Abstract：In order to overcome the problem of backlash nonlinearity and parameter time-varying in mechatronic servo systems,a chattering free full order sliding mode control strategy is proposed.The dead zone model of the backlash nonlinearity can be approximated by the proposed differentiable function.The superposition of the approximation error,the unmodeled dynamics,and the external disturbance can be regarded as the disturbance-like term.The continuous state-space model of the servo systems with the backlash nonlinearity is established and divided into three subsystems.The terminal sliding mode control law is constructed based on the backstepping design principle,which can make the tracking error converge to an arbitrarily small residual within finite time and achieve the precise compensation of the backlash.The finite-time convergence condition of the closed-loop system is analyzed using the Lyapunov theory.The experimental test verifies the effectiveness of the proposed control approach.
李兵强, 陈晓雷, 林辉, 吕帅帅, 马冬麒. 机电伺服系统齿隙补偿及终端滑模控制[J]. 电工技术学报, 2016, 31(9): 162-168.
Li Bingqiang, Chen Xiaolei, Lin Hui, Lü Shuaishuai, Ma Dongqi. Terminal Sliding Mode Control for Mechatronic Servo Systems with Backlash Nonlinearity Compensation. Transactions of China Electrotechnical Society, 2016, 31(9): 162-168.
[1] Gang T,Kokotovic P V.Adaptive control of systems with backlash[J].Automatica,1993,29(2):323-335. [2] Mattias N,Per G.Controlling mechanical systems with backlash:a survey[J].Automatica,2002,38(10):1633-1649. [3] Zhou J,Wen C Y,Zhang Y.Adaptive backstepping control of a class of uncertain nonlinear systems with unknown backlash-like hysteresis[J].IEEE Transactions on Automatic Control,2004,49(10):1751-1759. [4] Zhou J,Zhang C J,Wen C Y.Robust adaptive output control of uncertain nonlinear plants with unknown backlash nonlinearity[J].IEEE Transactions on Automatic Control,2007,52(3):503-509. [5] Liu Y J,Tong S C.Adaptive fuzzy control for a class of nonlinear discrete-time systems with backlash[J].IEEE Transactions on Fuzzy Systems,2014,22(5):1359-1365. [6] Wang H Q,Chen B,Liu K F,et al.Adaptive neural tracking control for a class of nonstrict-feedback stochastic nonlinear systems with unknown backlash-like hysteresis[J].IEEE Transactions on Neural Networks and Learning Systems,2014,25(5):947-958. [7] Tarbouriech S,Queinnec I,Prieur C.Stability analysis and stabilization of systems with input backlash[J].IEEE Transactions on Automatic Control,2014,59(2):488-494. [8] Philipp R,Thomas B,Miroslav B,et al.Hybrid approach to modeling,control and state estimation of mechanical systems with backlash[J].International Journal of Control,2007,80(11):1729-1740. [9] Corradini M L,Orlando G.Robust stabilization of nonlinear uncertain plants with backlash or dead zone in the actuator[J].IEEE Transactions on Control Systems Technology,2002,10(1):158-166. [10]朱胜,孙明轩,何熊熊.齿隙非线性输入系统的迭代学习控制[J].自动化学报,2011,37(8):1014-1017. Zhu Sheng,Sun Mingxuan,He Xiongxiong.Iterative learning control of a class of nonlinear systems with input backlash[J].Acta Automatica Sinica,2011,37(8):1014-1017. [11]Taware A,Tao G,Teolis C.Design and analysis of a hybrid control scheme for sandwich nonsmooth nonlinear systems[J].IEEE Transactions on Automatic Control,2002,47(1):145-150. [12]Tao G,Ma X L,Ling Y.Optimal and nonlinear decoupling control of systems with sandwiched backlash[J].Automatica,2001,37(2):165-176. [13]Shi Z G,Zuo Z Y.Backstepping control for gear transmission servo systems with backlash nonlinearity[J].IEEE Transactions on Automation Science and Engineering,2015,12(2):752-757. [14]杜仁慧,吴益飞,陈威,等.考虑齿隙伺服系统的反步自适应模糊控制[J].控制理论与应用,2013,30(2):254-260. Du Renhui,Wu Yifei,Chen Wei,et al.Adaptive backstepping fuzzy control for servo systems with backlash[J].Control Theory & Applications,2013,30(2):254-260. [15]付培华,陈振,丛炳龙,等.基于反步自适应滑模控制的永磁同步电机位置伺服系统[J].电工技术学报,2013,28(9):288-293. Fu Peihua,Chen Zhen,Cong Binglong,et al.A position servo system of permanent magnet synchronous motor based on back-stepping adaptive sliding mode control[J].Transactions of China Electrotechnical Sosiety,2013,28(9):288-293. [16]黄庆,黄守道,伍倩倩,等.基于模糊自抗扰控制器的永磁同步电动机伺服系统[J].电工技术学报,2013,28(9):294-301. Huang Qing,Huang Shoudao,Wu Qianqian,et al.PMSM servo system based on fuzzy active-disturbance rejection controller[J].Transactions of China Electrotechnical Sosiety,2013,28(9):294-301. [17]Merzouki R,Davila J A,Fridman L,et al.Backlash phenomenon observation and identification in electromechanical system[J].Control Engineering Practice,2007,15(4):447-457. [18]Feng Y,Han F L,Yu X H.Chattering free full-order sliding-mode control[J].Automatica,2014,50(4):1310-1314. [19]许叙遥,林辉.基于动态滑模控制的永磁同步电机位置速度一体化设计[J].电工技术学报,2014,29(5):77-83. Xu Xuyao,Lin Hui.Integrated design for permanent magnet synchronous motor servo systems based on dynamic sliding mode control[J].Transactions of China Electrotechnical Sosiety,2014,29(5):77-83. [20]Levant A.Chattering analysis[J].IEEE Transactions on Automatic Control,2010,55(6):1380-1389. [21]Yu S H,Yu X H,Bijan S,et al.Continuous finite-time control for robotic manipulators with terminal sliding mode[J].Automatica,2005,41(11):1957-1964. [22]Nekoukar V,Erfanian A.Adaptive fuzzy terminal sliding mode control for a class of MIMO uncertain nonlinear systems[J].Fuzzy Sets and Systems,2011,179(1):34-49.
2016, Vol. 31 
