一种新型变指数幂次趋近律的设计与分析
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摘要
针对传统滑模趋近律中的抖振现象、收敛速度慢等不足,提出一种新型变指数幂次趋近律。该趋近律通过使用变指数幂次项,实现了在系统趋近过程中根据不同阶段进行自适应调节的功能,大幅提高了系统的收敛速度,并具有全局有限时间收敛特性。当系统存在模型不确定型和外部有界扰动时,滑模变量可在有限时间内收敛到边界层宽度为1左右的稳态误差界内,且该稳态误差小于现有的双幂次趋近律、快速幂次趋近律和多幂次趋近律等方法的结果。仿真算例验证了所提出趋近律的有效性和优越性。
A variable power reaching law for sliding mode control is proposed aiming at reducing the chattering phenomenon in traditional sliding mode control methods and speeding up the convergence speed.The proposed reaching law adjusts the convergence process adaptively by using a variable power term, so that the system has an obviously faster convergence and has no chattering phenomenon, and it also has the characteristic of global finite-time convergence. It is proved that, for a class of bounded external disturbance,the sliding mode variable converges to a preset steady-state error with the boundary layer width of about 1 within finite time, and the value of the steady-state error is less than the existed reaching laws such as double power reaching law, the fast power reaching law, and so on. Simulation results are given, which demonstrate the validity and superiority of the proposed method.
A variable power reaching law for sliding mode control is proposed aiming at reducing the chattering phenomenon in traditional sliding mode control methods and speeding up the convergence speed.The proposed reaching law adjusts the convergence process adaptively by using a variable power term, so that the system has an obviously faster convergence and has no chattering phenomenon, and it also has the characteristic of global finite-time convergence. It is proved that, for a class of bounded external disturbance,the sliding mode variable converges to a preset steady-state error with the boundary layer width of about 1 within finite time, and the value of the steady-state error is less than the existed reaching laws such as double power reaching law, the fast power reaching law, and so on. Simulation results are given, which demonstrate the validity and superiority of the proposed method.
引文
[1] Utikn V I. Variable structure systems with sliding modes[J]. IEEE Transactions on Automatic Control, 1977, 22(2):212-222.
[2] Thiago B, Vinicius F M, Hilton A G, et al. Discrete time sliding mode observer for sensor-less vector control of permanent magnet synchronous machine[J]. IEEE Transactions on Industrial Electronics, 2014, 61(4):1679-1691.
[3]张居乾,师玉茹,任朝晖,等.基于扩张观测器的四旋翼无人机轨迹鲁棒滑模控制[J].中国惯性技术学报, 2018,26(2):247-254.Zhang J, Shi Y, Ren Z, et al. Robust sliding mode control for quadrotor UAV trajectory based on extended state observer[J]. Control and Decision, 2018, 26(2):247-254.
[4]花文华,张拥军,张金鹏,等.多导弹攻击时间协同的滑模制导律[J].中国惯性技术学报, 2018, 26(1):98-102.Hua W, Zhang Y, Zhang J, et al. Sliding-mode guidance law for attack time cooperation of multi-missiles[J]. Journal of Chinese Inertial Technology, 2018, 26(1):98-102.
[5]宋俊红,宋申民.考虑输入受限和自动驾驶仪延迟的自适应滑模制导律[J].中国惯性技术学报, 2015, 23(3):339-344.Song J, Song S. Adaptive sliding mode guidance law with input constraints and autopilot lag[J]. Journal of Chinese Inertial Technology, 2015, 23(3):339-344.
[6] Xu S, Chen C, Wu Z. Study of nonsingular fast terminal sliding mode fault tolerant control[J]. IEEE Trans on Industrial Electronics, 2015, 62(6):3906-3913.
[7] Yu S, Yu X, Shirinzadeh B, et al. Continuous finite-time control for robotic manipulators with terminal sliding mode[J]. Automatica, 2005, 41(11):1957-1964.
[8]李慧洁,蔡远利.基于双幂次趋近律的滑模控制方法[J].控制与决策, 2016, 31(3):498-502.Li H, Cai Y. Sliding mode control with double power reaching law[J]. Control and Decision, 2016, 42(3):466-472.
[9]廖瑛,杨雅君,王勇,等.滑模控制的新型双幂次组合函数趋近律[J].国防科技大学学报, 2017, 39(3):105-110.Liao Y, Yang Y, Wang Y. Novel double power combination function reaching law for sliding mode control[J].Journal of National University of Defense Technology,2016, 42(3):466-472.
[10]张瑶,马广富,郭延宁,等.一种多幂次滑模趋近律设计与分析[J].自动化学报, 2016, 42(3):466-472.Zhang Y, Ma G, Guo Y, et al. A multi power reaching law of sliding mode control design and analysis[J]. Acta Automatica Sinica, 2016, 42(3):466-472.
[11] Bhat S P, Bernstein D S. Continuous finite-time stabilization of the translational and rotational double integrators[J]. IEEE Transactions on Automatic Control, 1998, 43(5):678-682.
[12] Tian Y, Cai Y. Quaternion based sliding mode attitude control design for spacecraft[J]. IEEE International Conference on Control Science and Systems Engineering,2017.
[2] Thiago B, Vinicius F M, Hilton A G, et al. Discrete time sliding mode observer for sensor-less vector control of permanent magnet synchronous machine[J]. IEEE Transactions on Industrial Electronics, 2014, 61(4):1679-1691.
[3]张居乾,师玉茹,任朝晖,等.基于扩张观测器的四旋翼无人机轨迹鲁棒滑模控制[J].中国惯性技术学报, 2018,26(2):247-254.Zhang J, Shi Y, Ren Z, et al. Robust sliding mode control for quadrotor UAV trajectory based on extended state observer[J]. Control and Decision, 2018, 26(2):247-254.
[4]花文华,张拥军,张金鹏,等.多导弹攻击时间协同的滑模制导律[J].中国惯性技术学报, 2018, 26(1):98-102.Hua W, Zhang Y, Zhang J, et al. Sliding-mode guidance law for attack time cooperation of multi-missiles[J]. Journal of Chinese Inertial Technology, 2018, 26(1):98-102.
[5]宋俊红,宋申民.考虑输入受限和自动驾驶仪延迟的自适应滑模制导律[J].中国惯性技术学报, 2015, 23(3):339-344.Song J, Song S. Adaptive sliding mode guidance law with input constraints and autopilot lag[J]. Journal of Chinese Inertial Technology, 2015, 23(3):339-344.
[6] Xu S, Chen C, Wu Z. Study of nonsingular fast terminal sliding mode fault tolerant control[J]. IEEE Trans on Industrial Electronics, 2015, 62(6):3906-3913.
[7] Yu S, Yu X, Shirinzadeh B, et al. Continuous finite-time control for robotic manipulators with terminal sliding mode[J]. Automatica, 2005, 41(11):1957-1964.
[8]李慧洁,蔡远利.基于双幂次趋近律的滑模控制方法[J].控制与决策, 2016, 31(3):498-502.Li H, Cai Y. Sliding mode control with double power reaching law[J]. Control and Decision, 2016, 42(3):466-472.
[9]廖瑛,杨雅君,王勇,等.滑模控制的新型双幂次组合函数趋近律[J].国防科技大学学报, 2017, 39(3):105-110.Liao Y, Yang Y, Wang Y. Novel double power combination function reaching law for sliding mode control[J].Journal of National University of Defense Technology,2016, 42(3):466-472.
[10]张瑶,马广富,郭延宁,等.一种多幂次滑模趋近律设计与分析[J].自动化学报, 2016, 42(3):466-472.Zhang Y, Ma G, Guo Y, et al. A multi power reaching law of sliding mode control design and analysis[J]. Acta Automatica Sinica, 2016, 42(3):466-472.
[11] Bhat S P, Bernstein D S. Continuous finite-time stabilization of the translational and rotational double integrators[J]. IEEE Transactions on Automatic Control, 1998, 43(5):678-682.
[12] Tian Y, Cai Y. Quaternion based sliding mode attitude control design for spacecraft[J]. IEEE International Conference on Control Science and Systems Engineering,2017.