Design and rule base reduction of a fuzzy ®lter for the estimation of motor currents

Fuzzy systems have been used extensively and successfully in control systems over the past few decades, but have been applied much less often to ®ltering problems. This is somewhat surprising in view of the dual relationship between control and estimation. This paper discusses and demonstrates the application of fuzzy ®ltering to motor winding current estimation in permanent magnet synchronous motors. Motor winding current estimation is an important problem because in order to implement e€ective closed-loop control, a good estimation of the current is needed. Motor winding currents are notoriously noisy because of electrical noise in the motor drive. We use a fuzzy system with correlation-product inference and centroid defuzzi®cation for motor winding current estimation. With the assumption that the membership functions are triangular (but not necessarily symmetric), we then optimize the membership functions using gradient descent. Next we use singular value decomposition to reduce the rule base for the fuzzy ®lter. Rule base reduction can be important for fuzzy systems in those cases where the fuzzy system needs to be implemented in real time. This is especially true with regard to fuzzy ®ltering in a real time motor controller. The methods discussed in this paper are demonstrated on real motor winding currents that were collected with a digital oscilloscope. It is demonstrated that fuzzy techniques provide a feasible approach to motor current estimation, that gradient descent optimization improves the performance of the ®lter, and that rule base reduction results in a relatively small degradation of ®lter performance. Ó 2000 Elsevier Science Inc. All rights reserved. International Journal of Approximate Reasoning 00 (2000) 00±00 ELSEVIER SCIENCE B.V. [DTD 4.1.0] JOURNAL IJA ARTICLE No. 6108 PAGES 1-23 DISPATCH 17 August 2000 IJA 6108 PROD. TYPE : FROM DISK A www.elsevier.com/locate/ijar E-mail address: [email protected] (D. Simon). 0888-613X/00/$ see front matter Ó 2000 Elsevier Science Inc. All rights reserved. PII: S 0 8 8 8 6 1 3 X ( 0 0 ) 0 0 0 5 4 2 UN CO RR EC TE D PR OO F