Fast Suboptimal Nonlinear Model Predictive Control of an Inverted Pendulum

The application of Nonlinear Model Predictive Control (NMPC) to systems with fast dynamics requires sample times in the range of milliseconds. Short sample intervals can be achieved by using suboptimal solutions of the underlying Nonlinear Program (NLP) and fast computation of the derivatives of the Lagrangian. To assure feasibility of suboptimal solutions, a sequential approach addresses the system dynamics equality constraint in the NLP. Fast computation of the derivatives can be achieved by considering the special structure of the underlying first-order sensitivities. Experimental results on a pendulum test rig, including the swing up, stabilization, set point change, and disturbance rejections, confirm the performance and robustness of the proposed NMPC approach.