Real-Time Swing-up and Stabilization Control of a Cart-Pendulum System with Constrained Cart Movement

Abstract

Abstract The cart-pendulum system is a typical benchmark problem in the control field. It is a fully underactuated system having one control input for two degrees-of-freedom (DOFs) system. It has highly nonlinear structure, which can be used to validate different nonlinear and linear controllers and has wide range of real-time (realistic) applications like rockets propeller, tank missile launcher, self-balancing robot, stabilization of ships, design of earthquake resistant buildings, etc. In this work, modeling, simulation and real-time control of a cart-pendulum system is performed. The mathematical model of the system is developed using Euler-Lagrange approach. In order to achieve a more realistic model, the actuator dynamics is considered in the mathematical model. The main aim of this work is to investigate the performance of two different control strategies- first to swing-up the pendulum to near unstable equilibrium region and second to stabilize the pendulum at unstable equilibrium point. The swing-up problem is addressed by using energy controller in which cart is accelerated by providing a force to the cart with a AC servo motor with the help of timing pulley arrangement. The initial velocity of the cart is taken into account to confirm swing-up in the restricted track length. The cart displacement in the restricted track length is verified by simulation and experimental test-run. The regulation problem of stabilization of pendulum is addressed by developing the controller using Pole Placement Controller (PPC) and LQR Controller (LQRC). Both the control strategies are performed analytically and experimentally using the Googoltech Linear Inverted Pendulum (GLIP) setup. The analytical results, simulated in MATLAB and SIMULINK environment, are found in close agreement with the experimental results. In order to demonstrate the effect of both the stabilizing controllers on the performance of the system, comparison of the experimental results is reported in this work. It is demonstrated experimentally that LQR controller outperforms the Pole Placement controller, in terms of reduction in the oscillations of the inverted pendulum (56 %), as well as the magnitude of maximum control input (66.7 %). Further, robustness of the closed-loop system is investigated by providing external disturbances.