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:
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.