Design and simulation of a PID Controller for Inverted Pendulum (Human Transportation Application)

Abstract

The inverted pendulum is a classical control problem in dynamics and control theory which is the system encounter highly nonlinear and unstable system. Basically, the design of an inverted pendulum system consist of a cart or carriage which it can move horizontally along its track, where there is DC motor embedded in the cart to drive it, while on the cart, there is pendulum that mounted on it. For visualization purpose, the inverted pendulum system had similar concept when trying to balance a broomstick with hand. Since inverted pendulum is unstable system, the controller was introduced. So, a systematic iterative method for the state feedback design by choosing weighting matrices key to proportional integrated derivative (PID) design is presented assuming all the states to be available at the output. Designing the PID controller and simulating in MATLAB for proper tuning and verification. Proportional integrated derivative (PID) will be developed as an optimal and effective controller that will be used to place cart at desired position and at the same time to make sure the pendulum is always erected in its inverted position during movement of cart.