Decomposition of a Fuzzy Controller

Decomposition of a Fuzzy Controller - Decomposition of a...

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Decomposition of a Fuzzy Controller Based on the Inference Break-up Method Marjan Golob, Laboratory for Process Automation, Faculty of Electrical Engineering and Computer Science, University of Maribor, Smetanova 17, 2000 Maribor, SLOVENIA, Tel: +386 62 2207161, Fax: +386 62 211-178 , Email: mgolob@uni- mb.si , URL: http://www.au.feri.uni-mb.si/~marjan/ Abstract A concept called the decomposition of multivariable control rules is presented. Fuzzy control is the application of the compositional rule of inference and it is shown how the inference of the rule base with complex rules can be reduced to the inference of a number of rule bases with simple rules. A fuzzy logic based controller is applied to a simple magnetic suspension system. The controller has proportional, integral and derivative separate parts which are tuned independently. This means that all parts have their own rule bases. By testing it was formed out that the fuzzy PID controller gives better performance over a typical operational range then a traditional linear PID controller. The magnetic suspension system and the contact-less optical position measurement system have been developed and applied for the comparative analysis of the real-time conventional PID control and the fuzzy control. 1. Introduction Fuzzy set theory was introduced by Zadeh [1] in 1965 and has been evolved as a powerful modelling tool that can cope with the uncertainties and non-linearities of modern control systems. Fuzzy controllers have become popular in recent years because they do not necessarily require a theoretical model of the plant which is to be controlled. Therefore, in order to develop a fuzzy controller, one needs to first have access to a human expert, find quantifiable means to present the expert’s experience, and determine a mapping from states of the plant to the fuzzy measures with which the expert’s knowledge is quantified. In [2] a supervisory fuzzy logic based controller is applied to the magnetic suspension system. The control architecture consists of two loops; a pole placement controller is utilised in the internal loop, and a supervisory fuzzy controller with a proportional-derivative structure is embedded in the other loop to enhance the transient response of the system. This control design is compared in simulation studies with a classical pole placement controller. Several magnetic suspension systems have been developed and applied for magnetically levitated transit systems by Japanese and American corporations during the last years [3] , [4] . In most cases the control system and energy supply requirements to levitate the vehicle have a higher level of complexity. The non-linear nature of the system dynamics coupled with non-linear characteristics of the actuators complicate the controller design. The classical controller development approach relies on a linearization of the system dynamics and on the application of a PID controller to compensate the effects of the non-modelled non-linearities. By this approach certain system is stabilized close to its nominal operating point. Problems could be existent in the
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case when the set point is changeable within wide operating range. The method of robust
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This note was uploaded on 12/29/2011 for the course ME 680 taught by Professor Na during the Fall '10 term at Purdue University-West Lafayette.

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Decomposition of a Fuzzy Controller - Decomposition of a...

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