A robust proportional filtered integral controller based on backpropagation neural network

This paper introduces a novel design of a proportional filtered-integral (P-FI) controller whose parameters are auto-tuned using the backpropagation neural networks (BPNN) algorithm. The proposed controller is designed to address the main challenges posed by a class of complex systems characterized by uncertain high-gain and pure integrator dynamics, including high-frequency noise amplification and poor robustness against parameter variations. Designing such a controller involves three main steps: First, a proportional–integral–derivative (PID) controller is designed, with its parameters auto-tuned online using the BPNN algorithm, resulting in the primary (BPNN-PID) controller. Second, the obtained parameters of the previous controller are utilized to compute those of a low-pass filter offline. This filter is then cascaded with the integral parts of a PID controller, forming a P-FI controller structure. This configuration introduces a phase lead within a specific frequency range without amplifying high-frequency noise, overcoming the primary disadvantage of the derivative term. Finally, the parameters of the resulting P-FI controller are again auto-tuned online using the BPNN algorithm, resulting in the final robust (BPNN-P-FI) controller. This novel controller structure and its parameters tuning procedure, based on a two-stage BPNN learning approach, constitute the main contributions of this paper. Simulation results demonstrate the superiority of the proposed controller in terms of time-domain performance, sensor noise attenuation, and closed-loop robustness compared to those obtained with the BPNN-PID and optimally tuned PID controllers.