Proportional-Integral Stabilizing Control of a Class of MIMO Systems Subject to Nonparametric Uncertainties by Additive-State-Decomposition Dynamic Inversion Design

Abstract

Based on the additive-state-decomposition (ASD) dynamic inversion design, a proportional-integral controller is designed to stabilize a class of multi-input multi-output (MIMO) systems subject to nonparametric time-varying uncertainties with respect to both state and input. By ASD and a new definition of output, the considered uncertain system is transformed into a first-order system, in which all original uncertainties are lumped into a new disturbance at the new defined output. Subsequently, the dynamic inversion control is applied to reject the lumped disturbance. Performance analysis of the resulting closed-loop dynamics shows that the stability can be ensured. Finally, to demonstrate its effectiveness, the proposed controller design is applied to two existing problems by numerical simulation. Furthermore, in order to show its practicability, the proposed controller design is also performed on a real quadrotor to stabilize its attitude when its inertia moment matrix is subject to a large uncertainty.