Parametric compensator design in the frequency domain

The parametric approach to the design of observer based compensators has hi therto only been formulated in the time domain. It yields an explicit param etric expression for the state feedback matrix (observer gain) given the cl osed loop eigenvalues and the corresponding sets of invariant parameter vec tors. Using the polynomial approach to the design of observer based compens ators this contribution presents an equivalent parameterization in the freq uency domain. By introducing the closed loop poles and the set of so-called pole directions as new design parameters, one obtains expressions in param etric form for the polynomial matrix (D) over tilde (s) ((D) over tilde (s) ), parameterizing the state feedback (state observer) in the frequency doma in. It is shown how the pole directions are related to the invariant parame ter vectors used in the time domain approach. Another new result is the par ametric design of reduced order observers both in the frequency domain, and derived from those results, in the time domain. The proposed design proced ure is also used to provide a parametric solution for the optimal LQG contr ol problem in the presence of partially perfect measurements. Simple exampl es demonstrate the design procedure.