Modified Fractional Order Sliding Model Control for DC Speed Regulating System

doi:10.16182/j.issn1004731x.joss.201803041

Abstract

Abstract: An improved fractional order sliding model control (FOSMC) is proposed for DC speed regulating system to eliminate static error easily caused by disturbance in sliding model control. Second order mathematical model is established through taking the derivative of first-order mathematical model of DC speed regulating system. The theory of fractional calculus is introduced to the switching function of sliding mode, and fractional sliding model is designed combining exponential reaching law and second order mathematical model. The control signal of voltage can be obtained through taking output of the controller and integrator in series. Stability analysis of the system is based on Lyapunov theorem and fractional calculus. The simulation and experimental results show that the proposed method not only eliminates static error when inference happens, but also reduces the chattering effectively.

Key words: DC speed regulating system, sliding model control, fractional order calculus, exponential reaching law, static error, chattering

CLC Number:

TP273

Zhao Zhicheng, Zhao Zhitao, Zhang Jinggang, Zhao Xianjiao. Modified Fractional Order Sliding Model Control for DC Speed Regulating System[J]. Journal of System Simulation, 2018, 30(3): 1096-1136.

References 17

[1]	Alexandridis A T, Konstantopoulos G C.Modified PI speed controllers for series-excited dc motors fed by dc/dc boostconverters[J]. Control Engineering Practice (S0967-0661), 2014, 23(2): 14-21.
[2]	Rajasekhar A, Jatoth R K, Abraham A.Design of intelligent PID/PIλDμ speed controller for chopper fed DC motor drive using opposition based artificial bee colony algorithm[J]. Engineering Applications of Artificial Intelligence(S0952-1976), 2014, 29(3): 13-32.
[3]	赵金亮, 贾彦斌. 抗干扰内模控制在直流调速系统中的应用[J]. 火力与指挥控制, 2013, 38(9): 71-73.Zhao Jinliang, Jia Yanbin. Application of an anti-disturbance IMC control in a class of DC speed regulation systems[J]. Fire Control and Command Control, 2013, 38(9): 71-73.
[4]	尹忠刚, 牛剑博, 钟彦儒. 采用免疫算法的感应电机内模控制策略[J]. 中国电机工程学报, 2013, 33(24): 97-105.Yin Zhonggang, Niu Jianbo, Zhong Yanru. Research on an internal model control strategy for induction motors using the immune algorithm[J]. Proceedings of the CSEE, 2013, 33(24): 97-105.
[5]	赵志诚, 桑海, 张井岗. 永磁同步电机速度伺服系统的分数阶内模控制[J]. 系统仿真学报, 2015, 27(2): 384-388.Zhao Zhicheng, Sang Hai, Zhang Jinggang. Fractional Order Internal Model Control of PMSM Speed Servo System[J]. Journal of System Simulation, 2015, 27(2): 384-388.
[6]	Premkumar K, Manikandan B V.Adaptive neuro-fuzzy inference system based speed controller for brushless DC motor[J]. Neurocomputing(S0925-2312), 2014, 138(22): 260-270.
[7]	Premkumar K, Manikandan B V.Fuzzy PID supervised online ANFIS based speed controller for brushless DC motor[J]. Neurocomputing(S0925-2312), 2015, 157(1): 76-90.
[8]	Peng J, Dubay R.Identification and adaptive neural network control of a DC motor system with dead-zone characteristics[J]. ISA Transactions(S0019-0578), 2011, 50(4): 588-598.
[9]	Zhang D, Li H.A stochastic-based FPGA controller for an induction motor drive with integrated neural network algorithms[J]. IEEE Transactions on Industrial Electronics(S0278-0046), 2008, 55(2): 551-561.
[10]	Wang Y, Zhang X, Yuan X, et al.Position-sensorless hybrid sliding-mode control of electric vehicles with brushless DC motor[J]. IEEE Transactions on Vehicular Technology(S0018-9545), 2011, 60(2): 421-432.
[11]	刘晓东, 吴云洁. 一种变结构控制系统设计方法[J]. 电机与控制学报, 2013, 17(6): 75-81.Liu Xiaodong, Wu Yunjie. Design method of variable structure control system[J]. Electric Machines and Control, 2013, 17(6): 75-81.
[12]	张碧陶, 皮佑国. 基于模糊分数阶滑模控制的永磁同步电机控制[J]. 华南理工大学学报(自然科学版), 2012, 40(3): 126-130.Zhang Bitao, Pi Youguo. Control of permanent magnet synchronous motor based on fuzzy fractional-order sliding mode control[J]. Journal of South China University of Technology (Natural Science Edition), 2012, 40(3): 126-130.
[13]	胡强晖, 胡勤丰. 全局滑模控制在永磁同步电机位置伺服中的应用[J]. 中国电机工程学报, 2011, 31(18): 61-66.Hu Qianghui, Hu Qinfeng. Global sliding mode control for permanent magnet synchronous motor servo system[J]. Proceedings of the CSEE, 2011, 31(18): 61-66.
[14]	Furat M, Eker İ.Second-order integral sliding-mode control with experimental application[J]. ISA Transactions(S0019-0578), 2014, 53(5): 1661-1669.
[15]	Zhang B T, Pi Y G, Luo Y.Fractional order sliding-mode control based on parameters auto-tuning for velocity control of permanent magnet synchronous motor[J]. ISA Transactions(S0019-0578), 2012, 51(5): 649-656.
[16]	张碧陶, 皮佑国. 永磁同步电机伺服系统模糊分数阶滑模控制[J]. 控制与决策, 2012, 27(12): 1776-1780.Zhang Bitao, Pi Youguo. Fractional order fuzzy sliding mode control for permanent magnet synchronous motor servo drive[J]. Control and Decision, 2012, 27(12): 1776-1780.
[17]	代群, 李辉来. 几类线性分数阶微分方程解的结构[J]. 吉林大学学报(理学版), 2011, 49(4): 580-586.Dai Qun, Li Huilai. Structures of solutions of several kinds of linear fractional differential equations[J]. Journal of Jilin University (Science Edition), 2011, 49(4): 580-586.