Stabilising an Inverted Pendulum with PID Controller

Abstract

Abstract. Inverted pendulum is a system in which the centre of the mass is above the pivot point, where the mass can freely rotate. The inverted pendulum has a unique trait; it is unpredictable, non-linear and consists of multiple variables. Balancing by PID controller is a continuous process where it corrects the feedback system error from the difference between the measured value and the desired value. This research mainly focusses on balancing an inverted pendulum with reaction wheel. The research objectives are to construct a self-balanced inverted pendulum and using PID controller to control the stability of the pendulum. The PID configuration is then evaluated based on the response of the system. The idea is to use the reaction torque generated by the motor to counter balance the inverted pendulum. The factor which governs the amount of torque generated is the height of the pendulum and the mass of the wheel. To balance the pendulum, tuning the PID gain is essential. Proportional gain is tuned first to get oscillation, next is to tune the integral and derivative gain to get a smoother and quicker response. Idea is to get short settling time, and minimum overshoot percentage. Hypothesis is that higher proportional gain will give a faster response rate and the acceleration of the motor is the key on generating torque. A simulation of the pendulum falling is simulated and the results are recorded in term of the response of the pendulum against time. At initial point, proportional gain, integral gain and derivative gain are set to zero to validate the simulation. The finding in this research is that torque is generated by the acceleration of the reaction wheel. Higher acceleration gives a high torque. Others findings is the PID parameter; Proportional gain increases the response rate; Integral gain is used to eliminate steady state error; Derivative gain is used to lessen the overshoot.

LQR and Fuzzy-PID Control Design on Double Inverted Pendulum

“…One example of an observable inverted pendulum is a human. To stand properly, the human body must always balance itself [1]. Another example is on a cart, where a system whose pendulum mass is above its fulcrum.…”