International Journal of Computer Applications (0975 – 8887) Volume 69– No.27, May 2013 7 Control of Non-Linear Inverted Pendulum using Fuzzy Logic Controller Arpit Jain Deep Tayal Neha Sehgal University of Petroleum & Energy Studies, Dept of Electrical, Electronics & Instrumentation Engineering Dehradun, India ABSTRACT This paper proposes an intelligent control approach towards Inverted Pendulum in mechanical engineering. Inverted Pendulum is a well known topic in process control and offering a diverse range of research in the area of the mechanical and control engineering. Fuzzy controller is an intelligent controller based on the model of fuzzy logic i.e. it does not require accurate mathematical modelling of the system nor complex computations and it can handle complex and non linear systems without linearization. Our objective is to implement a Fuzzy based controller and demonstrate its application to Inverted Pendulum. Model design and simulation are done in MATLAB SIMULINK ® software. Keywords-Inverted Pendulum, Fuzzy logic, Fuzzy controller 1. INTRODUCTION The fact that fuzzy systems are universal approximators has been shown and proven by several sources [1, 2]. These proofs arise from the isomorphism between two algebras: an abstract algebra (one dealing with groups, fields, and rings) and a linear algebra (one dealing with vector spaces, state vectors, and transition matrices) and the structure of a fuzzy system which constitutes of an implication between actions and conclusions. This isomorphism is achieved because both entities involve a mapping between elements of two more domains. Like an algebraic function maps an input variable to an output variable, a fuzzy system maps an input group to an output group: in the latter these group can be linguistic assertions or forms of fuzzy information. The underlying principle on which fuzzy systems theory rests is a fundamental theorem from real analysis in algebra known as Stone – Weierstrass theorem, first developed in the late nineteenth century by Weierstrass[3], then simplified by Stone[4]. Although fuzzy systems are shown to be universal approximators to algebraic functions, it is not this attribute that actually makes them valuable to us in grasping new or evolving problems. Rather, the primary advantage of fuzzy systems theory is to approximate system behaviour where analytic functions or numerical relations are absent. Therefore, fuzzy systems have high potential to understand the very systems that lack analytic formulations: complex systems. Instead, fuzzy systems theory can be useful in assessing some of our more conventional, less complex systems. For example, suppose a controller is required to bring an aircraft out of a vertical dive. Conventional controllers, as they are restricted to linear ranges of variables, cannot handle this scenario; a dive situation is highly non-linear. Fuzzy controller can be used in this case, which is adept at handling non linear situation albeit in an imprecise fashion, to bring the plane out of the dive into a more linear range, then handoff the control to the aircraft to a conventional, linear, highly precise controller. As pointed out by Ben – Haim[5], this is a distinction between models of systems and models of uncertainty. A fuzzy system can be thought of as a collection of both because it attempts to understand a system for which no model exist, and it does so with information that can be uncertain in a sense of being vague, or fuzzy, or altogether lacking. Fuzzy systems are robust because the uncertainties contained in both the inputs and outputs of the system are used in formulating the system structure itself, unlike conventional system analysis which first poses a model, based on a collective set of assumptions needed to formulate a mathematical form, then uncertainties in each of the parameters of that mathematical abstractions are considered which could be misleading. 2. INVERTED PENDULUM ON A CART A pendulum which has its center of mass above its pivot point is known as an Inverted Pendulum. It is usually implemented with the pivot point mounted on a cart that can move horizontally and may be called a cart and pole. Many applications limit the pendulum to 1 (single) degree of freedom by affixing the pole to an axis of rotation. While a normal pendulum is stable when hanging downwards, an inverted pendulum is inherently unstable, and must be aptly balanced in order to remain upright; this hasbeen done either by application of a torque at the pivot point, by moving the pivot point in horizontal motion as part of a feedback system, altering the rate of rotation of a mass mounted on the pendulum on an axis parallel to the pivot axis and thereby generating a net torque on the pendulum, or by oscillation of the pivot point vertically. A simple demonstration of moving the pivot point in a feedback system is achieved by balancing an upturned broomstick on the end of one's finger. The inverted pendulum is a standard problem in dynamics and control theory and is used as a benchmark for testing control strategies.