Optimization of controller gains for FPGA-based multivariable motion controller using response surface methodology

Abstract

Field Programmable Gate Arrays (FPGA) has become increasingly popular in recent years for control applications. Using contemporary FPGA technology, a powerful virtual processor can be synthesized and integrated with custom hardware to create a dedicated controller that outperforms conventional microcontroller and microprocessor based designs. The FPGA based controller takes advantage of both hardware features and virtual processor technology. This study details the development of a cascaded type Proportional-Derivative (PD) controller for an inverted pendulum system implemented on a single FPGA device. The controller includes a hardware based implementation of the Input Output (IO) modules including quadrature decoders/counters and a Pulse Width Modulation (PWM) controller for the motor driver. The NIOS II processor was synthesized to implement the cascaded PD controller algorithm. This study also proposes a novel method for obtaining the optimal controller gains for the system. It uses Design of Experiments (DoE) techniques for obtaining optimal gain values. In this study three Response Surface Methodology (RSM) designs: Central Composite, Box-Behnken and Uniform Design are used for obtaining optimal gain values. Based on the results of this study, the uniform design approach yielded the most satisfactory results. The gains provided by the response surface model from the uniform design experiment are verified experimentally to validate the proposed controller tuning method. A classic inverted pendulum system was selected to demonstrate the applicability of the proposed approach.