ANALYSIS AND DESIGN OF ROBUST CONTROLLER OF INVERTED PENDULUM SYSTEM

Abstract

This work is dedicated to analysis and designing of robust controller using H-°° technique. In initial chapters the basic definition about robust controller is presented. It is shown how the uncertainties evolved in the system and need of robust controller are discussed. Different type of uncertainties classified as structured and unstructured uncertainties are explained briefly and their effect is shown in the designing. Mathematical modeling of uncertainties is discussed in separate chapter using different type of techniques such as input multiplicative perturbation; output multiplicative perturbation etc. various control goals and objective such as good disturbance rejection , low sensor noise , good tracking are analyzed and role of sensitivity and complimentary sensitivity has been discussed. In robust control designing the mathematics is quite cumbersome so some basic concepts of math's such as norms, Linear Fraction Transformation(LFT),system norms that are commonly used in the controller designing are discussed briefly. In robust controller designing the most important step of weighting filter selection is discussed in detail and various methods to use these filters are discussed. Further Hoo technique of robust controller is discussed and j.. analysis method is presented to analyze the robustness of closed loop system. In the later part of the work the model of inverted pendulum with three arms are taken and mathematical model is taken to design a robust controller for the system. First the nominal model is presented then uncertainties are introduced in the system and their mathematical modeling is presented. Various performance objectives are defined for the system and Hoo controller is derived for the system. The performance of system in the presence of disturbance and in presence of uncertainties is analyzed using p-analysis. Robust Control Toolbox of MATLAB is used for the whole designing and analysis part