State Observers/Kalman Filters are Generally Unsuitable for Feedback Control While a Far More Rational and Superior Solution is Available

Abstract

-An observer that estimates system state vector x(t) is a state observer. Although a state observer can generate state feedback control signal Kx(t) where the constant gain K can bese parately designed before its realizing observer, the actual observer feedback system cannot have its loop transfer function equal K(sI – A)-1B, the loop transfer function of the direct state feedback control, for a great majority of plant systems. Because loop transfer function determines the sensitivity function and robust properties of the corresponding feedback system, this implies that the robust properties of the Kx(t)-control are failed to be realized by state observers for a great majority of plant systems.Because robustness against system model uncertainty and terminal disturbance is foremost of feedback control even above performance, state observers are unsuitable for feedback control. Although this problem has initiated a vibrant robust control research in the past 40+ years, the result of that research has been unsatisfactory if parameter K is designed separately and prior to observer design. As a result, control theory remains essentially stagnant and a large amount of works still applied Kalman filters and state observers to feedback control applications. Fortunately, this vital problem has found a fundamentally novel yet decisively satisfactory solution, that is to design parameter K based on the key observer parameters! These new observers are not restricted to be state observers, and can have freely designed and reduced observer order for the first time, and thus can guarantee the full realization of loop transfer function and robust properties of their corresponding Kx(t)-control. Such an observer exits for a great majority of plant systems!In addition, this new design principle is very simple to be learned, and adjusted very easily. Thus, a design methodology that can achieve high performance and robustness for general L-T-I systems is finally developed