Optimal mechanical design of a rotary inverted pendulum

Motivated by the ever increasing demand for higher performance and lower cost, there have been growing efforts to conduct mechanical and control system designs concurrently rather than sequentially. Indeed, the area of mechatronics has sprung forth largely motivated by the desire to consider the mechanical control system design as an integrated process rather than disjointed pieces. In this paper, we present a case study of the optimal mechanical design of a rotary inverted pendulum by incorporating the control objectives involving disturbance tolerance and domain of attraction. These objectives are converted to two related metrics, controllability and unstable pole location of the open-loop system, which can be computed efficiently and do not depend on the chosen control algorithm. Since the optimization is multi-objective, and does not possess a unique optimum, a family of Pareto designs is generated. The original objectives in terms of disturbance rejection and domain of attraction are then evaluated in simulation and experimentation along the Pareto optimal solutions to provide the quantitative trade-offs of different designs.