Inverted Pendulum Analysis

The Inverted Pendulum is inherently unstable, higher order multi-variable and highly coupled system which can be treated as typical non-linear control problem. [1] This is the benchmark for designing, testing, evaluating and comparing of different classical and contemporary control methods. The control of IP has been a research interest in the field of control engineering because it is the most difficult system being an inherently unstable and highly nonlinear. So this system became a choice of dynamic system for analysis of its dynamic model and develop a control law. The aim of this work is to stabilize the Inverted Pendulum (IP) and the position of the cart on the track is controlled quickly and accurately so that the pendulum is always
The main difficulty in these kind of system is that it cannot be controlled satisfactorily by linear control methods in all the conditions. The recent development in the area of Artificial Intelligence techniques has given novel solution to different typical control system problem [1,2]. PID and FOPID has been applied for optimization and tracking control problem of Inverted Pendulum system [4] and particle swamp optimization (PSO) is used.
There are different Artificial Intelligence (AI) techniques, such as fuzzy logic theory (FL), artificial neural network (ANN), [2], and evolutionary computational methods, as genetic algorithm (GA), particle swarm optimization (PSO) [4], etc., commonly all these are known as intelligent computational techniques which have given novel more accurate solutions to various control problems. Adaptive Control as a set of techniques for automatic adjustment in real time of controllers in order to achieve or maintain a desired level of performance of a control system for unknown and varying parameter. In [7, 8] adaptive control technique of control system is explained and there are different techniques of adaptive control method. The Model Reference Adaptive Control (MRAC) approach and application is shown in [9, 10, 11]. The application of fuzzy logic controller for Inverted Pendulum has been performed [13] and proved to be
[16]. Artificial neural networks have been applied successfully for identification and control of dynamic systems because of their learning capability and ability to tolerate incorrect data or disturbances.
Artificial Neural Networks (ANN) can be used for system identification and adaptive control of non-linear systems. Neural Networks are used for approximating complex control problems where the accurate mathematical model of the system can’t be determined as in the case of Inverted Pendulum. The Artificial Neural Network (ANN) controller behaves in such a way that it counteracts any disturbance in the system. [16]. Artificial Neural Network (ANN) control is classified into three types- supervised, direct inverse and unsupervised [17].
The PID (Proportional-Integral-Derivative) control technique is applied to this system. PID control gives the simplest and efficient result to various real-world problem. By using PID control both the transient and steady state response can be