Balancing Inverted Pendulum by Angle Sensing Using Fuzzy Logic ...

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Sensors & Transducers Journal, Vol. 133, Issue 10, October 2011, pp. 74-82The values of KPobtained from fuzzy system is fed into GA system. The optimal value of K P isobtained on the basis of cost functionCost function = 0.8 + 0.2 overshoot(in this case) (13)eSSFigs. 6 and 7 are the step responses for K GA , where K GA is the value of K P obtained from GA system.Fig. 6. Step Response of the System at K P =456.Fig. 7. Step Response of the System at K P =410.3. ConclusionAs depicted in Fig. 8. the results from fuzzy system have been improved by GA system. The GAsystem finds such a value of K P for each input, so that the cost function is decreased for each input.80
Sensors & Transducers Journal, Vol. 133, Issue 10, October 2011, pp. 74-82Here we have given more weightage to error than overshoot. So the output values of K P are closer toupper limit (K P =529). If more weightage is given to overshoot, then the output values of K P will becloser to lower limit (K P =264).Comparison of cost functionCost Function2.22.182.162.142.122.12.082.062.042.0221 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21Data PointsFig. 8. Comparison of Cost Function.KfuzzifiedKgaAs we can see in Fig. 8, the proposed controller gives the satisfactory response for the rule base offuzzy logic, and the results are further improved by the use of GA supervisor after Fuzzy logicSupervisor. Hence for the given design requirement the above simulated controller is satisfactory. Wealso can conclude that the system approaches towards stability with time.AcknowledgmentThe authors are grateful to the management of Krishna Engineering College for giving all the facilitiesrequired to carry out the work. We thank Prof S. B. Bajpayee and Prof T. Ramanujam for theirencouragement.References[1]. Hauser John, Saccon Alessandro, and Frezza Ruggero, On the Driven Inverted Pendulum, in Proc. of the44 th IEEE Conference on Decision and Control, and the European Control Conference, 2005,pp. 6176-6180.[2]. Furuta K., M. Yamakita M and S. Kobayashi, Swing-up control of inverted pendulum using pseudo-statefeedback, in Proceedings of the Institution of Mechanical Engineers, Part I: Journal of Systems andControl Engineering November, 206, no.6, 1992, pp. 263-269.[3]. A. Ohsumi and T. Izumikawa, Nonlinear Control of Swing-up and Stabilization of an Inverted pedndulum,in Proceedings of the 34 th Conference on Decision & Control, 1995, pp. 3873-3880.[4]. Wang Q., Spronck Pieter, and Tracht Rudolf, An overview of Genetic Algorithms Applied to ControlEngineering Problems, in Proc. of the International Conference on Machine Learning and Cybernetics,2003, pp. 1651 – 1656.[5]. Kui Fu Chen, Standing Human - an Inverted Pendulum, Lat. Am. J. Phys. Educ., Vol. 2, No. 3, Sept. 2008.[6]. W. Zhong and H. Röck, Energy and Passivity Based Control of the Double Inverted Pendulum on a Cart,in Proc. of the IEEE Conference on Control Applications, 2001.[7]. Samatthachai Panya, Taworn Benjanarasuth, Songmoung Nundrakwang, Jongkol Ngamwiwit and NoriyukiKomine, Hybrid Controller for Inverted Pendulum System, in Proc. of the IEEE International Symposium81
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