A novel performance synthesis method for unknown mismatched disturbances with finite-frequency specifications

A novel synthesis method of disturbance-rejection performance is developed for equivalent-input-disturbance (EID)-based control systems regardless of the unknown and mismatch of disturbances in this paper. It removes the prior assumption on the existence of an EID on the control input channel and guarantees a prescribed finite-frequency performance. First, by treating the Luenberger observer as an ideal dynamic, an auxiliary indicator, i.e., an intermediate variable, is introduced to facilitate performance evaluation. Then, the control mechanism of disturbance-rejection performance is revealed for both single-input, single-output (SISO) and multi-input, multi-output (MIMO) systems with the aid of a commutative condition. More specifically, the commutative condition is always true for SISO systems, but it is a bit challenging to find appropriate parameters such that the commutative condition holds for MIMO systems. To facilitate implementation, a practical commutative condition is developed and used instead of the original commutative condition. Further, taking into account the practical commutative condition, a performance-oriented design algorithm is given, which ensures the prescribed finite-frequency and entire-frequency disturbance-rejection performance requirements. Finally, by comparing with other methods, case studies of a quarter-vehicle suspension system and an MIMO system are carried out to demonstrate the advantages of the developed method.