Neural Fuzzy Control of Ball and Beam System

Introduction

Ball and Beam systems are underactuated systems and are widely used for control applications due to their inherent non-linearity and instability (Chang et al., 2011; Frank et al., 2015). It is common control engineering problem and consists of a ball mounted on beam, servo motor and various sensors (Keshmiri et al., 2012; Cheng and Tsai, 2016). The objective is to control the ball position by changing angle of the beam (Li & Wu, 2010; Shirke & Kulkarni, 2015). The information from sensors can be taken and their difference can be fed back into the controller in order to gain the desired position of the ball. These systems are widely used for verifying control performances of various nonlinear systems (Yang et al., 2014). It mimics the dynamics of aircraft during flight, landing and turbulence (Kocaoglu & Kuscu, 2013). Many classical and modern methods have been successfully applied for control of these systems (Colon et al., 2015). In a study by Chang et al. (2011) control of ball and beam system using an adaptive fuzzy scheme has been investigated. The authors optimised parameters of fuzzy controllers using proposed approach. The Lyapunov theorem was further used to analyse the close loop stability of the system. Song & Smith (2002) applied incremental best estimate directed search (IBEDS) to fuzzy logic controller for optimisation of ball and beam system. The study showed that it was much easier to control a 4-dimensional ball and beam system than a 4-dimensional inverted pendulum system.

Recently, Lin et al. (2014) proposed a fuzzy neural network (FNN) for position control of a ball and beam system. A cascaded inner-outer loop scheme was constructed and parameters of inner loop FNN were tuned using gradient descent method. In another study by Bhushan et al. (2013) an adaptive control of ball and beam and cart pole system using Lyapunov function with fuzzy approach has been proposed. The adaptive control comprises of an ideal control and a sliding mode control. The sliding mode control was used for ensuring the stability of Lyapunov function. Oh et al. (2009) introduced an optimised fuzzy cascade controller for ball and beam system using hierarchical fair-competition based genetic algorithm (HFCGA). The proposed scheme consists of outer and inner controller in a cascaded architecture. The parameters of fuzzy controller were auto tuned using HFCGA. In a work by Almutairi & Zribi (2010) a sliding mode control of ball on a beam system has been proposed. The authors developed a static and dynamic sliding mode controller using both simplified and complete model. The results showed better performance of controllers designed using complete model of the system. Naredo & Castillo (2011) used ant colony optimisation (ACO) for tuning fuzzy controller of ball and beam system. The study considers four inputs with two membership functions. The results showed that ACO with three parameter coding provides an optimal set of parameters for fuzzy control.