Inversion Based Adaptive Feedforward Control for Multivariable Systems

Abstract

Abstract This paper presents a novel adaptive feedforward control (AFC) method for rejecting sinusoidal disturbances with known frequencies acting on multi-input-multi-output (MIMO) discrete time linear systems based on the H-infinity synthesis. First, the gradient AFC (GAFC) for MIMO systems is reviewed, and the linear time invariant (LTI) equivalent form of the GAFC is approximated for stability analysis. For single-input-single-output (SISO) systems, this paper shows small adaptation gains guarantee the stability of GAFC for any disturbance frequency. Then inspired by the stability of SISO GAFC, the inversion based AFC (IAFC) is proposed for MIMO systems. In this method, the GAFC is compensated by an H-infinity model matching filter, which renders nearly decoupled systems with fixed time delays. The LTI analysis, simulation study and experimental results from an open-loop unstable MIMO Active Magnetic Bearing Spindle (AMBS) are presented to demonstrate the stability and effectiveness of the proposed IAFC in rejecting narrow-band disturbances.