Research For Intelligent Fractional Order Sliding Mode Control And System Parameters Tuning

One of the most distinguished features of the sliding mode control(SMC) is that afterreaching the sliding mode, the system is robust to parameter uncertainties and disturbances.And the control algorithm is simple and easy to be realized. All these fetures of SMC lead tothe importamt position of SMC theory. However, the chattering existed in SMC system limitsits application. Thus, counteracting the chattering for SMC system interests many researchers.And the study of this paper focusing on reducing the chattering is valuable.For dealing with the chaterring, this paper integrates the advantage of fractional ordercalculus and SMC to propose a fractional order calculus SMC system. The stability andmechanism for descring the chaterring are analysed. Considering the uncertainties impact onchattering, a tuning method based on intenlegent algorithm is proposed to obtain the gain offractional order SMC system. Based on a deep analysis of the chaterring occurring, afractional order SMC is propsed, which is robust with regard to parameters variations anddisturbances as well as eliminating the chaterring. And a tuning method is proposed for thiscontrol scheme. This paper integrates the fractional calculus and intelligent algorithm intoSMC to deal with chattering and give the parameters tuning methods. The research contentsare as follow:Based on depth analysis of chattering phenomenon existing in the traditional firstorder SMC systems, a hybrid first order and second order SMC system isproposed, the stability proof of the hybrid SMC system is given. The advantages of the hybridcontrol system in descring the chaterring is superior to that of a single first order or secondorder SMC system. Simulations and experiments based on permanent magnet synchronousmotor servo system verificate that the control method is effective.Using the unique convergence properties that the energy transmission speed of fractionalorder systems is slower than that of integer order system in the sliding phase,a fractional order sliding mode interface is designed to drive the systemstatus slowly converge to zero. Fractional calculus is introduced to enhance the controlperformance, but it also adds the difficulty in parameters tuning. Based on the tradicionalcontrol theory, this paper gives the tuning rules for the control law. And using fuzzy inference algorithm, a tuning method is proposed for switching gain. Since the reaching phase of SMCis sencetive to parameters variations and disturbances, a control scheme based on overallrobustness sliding mode interface is proposed. Simulations and experiments basedon permanent magnet synchronous motor servo system verificate that the control methodrudecues the chaterring effectively.Since the design of SMC relaies on dynamic model, it is difficult for complex system toyield the control law. Using the advantages of fuzzy inference system and fractional calculus,a fuzzy controller based on fractional order sliding mode interface is proposed. Consideringthe uncertainties, a fuzzy logic inference sysem is adopted to obtain the gain of SMC based onequivalent control law. Simulations and experiments based on permanent magnet synchronousmotor servo system verificate that the control schemes are not only robust to disturbance, butachieve high control performance.The building of fuzzy controller requires some experiences. It is not easy to apply.Instead, using the learning function of neural network, a tuning method based on neuralnetwork control algorithm is designed to obtain the gain of fractional order SMC system. Anda neural network controller is proposed to deal with the static error existing in fuzzy controlsystem. The stability sproof is given for fractional order system with the stability theory ofinteger order system. Simulations results show that the control schemes achieve high controlperformance under the existence of external disturbances and parameters variations.Even though the intelligent algorithm is used to design the fractional order SMC, thechaterring can not be elminated. This paper proposed a continue PI~λD~μcontrol law to replacethe switching control action. It can drive the system states to given sliding interface whereverthe initial states are. The given lemma shows validate that when some conditions are satisfied,this control schem is robut with regard to disturbances and parameters variations. And thetuning method for controller parameters is given. Simulations results show that the controlschemes achieve high control performance under the existence of external disturbances andparameters variations.