Simulink Control Design™ - MathWorks

LQR/LQG Goal

Purpose

Minimize or limit Linear-Quadratic-Gaussian (LQG) cost in response to white-noise inputs,

when using Control System Tuner.

Description

LQR/LQG Goal specifies a tuning requirement for quantifying control performance as an

LQG cost. It is applicable to any control structure, not just the classical observer

structure of optimal LQG control.

The LQG cost is given by:

J = E(z(t)′ QZ z(t)).

z(t) is the system response to a white noise input vector w(t). The covariance of w(t) is

given by:

E(w(t)w(t)′) = QW.

The vector w(t) typically consists of external inputs to the system such as noise,

disturbances, or command. The vector z(t) includes all the system variables that

characterize performance, such as control signals, system states, and outputs. E(x)

denotes the expected value of the stochastic variable x.

The cost function J can also be written as an average over time:

J= lim

T ∞

E

1

T∫ 0

T

zt′QZztdt.

Creation

In the Tuning tab of Control System Tuner, select New Goal > LQR/LQG objective to

create an LQR/LQG Goal.

Command-Line Equivalent

When tuning control systems at the command line, use TuningGoal.LQG to specify an

LQR/LQG goal.

10 Control System Tuning