Stabilization and Control of Elastic Inverted Pendulum System (EIPS) Using Adaptive Fuzzy Inference Controllers

Stabilization and Control of Elastic Inverted Pendulum System (EIPS) Using Adaptive Fuzzy Inference Controllers

Ashwani Kharola (Department of Mechanical Engineering, Graphic Era University, Dehradun, India) and Pravin P. Patil (Department of Mechanical Engineering, Graphic Era University, Dehradun, India)
Copyright: © 2017 |Pages: 12
DOI: 10.4018/IJFSA.2017100102
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Elastic Inverted Pendulum system (EIP) are very popular objects of theoretical investigation and experimentation in field of control engineering. The system becomes highly nonlinear and complex due to transverse displacement of elastic pole or pendulum. This paper presents a comparison study for control of EIP using fuzzy and hybrid adaptive neuro fuzzy inference system (ANFIS) controllers. Initially a fuzzy controller was designed, which was used for training and tuning of ANFIS controller using gbell shape membership functions (MFs). The performance of complete system was evaluated through output responses of settling time, steady state error and maximum overshoot. The study also highlights effect of varying number of MFs on training error of ANFIS. The results showed better performance of ANFIS controller compared to fuzzy controller.
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The EIP belongs to a class of highly non-linear, multivariable, strong coupling and unstable control system. It attracts attention of many researchers and mimics dynamics behaviour of various nonlinear systems resulting in weight reduction of robotic assemblies for increased speed and efficiency. The induction flexible rod makes control of EIP more challenging compared to conventional rigid inverted pendulum (Xu & Yu, 2004). Elasticity is an essential criterion which is always considered for control of flexible mechanical structures (Kawaji & Kanazawa, 1991). It results due to trading off between mass and length requirement in optimising effectiveness of the system (Moudgal, Kwong, Passino & Yurkovich, 1995). Several physical models like elastic columns (Azimi and Koofigar, 2015), rockets (Dadios and Williams, 1998) and walking robots can be considered as EIP systems. Various control techniques has been successfully applied for control of these nonlinear systems. According to Kawaji and Kanazawa (1991) a simple model of flexible inverted pendulum can be derived using an elastic joint double inverted pendulum. The model has been built and verified through experiments using a H/sub-infinity controller. According to Dadios and Williams (1996), genetic algorithm can be combined with fuzzy logic to control flexible pendulum system. The genetic algorithm was employed to provide values for extracting rules of fuzzy controller. Results showed better accuracy of proposed controller while predicting output of flexible pendulum system. Loginov (2002) considered stabilisation of inverted pendulum connected by two elastic levers. The study elaborates applicability of parametric amplification through resonant perturbation of elastic oscillations. The authors further compared resonant mechanism of instable equilibrium to direct dynamic stabilisation of inverted pendulum.

In a study by Galan et al. (2005) a new optimal type-2 fuzzy sliding mode control of Inverted pendulum systems has been presented. The authors designed a novel heuristic algorithm using particle swarm optimization with random inertia weight (RNN-PSO) for realization of the proposed system. Lobus et al. (2007) examined effect of different types of springs on equilibrium states of conventional inverted pendulum. The authors analysed angular and linear eccentricities of follower force during control of proposed system. Arinstein and Gitterman (2008) investigated control of spring inverted pendulum subjected to vertical oscillations at suspension point. The authors analysed interaction between radial and oscillating modes for attaining better stability of proposed system. Jiali and Gexue (2009) proposed a dynamic model of flexible inverted pendulum using floating frame of reference formulation (FFRF). The state space equations of proposed system were established and verified through simple low pass filters for control.

Le et al. (2010) performed stabilisation of a damped-elastic-jointed inverted pendulum which was subjected to a periodic force. The study considered three controllers namely optimal fuzzy control using hedge algebras (OFCHA), fuzzy control using hedge algebras (FCHA) and conventional fuzzy control (CFC) for control of proposed system. Litak and Coccolo (2012) studied dynamics of EIP having tip mass under horizontal harmonic excitation. The authors examined the conditions for overcoming large oscillations and tip mass using Melnikov criterion. The simulation results verified validity of proposed approach. In a study by Semenov et al. (2015), hysteretic nonlinearity in suspension point of EIP has been investigated. The authors performed stabilisation and optimisation of proposed system. An algorithm based on bionic model was applied to find optimal parameters of system. This paper illustrates a new approach of learning and tuning ability of ANFIS controllers. The results of fuzzy were further used for optimising and tuning of ANFIS controller. The study also highlights a relationship between training error and number of MFs. Finally, a comparison is made to judge performance of both controllers.

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