Output Recurrent Fuzzy Broad Learning Systems for Adaptive MIMO PID Control: Theory, Simulations, and Application

This paper proposes a novel adaptive predictive Proportional-Integral-Derivative (PID) controller utilizing an output recurrent fuzzy broad learning systems (ORFBLS) for Multiple-Input Multiple-Output (MIMO) digital control systems, aiming to effectively adapt to changing setpoints and dynamic environments. The proposed controller, MIMO ORFBLS-APPID controller in short, is proposed to extend the application of ORFBLS as an adaptive adjustment mechanism for PID gains parameters, where the controller gain matrices are automatically tuned over time by employing the Jacobian transformations of the MIMO ORFBLS identifier. Three theorems are established to ensure proper usage and successful applications of the proposed controller. The setpoints tracking control performance and disturbance rejection abilities are firmly illustrated by performing three simulations to the multivariable nonlinear dynamic systems. Moreover, one experimental study to the laboratory-built extrusion barrel in a plastic injection molding machine is done to validate the effectiveness and practicality of the proposed control method. Through comparative simulations and experimental results, the proposed controller has been shown to outperform two existing control methods in terms of control performance indexes.