Simulink Control Design™ - MathWorks

Weighted Variance Goal

Purpose

Frequency-weighted limit on noise impact on specified output signals for tuning with

Control System Tuner.

Description

Weighted Variance Goal limits the noise impact on the outputs of the frequency-weighted

transfer function WL(s)H(s)WR(s), where H(s) is the transfer function between inputs and

outputs you specify. WL(s) and WR(s) are weighting functions you can use to model a

noise spectrum or emphasize particular frequency bands. Thus, you can use Weighted

Variance Goal to tune the system response to stochastic inputs with a nonuniform

spectrum such as colored noise or wind gusts.

Weighted Variance minimizes the response to noise at the inputs by minimizing the H 2

norm of the frequency-weighted transfer function. The H 2 norm measures:

• The total energy of the impulse response, for deterministic inputs to the transfer
  function.


• The square root of the output variance for a unit-variance white-noise input, for
  stochastic inputs to the transfer function. Equivalently, the H 2 norm measures the root-
  mean-square of the output for such input.

Creation

In the Tuning tab of Control System Tuner, select New Goal > Frequency-weighted

variance attenuation to create a Weighted Variance Goal.

Command-Line Equivalent

When tuning control systems at the command line, use

TuningGoal.WeightedVariance to specify a weighted gain goal.

I/O Transfer Selection

Use this section of the dialog box to specify noise input locations and response outputs.

Also specify any locations at which to open loops for evaluating the tuning goal.

Weighted Variance Goal