伺服电机驱动的连铸结晶器振动系统受限状态下预设性能控制
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摘要
以伺服电机驱动的连铸结晶器振动位移系统为研究对象,针对系统输入和状态受限问题,考虑系统存在的参数不确定性和负载转矩扰动影响,设计一种基于观测器的预设性能自适应控制器.首先,针对系统存在的参数不确定性、负载转矩扰动等问题,基于Lyapunov函数设计变增益扩张状态观测器,在保证观测精度的同时,削弱峰值现象;其次,考虑状态和输入受限的情况,将预设性能函数与Backstepping技术相结合设计控制器,构建指令滤波器解决"计算膨胀"问题,引入动态补偿量对观测器及受限状态产生的误差进行补偿,并对所设计的控制器进行稳定性分析;最后,通过仿真对比实验验证控制器的有效性.
With the continuous casting mold vibration displacement system driven by a servo motor as the research object, in view of the constrained input and states, the system parameter uncertainties and the load torque disturbance, an observer-based adaptive prescribed performance controller is proposed. Firstly, as to the parameter uncertainties and the load torque disturbance, an extended state observer with time-varying gain is designed based on the Lyapunov function,which can preserve the estimation accuracy as well as weakening the peaking phenomenon. The controller is designed by combining the prescribed performance function and the adaptive backstepping technique. Take into account the issue of states and input constraints, the constrained command filters are adopted to solve the problem of "computing inflation". A dynamic compensator is introduced to compensate the error caused by the observer and constrained states,and the stability of the controller is analyzed. Finally, the simulation results show the effectiveness of proposed control scheme.
With the continuous casting mold vibration displacement system driven by a servo motor as the research object, in view of the constrained input and states, the system parameter uncertainties and the load torque disturbance, an observer-based adaptive prescribed performance controller is proposed. Firstly, as to the parameter uncertainties and the load torque disturbance, an extended state observer with time-varying gain is designed based on the Lyapunov function,which can preserve the estimation accuracy as well as weakening the peaking phenomenon. The controller is designed by combining the prescribed performance function and the adaptive backstepping technique. Take into account the issue of states and input constraints, the constrained command filters are adopted to solve the problem of "computing inflation". A dynamic compensator is introduced to compensate the error caused by the observer and constrained states,and the stability of the controller is analyzed. Finally, the simulation results show the effectiveness of proposed control scheme.
引文
[1]干勇,唐红伟,仇圣桃.连续铸钢在钢铁生产流程中的作用及现代连铸技术简介[J].中国科学(E辑:技术科学), 2008, 38(9):1384-1390.(Gan Y, Tang H W, Chou S T. Research on Nonsinusoidal The role of Continuous Casting in steel production process and introduction of the modern continuous casting technology[J]. Science in China(Series E:Technological Sciences), 2008, 38(9):1384-1390.)
[2] Meng X, Zhu M. Optimization of non-sinusoidal oscillation parameters for slab continuous casting mold with high casting speed[J]. Iron Making&Steel Making,2009, 36(4):300-310.
[3]李炜,王可宏.基于变增益ESO与逆系统方法的非线性系统故障调节[J].北京工业大学学报, 2017, 43(5):736-744.(Li W, Wang K H. Fault accommodation method of nonlinear system based on time-varying gain extended state observer and inverse system method[J]. J of Beijing Universiyt of Technology, 2017, 43(5):736-744.)
[4]卢晓东,赵辉,赵斌,等.基于干扰补偿的拦截弹制导控制一体化设计[J].控制与决策, 2017, 32(10):1782-1788.(Lu X D, Zhao H, Zhao B, et al. Disturbance compensation-based integrated guidance and control design for near space interceptor[J]. Control and Decision, 2017, 32(10):1782-1788.)
[5]于洪国,康忠健,陈瑶.基于双曲正切函数的二阶时变参数扩张状态观测器[J].控制理论与应用, 2016,33(4):530-534.(Yu H G, Kang Z J, Chen Y. Time-varying parameter second-order extended state observer based on hyperbolic tangent function[J]. Control Theory&Applications,2016, 33(4):530-534.)
[6] Hoo C L, Haris S M, Chung E C Y, et al. New integral antiwindup scheme for PI motor speed control[J]. Asian J of Control, 2015, 17(6):2115-2132.
[7] Chunyu Yang, Lingli Zhang, Jing Sun. Anti-windup controller design for singularly perturbed systems subject to actuator saturation[J]. IET Control Theory&Applications, 2016, 10(4):469-476.
[8]李理,刘杨,陈兴林.考虑输入饱和的离散最优积分滑模控制[J].控制与决策, 2016, 31(7):1317-1320.(Li L, Liu Y, Chen X L. Discrete-time optimal integral sliding mode control with input saturation[J]. Control and Decision, 2016, 31(7):1317-1320.)
[9] Egashira Y, Harakawa M, Ozaki T, et al. Current command compensation for PM servo motor considering voltage saturation caused by both rapid change in the current command and high speed rotation[J]. Electrical Engineering in Japan, 2016, 196(2):24-33.
[10] Charalampos P B, George A R. Prescribed performance adaptive control of SISO feedback linearizable systems with disturbances[C]. The 16th Mediterranean Conf on Control and Automation. Ajaccio:IEEE, 2008:1035-1040.
[11] Kostarigka A K, Rovithakis G A. Prescribed performance output feedback control:An approximate passivation approach[C]. The 18th Mediterranean Conf on Control and Automation. Morocco:IEEE, 2010:11–16.
[12] Seong I Han, Jang M Lee. Dynamic surface control for prescribed performance of a nonlinear danamic system[J].IEEE Trans on Industrial Electronics, 2014, 61(2):1099-1112.
[13] Jing N, Qiang C, Ren X M, et al. Adaptive prescribed performance motion control of Servo mechanisms with friction compensation[J]. IEEE Trans on Industrial Electronics, 2014, 61(1):486-494.
[14] Charalampos P Bechlioulis, George A Rovithakis Prescribed. Performance adaptive control for multi-input multi-output affine in the control nonlinear systems[J].IEEE Trans on Automatic Control, 2008, 53(9):2090-2099.
[15] Bechlioulis C P, Rovithakis G A. Prescribed performance adaptive control for multi-input multi-output affine in the control nonlinear systems[J]. IEEE Trans on Automatic Control, 2010, 55(5):1220-1226.
[16] Liu Le, Yan-ru Dun, Yi-ming Fang, et al. Modeling and verification of the nonlinear system of oscillation platform of continuous casting mold driven by servo motor[J].Advances in Mechanical Engineering, 2016, 8(7):1-9.
[17]亢克松,刘乐,方一鸣,等.伺服电机驱动的连铸结晶器振动位移系统反步滑模控制[J].控制理论与应用,2016, 33(11):1442-1448.(Kang K S, Liu L, Fang Y M, et al. Backstepping sliding mode control for continuous cast mold oscillation displacement system driven by servo motor[J]. Control Theory&Applications, 2016, 33(11):1442-1448.)
[18] Angelo Alessandri, Anna Rossi. Increasing-gain observers for nonlinear systems:Stability and design[J].Automatica, 2015, 57:180-188.
[19] Khalil H K. Nonlinear systems[M]. 3rd ed. New Jersey:Prentice Hall, 2001:102-105.
[2] Meng X, Zhu M. Optimization of non-sinusoidal oscillation parameters for slab continuous casting mold with high casting speed[J]. Iron Making&Steel Making,2009, 36(4):300-310.
[3]李炜,王可宏.基于变增益ESO与逆系统方法的非线性系统故障调节[J].北京工业大学学报, 2017, 43(5):736-744.(Li W, Wang K H. Fault accommodation method of nonlinear system based on time-varying gain extended state observer and inverse system method[J]. J of Beijing Universiyt of Technology, 2017, 43(5):736-744.)
[4]卢晓东,赵辉,赵斌,等.基于干扰补偿的拦截弹制导控制一体化设计[J].控制与决策, 2017, 32(10):1782-1788.(Lu X D, Zhao H, Zhao B, et al. Disturbance compensation-based integrated guidance and control design for near space interceptor[J]. Control and Decision, 2017, 32(10):1782-1788.)
[5]于洪国,康忠健,陈瑶.基于双曲正切函数的二阶时变参数扩张状态观测器[J].控制理论与应用, 2016,33(4):530-534.(Yu H G, Kang Z J, Chen Y. Time-varying parameter second-order extended state observer based on hyperbolic tangent function[J]. Control Theory&Applications,2016, 33(4):530-534.)
[6] Hoo C L, Haris S M, Chung E C Y, et al. New integral antiwindup scheme for PI motor speed control[J]. Asian J of Control, 2015, 17(6):2115-2132.
[7] Chunyu Yang, Lingli Zhang, Jing Sun. Anti-windup controller design for singularly perturbed systems subject to actuator saturation[J]. IET Control Theory&Applications, 2016, 10(4):469-476.
[8]李理,刘杨,陈兴林.考虑输入饱和的离散最优积分滑模控制[J].控制与决策, 2016, 31(7):1317-1320.(Li L, Liu Y, Chen X L. Discrete-time optimal integral sliding mode control with input saturation[J]. Control and Decision, 2016, 31(7):1317-1320.)
[9] Egashira Y, Harakawa M, Ozaki T, et al. Current command compensation for PM servo motor considering voltage saturation caused by both rapid change in the current command and high speed rotation[J]. Electrical Engineering in Japan, 2016, 196(2):24-33.
[10] Charalampos P B, George A R. Prescribed performance adaptive control of SISO feedback linearizable systems with disturbances[C]. The 16th Mediterranean Conf on Control and Automation. Ajaccio:IEEE, 2008:1035-1040.
[11] Kostarigka A K, Rovithakis G A. Prescribed performance output feedback control:An approximate passivation approach[C]. The 18th Mediterranean Conf on Control and Automation. Morocco:IEEE, 2010:11–16.
[12] Seong I Han, Jang M Lee. Dynamic surface control for prescribed performance of a nonlinear danamic system[J].IEEE Trans on Industrial Electronics, 2014, 61(2):1099-1112.
[13] Jing N, Qiang C, Ren X M, et al. Adaptive prescribed performance motion control of Servo mechanisms with friction compensation[J]. IEEE Trans on Industrial Electronics, 2014, 61(1):486-494.
[14] Charalampos P Bechlioulis, George A Rovithakis Prescribed. Performance adaptive control for multi-input multi-output affine in the control nonlinear systems[J].IEEE Trans on Automatic Control, 2008, 53(9):2090-2099.
[15] Bechlioulis C P, Rovithakis G A. Prescribed performance adaptive control for multi-input multi-output affine in the control nonlinear systems[J]. IEEE Trans on Automatic Control, 2010, 55(5):1220-1226.
[16] Liu Le, Yan-ru Dun, Yi-ming Fang, et al. Modeling and verification of the nonlinear system of oscillation platform of continuous casting mold driven by servo motor[J].Advances in Mechanical Engineering, 2016, 8(7):1-9.
[17]亢克松,刘乐,方一鸣,等.伺服电机驱动的连铸结晶器振动位移系统反步滑模控制[J].控制理论与应用,2016, 33(11):1442-1448.(Kang K S, Liu L, Fang Y M, et al. Backstepping sliding mode control for continuous cast mold oscillation displacement system driven by servo motor[J]. Control Theory&Applications, 2016, 33(11):1442-1448.)
[18] Angelo Alessandri, Anna Rossi. Increasing-gain observers for nonlinear systems:Stability and design[J].Automatica, 2015, 57:180-188.
[19] Khalil H K. Nonlinear systems[M]. 3rd ed. New Jersey:Prentice Hall, 2001:102-105.