Logic-based Switching Adaptive Stabilization Of Linear Single Inverted Pendulum System

As a typical multivariable under-actuated system of high nonlinearity and strong-coupling,inverted pendulum has always been a challenge for modern control theories.Since inverted pendulum is a model abstracted from numerous control problems,researching of inverted pendulum has significant realistic meaning in engineering.This paper used logic-based switching control method to stabilize an inverted pendulum system.It is organized as follows:Based on the Euler-Lagrange equation for mechanical control systems,a procedure to reduce control design for original UMS is developed.By considering that mechanical control systems possess kinetic symmetry properties,several closed-loop changes of coordinates are designedto transform UMS into cascaded nonlinear systems with structural properties.The proposed changes of coordinates are successfully employed to transform the original inverted pendulum system.Many practical nonlinear systems possess the upper-triangular structure and upper-triangular systems are not feedback-linearizable in general.We will use logic-based switching approach to study control of nonlinear systems.Based on cascaded model of inverted pendulum,we design a logic-based controller for inverted pendulum and do simulation experiments.Then,we build up MATLAB models of inverted pendulum and debug software environment.Experiments on real system are completed.The result shows that the cart and pole both convergence to equilibrium position quickly.The conclusion is that this method fits inverted pendulum system well.