Anti Wind‐Up and Robust Data‐Driven Model‐Free Adaptive Control for MIMO Nonlinear Discrete‐Time Systems

Abstract

This article addresses a solution to one of the main challenges of online data‐driven control (DDC) methods: reducing the sensitivity of the model‐free adaptive control (MFAC) method to initial conditions and control parameters with the new control cost function and added the output error rate and integral along with a new anti‐wind up strategy for multi‐input multi‐output (MIMO) systems. The parameters introduced to the new control law have been validated using the boundary‐input boundary‐output (BIBO) approach to design and converge the controller. The simulation findings on a nonlinear auto‐regressive moving average model with exogenous inputs (NARMAX) system with triangular control input demonstrate that the proposed control rule will outperform to prototype MFAC. Furthermore, to analyze the sensitivity of the controller to the initial conditions and the uncertainties of the control parameters, 30 Monte Carlo simulations were performed with random initial conditions in the presence of disturbance in the control input, and output noise, and the results were compared with the prototype MFAC and conventional PID controller using standard criteria such as integral time absolute error, standard deviation, steady‐state error, and mean maximum error, which shows a noticeable superiority of proposed controller relative to the prototype MFAC.