Simulink Control Design™ - MathWorks

Passivity Goal

Purpose

Enforce passivity of specific input/output map when using Control System Tuner.

Description

Passivity Goal enforces passivity of the response of the transfer function between the

specified signal locations. A system is passive if all its I/O trajectories (u(t),y(t)) satisfy:

∫ 0

T

ytTutdt> 0,

for all T > 0. Equivalently, a system is passive if its frequency response is positive real,

which means that for all ω > 0,

Gjω +GjωH> 0

Passivity Goal creates a constraint that enforces:

∫ 0

T

ytTutdt>ν∫

0

T

utTutdt+ρ∫

0

T

ytTytdt,

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, set ν or ρ to a positive value. To permit a shortage of

passivity, set ν or ρ to a negative value. See “About Passivity and Passivity Indices”

(Control System Toolbox) for more information about these indices.

10 Control System Tuning