Utilizing FPGAs for Real Time Control and Stabilization of Multibody Mechatronic Systems

Abstract

This work aims to design and implement an FPGAbased embedded controller for multibody mechatronic systems. The application considered is a wheeled self-balancing robot. The main objective is to stabilize the inverted body of the robot in its vertical position. It is done by precisely driving its wheels forward and reverse direction until stabilization occurs within a small distance. Using the multibody dynamics approach for the control system design of such systems is a challenging task due to the resulting differential nonlinear algebraic equations. In this article, development, verification, and simulation were done for the resulting model. The bumgrate stabilization method was used with the parameter α = β = 10 shows acceptable violations of ±10−6 and ±10−4 for both holonomic and nonholonomic constraints, respectively, during the dynamic equations solution. Next, we designed and simulated optimal feedback controllers and classical PID controllers for both linear and nonlinear multibody models. In addition, our testing of the digital PID controller on an FPGA shows that the steady-state error for successful stabilization is around ±0.2 degrees, and it takes 2 seconds for the zero-tilt angle setpoint to settle. Finally, we implemented a PID controller on the NI-SBRIO 9631 with a 266MHz real-time processor, and a 40MHz Xilinx FPGA target. Using such RIO board enables the rapid development of such control systems. The results of this implementation reveals that the controller is able to stabilize the robot in the range of the tilt angles θ 3 = ±15◦ due to the DC motors torque specifications. Furthermore, the paper proves the effectiveness of using the coordinate partitioning method for the state-space formulation of such under-actuated nonlinear systems.