Abstract

A comparison between an \(\mathcal{H}_\infty\) and \(\mathcal{H}_2\) multivariable controller designed for and implemented on the MIT SERC Interferometer testbed is presented. The testbed is a modally rich, lightly damped structure that exhibits non-minimum phase behavior and has a disturbance rejection performance metric. Both controllers were 38 state two-input two-output digital compensators implemented at a sampling frequency of 2 kHz, and both were designed using a frequency weighted loop shaping approach. The details of how the various design variables and their values were chosen for both methods are compared. Comparing the methods and the resulting control designs illustrates that the \(\mathcal{H}_\infty\) and \(\mathcal{H}_2\) controllers are quite similar. The similarity is in part due to the fact that both controllers nearly cancel all the minimum phase transmission zeros of the plant. We also analyze performance robustness properties using structured singular value (μ) methods together with experimental frequency response data.

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