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Some fundamental limitations in the control of two-mass systems

In this paper fundamental limitations in the control of two-mass systems are discussed, giving particular emphasis to the role of the minimum-phase lightly damped zeros of the system. Cheap control theory for SITO (Single Input Two Outputs) systems is used to quantify performance limitations on the class of all the stabilizing controllers, even allowing arbitrarily high control effort. These fundamental limitations arise even if all the transfer functions of the systems are stable and minimum phase, and are strictly related to the minimum phase zeros near the imaginary axis. Use of recent results on the best tracking performance achievable under control effort constraint confirms the limiting effect of such zeros.