Interval Type-2 Fuzzy Logic PID Controller Based on Differential Evolution with Better and Nearest Option for Hydraulic
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ISSN:1598-6446 eISSN:2005-4092 http://www.springer.com/12555
Interval Type-2 Fuzzy Logic PID Controller Based on Differential Evolution with Better and Nearest Option for Hydraulic Serial Elastic Actuator Haozhen Dong, Xinyu Li, Pi Shen, Liang Gao*, and Haorang Zhong Abstract: Interval type-2 fuzzy logic controller (IT2FLC) owns good performance under uncertainty and nonlinearity environments while its optimization is hard and complicated. In this work, we propose an optimization method based on differential evolution with better and nearest option (NbDE) for interval type-2 fuzzy logic PID controller (IT2FL-PID-C) in order to control the position of hydraulic serial elastic actuator (SEA). Firstly, a simplified IT2FLPID-C structure with fewer parameters is proposed to reduce the difficulty of the optimization of IT2FL-PID-C. To balance its frequency and step performance, an objective function with weighted integral time absolute error and integral square error is given. Secondly, to investigate the performance of NbDE based IT2FL-PID-C, three experiments are conducted. A set of experiments is taken to determine the weight for fitness function. Then we compare NbDE with other algorithms. In addition, NbDE-IT2FL-PID-C is also compared with other optimization methods. At last, NbDE-IT2FL-PID-C is applied to hydraulic SEA and compared with PID. And a range for the weight of fitness function is given. The results have shown the superiority of NbDE with proposed fitness function to optimize IT2FL-PID-C and the superiority of NbDE-IT2FL-PID-C to control the position of hydraulic SEA. Keywords: Differential evolution with better and nearest option, hydraulic serial elastic actuator, interval type-2 fuzzy logic PID controller, optimization, position control.
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INTRODUCTION
Fuzzy system is a kind of nonlinear system, which has been successfully applied in the field of engineering, such as control [1], fault diagnosis [2], system modeling [3]. Compared with conventional PID system, fuzzy system performeds much better especially for the systems with strong nonlinearity because fuzzy system can be regarded as a special sectional PID system based on human expertise [4, 5]. Fuzzy system consists of two types, Mamdani fuzzy model and Takagi-Sugeno (T-S) fuzzy model. Compared with T-S fuzzy model, Mamdani fuzzy model needs too much computation resource, so current researches concentrate on T-S model [6]. Distinguished from the fuzzy set, fuzzy system is of two types, type-1 fuzzy logic system (T1FLS) and type-2 fuzzy logic system (T2FLS). In real world engineering problems, uncertainty mainly derives from the changing of dynamic property and noise, and obviously it will affect the control performance [7]. T1FLS is sufficient to handle low level of
uncertainties [8–10], while for the system with strong uncertainties, T2FLS may be the better controller because T2FLS utilizes type-2 fuzzy set which offers better capabilities to handle linguistic uncertainties [11]. T2FLS can be divided into two types, interval type-2 fuzzy logi
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