Wiener-Hopf design of the general two-degree-of-freedom controllers and the connection to state-space formulas

摘要

H-2 design of the two-degree-of-freedom controller configuration is treated for the generalized plant in both the frequency and state-space domains. A frequency domain Wiener-Hopf formula is derived-first under a set of compact assumptions that gives the entire class of controllers for which the feedback control system is stable and a quadratic cost functional is finite. The H-2 design method suggested in this paper allows the reference inputs to include the persistent signals such as step or ramp functions and the class of persistent reference inputs that can be tracked with zero steady-state error is characterized explicitly. To circumvent the computational difficulties of the Wiener-Hopf formulas, the corresponding state-space domain formulas are derived by rationalizing the polynomial fractional descriptions. It is shown that the well-known standard time domain assumptions for the H-2 design problem have the corresponding equivalent frequency domain conditions and this equivalence relationship is shown to be useful to choose correct design parameters via an illustrative example. [References: 15]