一阶不确定系统的固定时间收敛扰动观测器
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摘要
针对一阶不确定系统中集总扰动的快速估计问题,基于误差放大策略和双极限齐次估计理论设计非递归形式的固定时间收敛扰动观测器,并提出利用幂次函数非线性特性削弱输入信号噪声影响的改进方案.误差放大策略是一种特殊的高增益方法,能够实现修正项中幂次函数支配范围的扩张,进一步提升观测器的收敛速度,并简化参数调试过程;合理选择误差放大系数并忽略修正项中的低阶幂次项,能够简化扰动观测器结构并增强对测量噪声的抑制能力.另外,以广义超螺旋算法为基础,构建固定时间收敛鲁棒扰动观测器.最后,在理论证明分析的基础上,针对是否存在测量噪声的两种情况,对所介绍的3种扰动观测器和一种扩张状态观测器进行对比仿真分析,并总结各类扰动观测器的特点和适用性.
In this paper, non-recursive fixed-time convergent disturbance observers are proposed to deal with the total disturbance fast observation problem for a first-order uncertain system. The primary disturbance observer is designed based on the observer error amplification strategy and bi-limit homogeneous approximation theory. Due to nonlinearity of power functions, a variant of the proposed disturbance observer is presented to obtain the noise tolerance ability. The observer error amplification strategy is actually a special high gain approach, based on which the domination scope of the power functions in the correction terms is extended. At the same time, the convergence rate of the observer is accelerated,and the parameters tuning process is simplified. By choosing a reasonable amplifier and removing the low-order power functions in the correction terms, the structure of the disturbance observer is simplified, and the noise tolerance ability is enhanced. In addition, a fixed-time convergent robust disturbance observer is designed based on generalized super-twisting algorithm as well. Except the detailed theoretical derivation, numerical simulations, with or without measurement noise,are carried out to verify the feasibilities of the proposed three types of the disturbance observers. And, an typical extended state observer is employed for comparison. Finelly, the characteristics and applicability of the disturbance observers are discussed.
In this paper, non-recursive fixed-time convergent disturbance observers are proposed to deal with the total disturbance fast observation problem for a first-order uncertain system. The primary disturbance observer is designed based on the observer error amplification strategy and bi-limit homogeneous approximation theory. Due to nonlinearity of power functions, a variant of the proposed disturbance observer is presented to obtain the noise tolerance ability. The observer error amplification strategy is actually a special high gain approach, based on which the domination scope of the power functions in the correction terms is extended. At the same time, the convergence rate of the observer is accelerated,and the parameters tuning process is simplified. By choosing a reasonable amplifier and removing the low-order power functions in the correction terms, the structure of the disturbance observer is simplified, and the noise tolerance ability is enhanced. In addition, a fixed-time convergent robust disturbance observer is designed based on generalized super-twisting algorithm as well. Except the detailed theoretical derivation, numerical simulations, with or without measurement noise,are carried out to verify the feasibilities of the proposed three types of the disturbance observers. And, an typical extended state observer is employed for comparison. Finelly, the characteristics and applicability of the disturbance observers are discussed.
引文
[1] Chen W H, Yang J, Guo L, et al. Disturbance observer based control and related methods-an overview[J].IEEE Trans on Industrial Electronics, 2016, 63(2):1083-1095.
[2] Shtessel, Y. Edwards C. Fridman L. et al. Sliding modes control and observation[M]. New York:Springer, 2014:251-320.
[3]韩京清.自抗扰控制技术—–估计补偿不确定因素的控制技术[M].北京:国防工业出版社, 2008:183-287.(Han J Q. Active disturbance rejection control technique—the technique for estimating and compensating the uncertainties[M]. Beijing:National Defense Industry Press, 2008:183-287.)
[4] Cruz-Zavala E, Moreno J A, Fridman L M. Uniform robust exact differentiator[J]. IEEE Trans on Automatic Control, 2011, 56(11):2727-2733.
[5] Basin M, Yu P, Shtessel Y. Finite-and fixed-time differentiators utilizing higher-order sliding mode techniques[J].IET Control Theory&Applications, 2017, 11(8):1144-1152.
[6] Andrieu V, Praly L, Astolfi A. Homogeneous approximation, recursive observer design, and output feedback[J]. SIAM J on Control and Optimization, 2008,47(4):1814-1850.
[7] Polyakov A, Fridman L. Stability notions and Lyapunov functions for sliding mode control systems[J]. J of the Franklin Institute, 2014, 351(4):1831-1865.
[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 J, Cai Y L. Sliding mode control with double power reaching law[J]. Control and Decision, 2016, 31(3):498-502.)
[9] Basin M, Panathula C B, Shtessel Y. Adaptive uniform finite-/fixed-time convergent second-order sliding-mode control[J]. Int J of Control, 2016, 89(9):1777-1787.
[10] Cruz-Zavala E, Moreno J A. A new class of fast finite-time discontinuous controllers[C]. The 13th Int Workshop on Variable Structure Systems. IEEE, 2014:1-6.
[11] Angulo M T, Moreno J A, Fridman L. Robust exact uniformly convergent arbitrary order differentiator[J].Automatica, 2013, 49(8):2489-2495.
[12] Lopez-Ramirez F, Polyakov A, Efimov D, et al.Finite-time and fixed-time observers design via implicit Lyapunov function[C]. 2016 European Control Conf.Aadborg:IEEE, 2016:289-294.
[13] Ni J, Liu L, Chen M, et al. Fixed-time disturbance obser-ver design for brunovsky system[J]. IEEE Trans on Circuits and Systems II:Express Briefs, 2017, 65(3):341-345.
[14] Levant A. Robust exact differentiation via sliding mode technique[J]. Automatica, 1998, 34(3):379-384.
[15] Levant A. Higher-order sliding modes, differentiation and output-feedback control[J]. Int J of Control, 2003,76(9/10):924-941.
[16] Guo B Z, Zhao Z. On the convergence of an extended state observer for nonlinear systems with uncertainty[J].Systems&Control Letters, 2011, 60(6):420-430.
[17] Gao Z. Scaling and bandwidth-parameterization based controller tuning[C]. Proc of the American Control Conference. Denver:IEEE, 2006:4989-4996.
[18] Zheng Q, Gao Z. Active disturbance rejection control:Between the formulation in time and the understanding in frequency[J]. Control Theory and Technology, 2016,14(3):250-259.
[19] Zhao Z L, Guo B Z. A nonlinear extended state observer based on fractional power functions[J]. Automatica, 2017,81:286-296.
[20] Zhu Z, Xu D, Liu J, et al. Missile guidance law based on extended state observer[J]. IEEE Trans on Industrial Electronics, 2013, 60(12):5882-5891.
[21] Kumar S R, Rao S, Ghose D. Nonsingular terminal sliding mode guidance with impact angle constraints[J]. J of Guidance, Control, and Dynamics, 2014, 37(4):1114-1130.
[22] Perruquetti W, Floquet T, Moulay E. Finite-time observers:Application to secure communication[J].IEEE Trans on Automatic Control, 2008, 53(1):356-360.
[23] Rosier L. Homogeneous Lyapunov function for homogeneous continuous vector field[J]. Systems&Control Letters, 1992, 19(6):467-473.
[24] Yang F, Wei C, Cui N, et al. Adaptive generalized super-twisting algorithm based guidance law design[C].The 14th Int Workshop on Variable Structure Systems.Nanjing:IEEE, 2016:47-52.
[25] Bhat S P, Bernstein D S. Geometric homogeneity with applications to finite-time stability[J]. Mathematics of Control, Signals, and Systems, 2005, 17(2):101-127.
[2] Shtessel, Y. Edwards C. Fridman L. et al. Sliding modes control and observation[M]. New York:Springer, 2014:251-320.
[3]韩京清.自抗扰控制技术—–估计补偿不确定因素的控制技术[M].北京:国防工业出版社, 2008:183-287.(Han J Q. Active disturbance rejection control technique—the technique for estimating and compensating the uncertainties[M]. Beijing:National Defense Industry Press, 2008:183-287.)
[4] Cruz-Zavala E, Moreno J A, Fridman L M. Uniform robust exact differentiator[J]. IEEE Trans on Automatic Control, 2011, 56(11):2727-2733.
[5] Basin M, Yu P, Shtessel Y. Finite-and fixed-time differentiators utilizing higher-order sliding mode techniques[J].IET Control Theory&Applications, 2017, 11(8):1144-1152.
[6] Andrieu V, Praly L, Astolfi A. Homogeneous approximation, recursive observer design, and output feedback[J]. SIAM J on Control and Optimization, 2008,47(4):1814-1850.
[7] Polyakov A, Fridman L. Stability notions and Lyapunov functions for sliding mode control systems[J]. J of the Franklin Institute, 2014, 351(4):1831-1865.
[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 J, Cai Y L. Sliding mode control with double power reaching law[J]. Control and Decision, 2016, 31(3):498-502.)
[9] Basin M, Panathula C B, Shtessel Y. Adaptive uniform finite-/fixed-time convergent second-order sliding-mode control[J]. Int J of Control, 2016, 89(9):1777-1787.
[10] Cruz-Zavala E, Moreno J A. A new class of fast finite-time discontinuous controllers[C]. The 13th Int Workshop on Variable Structure Systems. IEEE, 2014:1-6.
[11] Angulo M T, Moreno J A, Fridman L. Robust exact uniformly convergent arbitrary order differentiator[J].Automatica, 2013, 49(8):2489-2495.
[12] Lopez-Ramirez F, Polyakov A, Efimov D, et al.Finite-time and fixed-time observers design via implicit Lyapunov function[C]. 2016 European Control Conf.Aadborg:IEEE, 2016:289-294.
[13] Ni J, Liu L, Chen M, et al. Fixed-time disturbance obser-ver design for brunovsky system[J]. IEEE Trans on Circuits and Systems II:Express Briefs, 2017, 65(3):341-345.
[14] Levant A. Robust exact differentiation via sliding mode technique[J]. Automatica, 1998, 34(3):379-384.
[15] Levant A. Higher-order sliding modes, differentiation and output-feedback control[J]. Int J of Control, 2003,76(9/10):924-941.
[16] Guo B Z, Zhao Z. On the convergence of an extended state observer for nonlinear systems with uncertainty[J].Systems&Control Letters, 2011, 60(6):420-430.
[17] Gao Z. Scaling and bandwidth-parameterization based controller tuning[C]. Proc of the American Control Conference. Denver:IEEE, 2006:4989-4996.
[18] Zheng Q, Gao Z. Active disturbance rejection control:Between the formulation in time and the understanding in frequency[J]. Control Theory and Technology, 2016,14(3):250-259.
[19] Zhao Z L, Guo B Z. A nonlinear extended state observer based on fractional power functions[J]. Automatica, 2017,81:286-296.
[20] Zhu Z, Xu D, Liu J, et al. Missile guidance law based on extended state observer[J]. IEEE Trans on Industrial Electronics, 2013, 60(12):5882-5891.
[21] Kumar S R, Rao S, Ghose D. Nonsingular terminal sliding mode guidance with impact angle constraints[J]. J of Guidance, Control, and Dynamics, 2014, 37(4):1114-1130.
[22] Perruquetti W, Floquet T, Moulay E. Finite-time observers:Application to secure communication[J].IEEE Trans on Automatic Control, 2008, 53(1):356-360.
[23] Rosier L. Homogeneous Lyapunov function for homogeneous continuous vector field[J]. Systems&Control Letters, 1992, 19(6):467-473.
[24] Yang F, Wei C, Cui N, et al. Adaptive generalized super-twisting algorithm based guidance law design[C].The 14th Int Workshop on Variable Structure Systems.Nanjing:IEEE, 2016:47-52.
[25] Bhat S P, Bernstein D S. Geometric homogeneity with applications to finite-time stability[J]. Mathematics of Control, Signals, and Systems, 2005, 17(2):101-127.