comparative study on several control strategies for inverted pendulum systems

This research undertakes the design and development of a series of control strategies, including Proportional-Integral-Derivative (PID), Linear-Quadratic-Regulator (LQR), robust and adaptive control approaches, for an inverted pendulum appended to a single-mass and inverted pendulum added to a double-mass system. The control objective is to keep the pendulum in the upright position while the base mass moves to a desired position. For this, the governing coupled equations of motion are first derived using Newtonian technique. Then PID controllers are developed for each system using and optimally tuned to arrive at the best gains for best control performance. Moreover, LQR controllers are designed for these systems and compared with PID controllers. Then, a hierarchical sliding mode control approach is proposed as the third controller. The two coupled systems, i.e., inverted pendulum appended to a single-mass and inverted pendulum added to a double-mass, can be divided into two subsystems and three subsystems respectively, and the sliding surface for each subsystem is then designed. According to the hierarchical structure, the final control law is derived from a Lyapunov-based approach and stability viewpoint. Lastly, an adaptive control strategy is presented to improve the performance of the systems. Extensive simulation and experimental results are provided to justify the comparative advantage of robust control and adaptive control methods over traditional linear controllers such as PID and LQR techniques.