POLE PLACEMENT AND MIXED SENSITIVITY OF LTI MIMO SYSTEMS HAVING CONTROLLED OUTPUTS DIFFERENT FROM MEASUREMENTS

摘要

Multi-Input Multi-Output (MIMO) Linear Time-Invariant (LTI) controllable and observable systems where the controller has access to some plant outputs but not others are considered. Analytical expressions of coprime factorizations of a given plant, a solution of the Diophantine equation and the two free parameters of a two-degrees of freedom (2DOF) controller based on observer stabilizing control are presented solving a pole placement problem, a mixed sensitivity criterion, and a reference tracking problem. These solutions are based on proposed stabilizing gains solving a pole placement problem by output feedback. The proposed gains simplify the coprime factorizations of the plant and the controller, and allow assigning a decoupled characteristic polynomial. The 2DOF stabilizing control is based on the Parameterization of All Stabilizing Controllers (PASC) where the free parameter in the feedback part of the controller solves the mixed sensitivity robust control problem of attenuation of a Low-Frequency (LF) additive disturbance at the input of the plant and of a High-Frequency (HF) additive disturbance at the measurement, while the free parameter in the reference part of the controller assures that the controlled output tracks the reference at LF such as step or sinusoidal inputs. With the proposed expressions, the mixed sensitivity problem is solved without using weighting functions, so the controller does not increase its order; and the infinite norm of the mixed sensitivity criterion, as well as the assignment of poles, is determined by a set of control parameters.