THIS IS DOCUMENTATION FOR AN OBSOLETE PRODUCT.
SEE THE DOCUMENTATION CENTER FOR THE LATEST INFORMATION.

DOCUMENTATION CENTER SEARCH

New to Mathematica? Find your learning path »

Mathematica > Mathematics and Algorithms > Control Systems > Design Using State-Space Models > LQGRegulator >

BUILT-IN MATHEMATICA SYMBOL

LQGRegulator

constructs the optimal feedback regulator for the StateSpaceModel ss using noisy measurements sensors and feedback inputs finputs. The process, measurement, and cross-covariance matrices are w, v, and h; and the state, input, and state-input weighting matrices are q, r, and p.

LQGRegulator

specifies einputs as the exogenous deterministic inputs.

MORE INFORMATION

The state-space model ss can be given as StateSpaceModel, where a, b, c, and d represent the state, input, output, and transmission matrices in either a continuous-time or a discrete-time system:

		continuous-time system
		discrete-time system

The input can include stochastic inputs , feedback inputs , and exogenous deterministic inputs .

The arguments finputs and einputs are lists of integers specifying the positions of and in .

The output consists of the noisy measurements as well as other outputs.

The argument sensors is a list of integers specifying the positions of in .

LQGRegulator is equivalent to LQGRegulator[{ss, sensors, finputs, None}, {...}].

If not specified, h and p are assumed to be zero matrices.

Block diagram of the continuous-time system with its regulator:

Block diagram of the discrete-time system with its regulator:

The system with the regulator has the following block diagram:

EXAMPLES

CLOSE ALL

Basic Examples (1)

Construct an LQG regulator for a system with one measured output and one feedback input:

In[1]:=

Out[1]=

Scope (3)

An LQG regulator for a continuous-time system with one measurement and two feedback inputs:

An LQG regulator for a system with two sensor outputs, one feedback input, one exogenous deterministic input, and one stochastic input:

Design an LQG regulator for a discrete-time system:

Applications (1)

An LQG regulator for a SISO system:

The closed-loop system:

The closed-loop output response:

Properties & Relations (2)

The closed-loop poles are the poles of the state-feedback and estimator subsystems:

Construct an LQG regulator from the optimal state-feedback gains and the Kalman estimator model:

LQGRegulator gives the same result: