Simulink Control Design™ - MathWorks

Weighted Passivity Goal

Purpose

Enforce passivity of a frequency-weighted transfer function when tuning in Control

System Tuner.

Description

Weighted Passivity Goal enforces the passivity of H(s) = WL(s)T(s)WR(s), where T(s) is the

transfer function from specified inputs to outputs. WL(s) and WR(s) are frequency weights

used to emphasize particular frequency bands. A system is passive if all its I/O

trajectories (u(t),y(t)) satisfy:

∫ 0

T

ytTutdt> 0,

for all T > 0. Weighted Passivity Goal creates a constraint that enforces:

∫ 0

T

ytTutdt>ν∫

0

T

utTutdt+ρ∫

0

T

ytTytdt,

for the trajectories of the weighted transfer function H(s), for all T > 0. To enforce the

overall passivity condition, set the minimum input passivity index (ν) and the minimum

output passivity index (ρ) to zero. To enforce an excess of passivity at the inputs or

outputs of the weighted transfer function, set ν or ρ to a positive value. To permit a

shortage of passivity, set ν or ρ to a negative value. See getPassiveIndex for more

information about these indices.

Weighted Passivity Goal