DESIGN AND IMPLEMENTATION OF CONTROLLERS OF INVERTED PENDULUM CART SYSTEM

Abstract

Pendulum on the cart has two equilibrium points. Pendulum in downward state is in stable equilibrium state as it is aligned to earth's gravitational force while pendulum in upward state is in unstable equilibrium state due to anti-gravitational alignment. Hence it requires controlling force in-order to maintain upright position. System is realized by Lypunov's Method and later linearized by Jacobian linearization technique at various points. This work proposed systematic method to obtain nonlinear compensator by interweaving the locally partitioned linear quadratic regulators along with consideration of constraints like track length and actuator output limit. LQR are obtained by linearizing model around desired points. These points are combined together with Fuzzy Logic Controller called f-LQR. Then performance of proposed controller (f-LQR) and LQR controller is compared. It was found that the f-LQR enhances the performance of LQR. Further on application of Genetic Algorithm for searching optimal values of states and input weight matrixes in LQR Performance Index. Hence fG-LQR controller is designed by embedding LQR, FLC and GA results into better results than f-LQR. Control schemes are coded into rn-file and tested on closed loop MATLAB-Simulink model. Performance of proposed controller is verified in presence of parameter variations and disturbances.