Lyapunov-based fractional-order PID controller design for coupled nonlinear system

Abstract

Coupled nonlinear systems are difficult to control due to the adverse effects of uncertainties and coupling effects with increased sensor noise. This paper proposes an improved Lyapunov-based composite controller consisting of fractional-order proportional–integral–derivative (FOPID) and velocity-based disturbance observer to deal with the motion control of uncertain, nonlinear, and coupled system. FOPID utilizes the stable filtered error to facilitate the control development and stability analysis for the multi-input multi-output (MIMO) coupled system. Moreover, a disturbance observer is developed by utilizing the velocity signals to provide robustness against the disturbances and parametric uncertainties. Enhanced infinite order disturbance observer (EIFDOB) structure is used to improve the robustness of the introduced technique despite the high-frequency sensor noise. Stability analysis is provided to verify the introduced controller through the Lyapunov stability theorem, LaSalle’s invariance principle, and Barbalat’s lemma. Signal chasing is also presented to show that all signals are ultimately bounded. Comprehensive numerical simulations are performed on high-fidelity and coupled nonlinear model of the twin rotor MIMO system where the efficiency of the presented technique is examined against the external disturbances, matched uncertainties, and sensor noise. The results presented with different scenarios show that the proposed technique performed better with more robustness than FOPID and integer order proportional–integral–derivative.