Modeling, identification and control of cart-pole system

Abstract

To understand any physical world system, a proper mathematical model is required. With the help of mathematical model, the system can be studied and controlled. There are different ways to develop a mathematical model such as first principle method and system identification method. First principle method is generally used when there is sufficient knowledge of the physical world system but system identification is used when there is no knowledge of the system. System identification is widely used to develop mathematical model of complex, non-linear systems. Cart-pole system is a benchmark problem in control system where the control objective is to balance the inverted pendulum mounted on the cart to a vertical position. This complete system is nonlinear in nature and the mathematical model can’t be efficiently calculated using first principle modeling. So system identification method is used to develop the mathematical model of the said system. This thesis finds out the linearized mathematical model of the said cart-pole system using parametric system identification procedure. Parametric system identification procedure consists of experiment design, model structure selection, parameter estimation and model validation. This thesis also designs linear and non-linear controller for the said system. For linearized model of cart-pole system some of the linear controllers designed are LQR, LQR-Pole-placement-PID, Fuzzy-PID, LQG and H-infinity. For the nonlinear model of cart-pole system, the control techniques discussed are the partial feedback linearization and classical feedback linearization control.