Evaluating PID, LQR, and LMPC on Furuta Pendulum with External Disturbance Considerations

Abstract

The Furuta pendulum is a well-known
underactuated and naturally unstable system, which makes
stabilization methods very interesting to discuss. This work
provides a performance comparison of three different types of
controllers, which are proportional-integral-derivative (PID),
linear quadratic regulator (LQR), and linear model predictive
control (LMPC), on a Furuta pendulum system with external
disturbance consideration. From the simulation results, the
stabilizing controller was activated after the swing-up process
reached its switching threshold. The controller can keep the
Furuta pendulum system around its equilibrium states, and
bring the system back after a disturbance injection. Each of the
controllers has its own advantages and disadvantages evaluated
using three performance index parameters, which are integral
of square control input (ISCI), integral of time-weighted
absolute error (ITAE), and settling time. In the overall
performance evaluation, LMPC has the best and reasonable
response both in the stabilization and disturbance rejection
phase.