Dynamic mathematical modeling and control algorithms design of an inverted pendulum system (ips)

The inimitable features of multivariable, instability, non-minimum phase and non-linearity has established an inverted pendulum system as benchmark to investigate and test new emerging control schemes. In this paper, the objectives are to explicitly model the system dynamics of an inverted pendulum and implement different control algorithms that will stabilize the pendulum in the upright vertical position by controlling the input force applied to the cart in the horizontal position. The mathematical model is derived based on the energy property of Lagrange approach and the control algorithms are expanded on the derived mathematical model in MATLAB-SIMULINK environment. Hence, we proposed four different controls algorithms proportional-integral-derivative controller (PID), pole placement feedback controller (PPFC), linear quadratic regulator controller (LQR) and linear quadratic regulator with estimator (LQR+Estimator) for the control of the linearized inverted pendulum system. The study compares the proposed control algorithms in terms of system response and performance.