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wcgainplot

Graphical worst-case gain analysis

Syntax

wcgainplot(sys)
wcgainplot(sys,w)
wcgainplot(sys,...,options)

Description

wcgainplot(sys) plots the nominal and worst-case gains of the uncertain system sys as a function of frequency. For multi-input, multi-output (MIMO) systems, gain refers to the largest singular value of the frequency response matrix. (See sigma for more information about singular values.) The plot includes:

  • Nominal — nominal gain of sys

  • Worst — the response falling within the uncertainty of sys that has the highest peak gain

  • Worst-case gain (lower bound) — the lowest worst-case gain at each frequency

  • Worst-case gain (upper bound) — the highest gain within the uncertainty at each frequency

  • Sampled Uncertainty — 20 responses randomly sampled from sys

wcgainplot(sys,w) focuses the plot on the frequencies specified by w.

  • If w is a cell array {wmin,wmax}, wcgainplot plots the worst-case gains in the range {wmin,wmax}.

  • If w is an array of frequencies, wcgainplot plots the worst-case gains at each frequency in the array.

wcgainplot(sys,...,options) uses the options set options to specify additional options for the computation of the worst-case gains. Use wcgainOptions to create the options set.

Input Arguments

sys

Uncertain dynamic system.

w

Frequencies of worst-case gain plots. Specify frequencies in radians/TimeUnit, where TimeUnit is the time unit of sys.

  • If w is a cell array {wmin,wmax}, wcgainplot plots the worst-case gains in the range {wmin,wmax}.

  • If w is an array of frequencies, wcgainplot plots the worst-case gains at each frequency in the array.

options

Options set specifying additional options for the computation of the worst-case gains. Use wcgainOptions to create the options set.

Examples

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Plot Worst-Case Gain of Uncertain System

Plot the worst-case gain of the following system:

$$sys = \frac{{{s^2} + 3s}}{{{s^2} + 2s + a}}.$$

The uncertain parameter a = 2 +/- 1. Plot the worst-case gain between 0.1 and 100 rad/s.

a = ureal('a',2);
sys = tf([1 3 0],[1 2 a]);
wcgainplot(sys,{.1 100})

The Worst curve identifies the single response within the uncertainty that yields the highest gain at any frequency. The Worst-case gain (upper bound) curve is the envelope produced by finding the highest gain within the uncertainty at each frequency.

More About

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Algorithms

wcgainplot uses wcgain to compute the worst-case gains. Use the options argument to wcgainplot to set options for the wcgain algorithm.

wcgainplot uses usample to compute the Sampled Uncertainty curves.

See Also

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