the reference as the sum of sinusoids:

Design a controller to track one output of a first-order system:

The dimensions of the state weighting matrix qq are k+m q:

Compute the controller:

The closed-loop system tracks the reference:

Compute the closed-loop system based on a linear design:

Assemble the closed-loop system with the nonlinear model:

Compare the response of the two systems:

Assemble the merged closed loop of a plant with an EstimatorRegulator:

The unmerged closed-loop system:

When merged, it gives the same result as before:

Explicitly specify the merged closed-loop system:

Create a closed-loop system with a desired name:

The closed-loop system has the specified name:

The name can be directly used to specify the closed-loop model in other functions:

The simulation result: