System and method for feedback control

Abstract

A system and method for controlling a plant having a minimum phase transfer function P(s) and given an input signal u, the plant having an output y and a plant frequency range comprising a transfer function J(s) comprising the product of a high gain filter J(s) having a gain ksufficient that when |ω|≦ωand |1+J(ω)|>1/M for all ω wherein ωis selected to obtain a desired time response, and a low pass filter J(s) selected such that |1+J(ω)|>1/M for all ω and J(s) is strictly proper, wherein ε<1 and M>1 and ε and M are selected to meet a desired sensitivity requirement. An error signal e is calculated comprising the difference between the system input signal u and the plant output signal y, and the error signal modified according to the transfer function C(s)=P(s)J(s)J(s) and inputting the error signal into the plant. The system and method can be extended to unstable invertible plants. A global sensitivity bound M≧1 could also be achieved for plants including right half planes zeros. The system and method are shown applied to a read-write head positioning actuator of a hard disk drive, but can be applied equally to other systems such as electrical systems, mechanical systems, industrial processes, military applications, flight control, power generation, computer servo systems, phase lock loops and the like.