Design and Implementation of an Advanced Control Algorithm for an Inverted Pendulum QUBE-Rotary Servo

The inverted pendulum represents a problem of considerable complexity in the field of systems control due to its unstable and nonlinear behavior. In this context, the objective of this research is to design and implement control algorithms for a QUBE-Rotary Servo inverted pendulum. The experimental system has voltage as its input and the arm angle (θ) and the pendulum angle (φ) as its outputs. The study begins by developing a mathematical model of the system, creating a simulator and a graphical interface for the 3D inverted pendulum which emulates its real behavior. Two conventional control algorithms, Proportional-Derivative (PD) and Proportional-Integral-Derivative (PID), are proposed and implemented through simulation and experimentation, along with an advanced control algorithm, the Linear Quadratic Regulator (LQR). The results show that LQR control performs better in terms of stability and settling time when compared to changes in the arm’s position which represent constant disturbances in the pendulum; also the system’s robustness to external physical disturbances was evaluated by analyzing five trials for each case.