Formulating Design Requirements as H-Infinity Constraints

Control design requirements are typically performance measures such as response speed, control bandwidth, roll-off, and steady-state error. To use hinfstruct, first express the design requirements as constraints on the closed-loop gain.

You can formulate design requirements in terms of the closed-loop gain using loop shaping. Loop shaping is a common systematic technique for defining control design requirements for H_∞ synthesis. In loop shaping, you first express design requirements as open-loop gain requirements.

For example, a requirement of good reference tracking and disturbance rejection is equivalent to high (>1) open-loop gain at low frequency. A requirement of insensitivity to measurement noise or modeling error is equivalent to a low (<1) open-loop gain at high frequency. You can then convert these open-loop requirements to constraints on the closed-loop gain using weighting functions.

This formulation of design requirements results in a H_∞ constraint of the form:

$${\Vert H\left(s\right)\Vert }_{\infty }<1,$$

where H(s) is a closed-loop transfer function that aggregates and normalizes the various requirements.

For an example of how to formulate design requirements for H_∞ synthesis using loop shaping, see Fixed-Structure H-infinity Synthesis with hinfstruct.

For more information about constructing weighting functions from design requirements, see H-Infinity Performance.

Related Topics

• Interpretation of H-Infinity Norm
• H-Infinity Performance
• Fixed-Structure H-infinity Synthesis with hinfstruct