Design of Model-Based Linear and Nonlinear Controllers to Stabilize a Simple Experimental Setup for Controls Education

This work aims to demonstrate the use of a simple experimental setup to study and benchmark different stabilizing control algorithms for introductory to elementary controls education. The experimental setup consists of a ping-pong ball rolling on a pivoted beam. The control task is to stabilize the ball at the center of the beam by systematically changing the angle of rotation of the beam through the servomotor. A control-oriented dynamic model is first obtained based on the standard Lagrangian approach. Two different model-based control design techniques are then outlined using the developed first-principles model. First, a state-space approach based on the linear-quadratic-regulator optimal control design is proposed using the linearized (approximate) model. An integrator is added to the standard LQR design to improve upon the closed-loop tracking performance. Next, a nonlinear robust design technique is outlined using the full (nonlinear) model in Sliding-Mode Control (SMC) strategy. Challenges for each control technique are discussed based on the initial results, and possible improvement areas are addressed.