Design of Adaptive Sliding Mode Controllers for Mismatched Perturbed Systems with Application to Underactuated Systems
详细信息 查看官网全文
- 英文论文题名：Design of Adaptive Sliding Mode Controllers for Mismatched Perturbed Systems with Application to Underactuated Systems
- 论文作者：Chih-Chiang Cheng ; Chao-Heng Ho
- 英文论文作者：Chih-Chiang Cheng ; Chao-Heng Ho ; Department of Electrical Engineering ; Sun Yat-Sen University
- 年：2017
- 作者机构：Department of Electrical Engineering, Sun Yat-Sen University;
- 英文论文关键词：adaptive sliding mode control ; underactuated systems ; mismatched perturbations ; Lyapunov stability theorem ; linear matrix inequality
- 会议召开时间：2017-07-26
- 会议录名称：第36届中国控制会议论文集（A）
- 英文会议录名称：Proceedings of the 36th Chinese Control Conference（A）
- 语种：英文
- 分类号：O231
- 学会代码：KZLL
- 会议名称：第36届中国控制会议
- 会议地点：中国辽宁大连
- 主办单位：中国自动化学会控制理论专业委员会
- 学会名称：中国自动化学会控制理论专业委员会
- 页数：8
- 文件大小：396k
- 原文格式：D
- 会议级别：全国
摘要
A methodology of designing adaptive sliding mode controllers for a class of nonlinear systems with matched and mismatched perturbations is proposed in this paper. Firstly, A specific designed sliding surface function is presented, and the controller with adaptive mechanisms embedded is also designed in accordance with the designated sliding surface function.Secondly, the coefficients of designated sliding surface function are determined by using Lyapunov stability theorem and linear matrix inequality(LMI) optimization technique. Not only the proposed control scheme can drive the trajectories of the controlled systems into the designed sliding surface within a finite time, but also it is able to suppress the mismatched perturbations when the controlled systems are in the sliding mode, and guarantee asymptotic stability. Furthermore, the proposed control scheme can be directly applied to a class of underactuated systems. A numerical example is given for demonstrating the feasibility of the proposed control scheme.
A methodology of designing adaptive sliding mode controllers for a class of nonlinear systems with matched and mismatched perturbations is proposed in this paper. Firstly, A specific designed sliding surface function is presented, and the controller with adaptive mechanisms embedded is also designed in accordance with the designated sliding surface function.Secondly, the coefficients of designated sliding surface function are determined by using Lyapunov stability theorem and linear matrix inequality(LMI) optimization technique. Not only the proposed control scheme can drive the trajectories of the controlled systems into the designed sliding surface within a finite time, but also it is able to suppress the mismatched perturbations when the controlled systems are in the sliding mode, and guarantee asymptotic stability. Furthermore, the proposed control scheme can be directly applied to a class of underactuated systems. A numerical example is given for demonstrating the feasibility of the proposed control scheme.
A methodology of designing adaptive sliding mode controllers for a class of nonlinear systems with matched and mismatched perturbations is proposed in this paper. Firstly, A specific designed sliding surface function is presented, and the controller with adaptive mechanisms embedded is also designed in accordance with the designated sliding surface function.Secondly, the coefficients of designated sliding surface function are determined by using Lyapunov stability theorem and linear matrix inequality(LMI) optimization technique. Not only the proposed control scheme can drive the trajectories of the controlled systems into the designed sliding surface within a finite time, but also it is able to suppress the mismatched perturbations when the controlled systems are in the sliding mode, and guarantee asymptotic stability. Furthermore, the proposed control scheme can be directly applied to a class of underactuated systems. A numerical example is given for demonstrating the feasibility of the proposed control scheme.
引文
[1]I.Fantoni,and R.Lozano,Non-linear Control for Underactuated Mechanical Systems,Springer,Berlin,2001.
[2]B.Siciliano,and K.P.Valavanis,Control Problems in Robotics and Automation,Springer,Berlin,1998.
[3]R.Olfati-Saber,Normal forms for underactuated mechanical systems with symmetry,IEEE Transactions on Automatic Control,47(2):305–308,2002.
[4]X.Z.Lai,J.H.She,S.X.Yang,and W.Min,Comprehensive unified control strategy for underactuated two-link manipulators,IEEE Transactions on Systems,Man,and Cybernetics,Part B:Cybernetics,39(2):389–398,2009.
[5]S.Riachy,Y.Orlov,T.Floquet,R.Santiesteban,and J.P.Richard,Second-order sliding mode control of underactuated mechanical systems i:local stabilization with application to an inverted pendulum,International Journal of Robust and Nonlinear Control,18:529–543,2008.
[6]I.Fantoni,R.Lozano,and M.W.Spong,Energy based control of the pendubot,IEEE Transactions on Automatic Control,45(4):725–729,2000.
[7]Z.Wang,and Y.Guo,Unified control for pendubot at four equilibrium points,IET Control Theory and Applications,5(1):155–163,2011.
[8]M.S.Park,and D.Chwa,Swing-up and stabilization control of inverted-pendulum systems via coupled sliding-mode control method,IEEE Transactions on Industrial Electronics,56(9):3541–3555,2009.
[9]R.Ortega,M.W.Spong,F.Gomez-Estern,and G.Blankenstein,Stabilization of a class of underactuated mechanical systems via interconnection and damping assignment,IEEE Transactions on Automatic Control,47(8):1218–1233,2002.
[10]L.Marton,A.S.Hodel,B.Lantos,and J.Y.Hung,Underactuated robot control:comparing lqr,subspace stabilization,and combined error metric approaches,IEEE Transactions on Industrial Electronics,55(10):3724–3730,2008.
[11]C.Aguilar-Ibanez,The lyapunov direct method for the stabilisation of the ball on the actuated beam,International Journal of Control,82(12):2169–2178,2009.
[12]W.Wang,X.D.Liu,and J.Q.Yi,Structure design of two types of sliding-mode controllers for a class of under-actuated mechanical systems,IET Control Theory and Applications,1(1):163–172,2007.
[13]Y.Fang,B.Ma,P.Wang,and X.Zhang,A motion planningbased adaptive control method for an underactuated crane system,IEEE Transactions on Control Systems Technology,20:241–248,2012.
[14]N.Sun,and Y.Fang,New energy analytical results for the regulation of underactuated overhead cranes:an end-effector motion-based approach,IEEE Transactions on Industrial Electronics,59:4723–4734,2012.
[15]N.Sun,Y.Fang,and X.Zhang,Energy coupling output feedback control of 4-dof underactuated cranes with saturated inputs,Automatica,49:1318–1325,2013.
[16]H.Ashrafiuon,and R.S.Erwin,Sliding mode control of underactuated multibody systems and its application to shape change control,International Journal of Control,81(12):1849–1858,2008.
[17]G.Hu,C.Makkar,and W.E.Dixon,Energy-based nonlinear control of underactuated euler-lagrange systems subject to impacts,IEEE Transactions on Automatic Control,52(9):1742–1748,2007.
[18]J.W.Grizzle,C.H.Moog,and C.Chevallereau,Nonlinear control of mechanical systems with an unactuated cyclic variable,IEEE Transactions on Automatic Control,50(5):559–576,2005.
[19]A.Shiriaev,J.W.Perram,and C.Canudas-de Wit,Constructive tool for orbital stabilization of underactuated nonlinear systems:virtual constraints approach,IEEE Transactions on Automatic Control,50(8):1164–1176,2005.
[20]A.Shiriaev,A.Robertsson,J.Perram,and A.Sandberg,Periodic motion planning for virtually constrained euler-lagrange systems,Systems and Control Letters,55:900–907,2006.
[21]A.S.Shiriaev,L.B.Freidovich,and S.V.Gusev,Transverse linearization for controlled mechanical systems with several passive degrees of freedom,IEEE Transactions on Automatic Control,55(4):893–906,2010.
[22]J.Ghommam,F.Mnif,and N.Derbel,Global stabilisation and tracking control of underactuated surface vessels,IET Control Theory and Applications,4(1):71–88,2010.
[23]K.D.Do,Global tracking control of underactuated odins in three-dimensional space,International Journal of Control,86:183–196,2013.
[24]J.Y.Hung,W.Gao,and J.C.Hung,Variable structure control:a survey,IEEE Transactions on Industrial Electronics,40(1):2–22,1993.
[25]C.Edwards,and S.K.Spurgeon,Sliding Mode Control,Theory and Applications,Taylor and Francis,N.Y.1998.
[26]V.Sankaranarayanan,and A.D.Mahindrakar,Control of a class of underactuated mechanical systems using sliding modes,IEEE Transactions on Robotics,25(2):459–467,2009.
[27]R.Xu,and¨U.zgüner,Sliding mode control of a class of underactuated systems,Automatica,44:233–241,2008.
[28]Y.F.Chen,and A.C.Huang,Controller design for a class of underactuated mechanical systems,IET Control Theory and Applications,6(1):103–110,2012.
[29]J.X.Xu,Z.Q.Guo,and T.H.Lee,Design and implementation of integral sliding-mode control on an underactuated twowheeled mobile robot,IEEE Transactions on Industrial Electronics,61:3671–3681,2014.
[30]Z.Q.Guo,J.X.Xu,and T.H.Lee,Design and implementation of a new sliding mode controller on an underactuated wheeled inverted pendulum,Journal of the Franklin Institute,351:2261–2282,2014.
[31]M.Reyhanoglu,A.van der Schaft,N.H.Mc Clamroch,and I.Kolmanovsky,Dynamics and control of a class of underactuated mechanical systems,IEEE Transactions on Automatic Control,44(9):1663–1671,1999.
[32]R.Jafari,F.B.Mathis,R.Mukherjee,and H.Khalil,Enlarging the region of attraction of equilibria of underactuated systems using impulsive inputs,IEEE Transactions on Control Systems Technology,24(1):334–340,2016.
[33]J.Moreno-Valenzuela,C.Aguilar-Avelar,S.A.PugaGuzman,and V.Santib′a?nez,Adaptive neural network control for the trajectory tracking of the Furuta pendulum,IEEE Transactions on Cybernetics,46(12):3439–3452,2016.
[34]N.Sun,Y.Wu,Y.Fang,H.Chen,and B.Lu,Nonlinear continuous global stabilization control for underactuated RTAC systems:design,analysis,and experimentation,IEEE/ASME Transactions on Mechatronics,,22(2):1104–1115,2017.
[35]P.S.Thakar,P.K.Trivedi,B.Bandyopadhyay,and P.S.Gandhi,A new nonlinear control for asymptotic stabilization of a class of underactuated systems:an implementation to slosh-container problem,IEEE/ASME Transactions on Mechatronics,22(2):1082–1092,2017.
[36]Z.Wang,L.B.Freidovich,and H.Zhang,Periodic motion planning and control for underactuated mechanical systems,International Journal of Control,Doi:10.1080/00207179.2017.1314022.
[37]S.Boyd,L.E.Ghaoui,E.Feron,and V.Balakrishnan,Linear Matrix Inequalities in System and Control Theory,SIAM,Philadelphia,PA,1994.
[38]J.J.E.Slotine,and W.Li,Applied Nonlinear Control.Prentice Hall,New Jersey,1991.
[39]G.Tao,Adaptive Control Design and Analysis,John Wiley and Sons,New Jersey,2003.
[2]B.Siciliano,and K.P.Valavanis,Control Problems in Robotics and Automation,Springer,Berlin,1998.
[3]R.Olfati-Saber,Normal forms for underactuated mechanical systems with symmetry,IEEE Transactions on Automatic Control,47(2):305–308,2002.
[4]X.Z.Lai,J.H.She,S.X.Yang,and W.Min,Comprehensive unified control strategy for underactuated two-link manipulators,IEEE Transactions on Systems,Man,and Cybernetics,Part B:Cybernetics,39(2):389–398,2009.
[5]S.Riachy,Y.Orlov,T.Floquet,R.Santiesteban,and J.P.Richard,Second-order sliding mode control of underactuated mechanical systems i:local stabilization with application to an inverted pendulum,International Journal of Robust and Nonlinear Control,18:529–543,2008.
[6]I.Fantoni,R.Lozano,and M.W.Spong,Energy based control of the pendubot,IEEE Transactions on Automatic Control,45(4):725–729,2000.
[7]Z.Wang,and Y.Guo,Unified control for pendubot at four equilibrium points,IET Control Theory and Applications,5(1):155–163,2011.
[8]M.S.Park,and D.Chwa,Swing-up and stabilization control of inverted-pendulum systems via coupled sliding-mode control method,IEEE Transactions on Industrial Electronics,56(9):3541–3555,2009.
[9]R.Ortega,M.W.Spong,F.Gomez-Estern,and G.Blankenstein,Stabilization of a class of underactuated mechanical systems via interconnection and damping assignment,IEEE Transactions on Automatic Control,47(8):1218–1233,2002.
[10]L.Marton,A.S.Hodel,B.Lantos,and J.Y.Hung,Underactuated robot control:comparing lqr,subspace stabilization,and combined error metric approaches,IEEE Transactions on Industrial Electronics,55(10):3724–3730,2008.
[11]C.Aguilar-Ibanez,The lyapunov direct method for the stabilisation of the ball on the actuated beam,International Journal of Control,82(12):2169–2178,2009.
[12]W.Wang,X.D.Liu,and J.Q.Yi,Structure design of two types of sliding-mode controllers for a class of under-actuated mechanical systems,IET Control Theory and Applications,1(1):163–172,2007.
[13]Y.Fang,B.Ma,P.Wang,and X.Zhang,A motion planningbased adaptive control method for an underactuated crane system,IEEE Transactions on Control Systems Technology,20:241–248,2012.
[14]N.Sun,and Y.Fang,New energy analytical results for the regulation of underactuated overhead cranes:an end-effector motion-based approach,IEEE Transactions on Industrial Electronics,59:4723–4734,2012.
[15]N.Sun,Y.Fang,and X.Zhang,Energy coupling output feedback control of 4-dof underactuated cranes with saturated inputs,Automatica,49:1318–1325,2013.
[16]H.Ashrafiuon,and R.S.Erwin,Sliding mode control of underactuated multibody systems and its application to shape change control,International Journal of Control,81(12):1849–1858,2008.
[17]G.Hu,C.Makkar,and W.E.Dixon,Energy-based nonlinear control of underactuated euler-lagrange systems subject to impacts,IEEE Transactions on Automatic Control,52(9):1742–1748,2007.
[18]J.W.Grizzle,C.H.Moog,and C.Chevallereau,Nonlinear control of mechanical systems with an unactuated cyclic variable,IEEE Transactions on Automatic Control,50(5):559–576,2005.
[19]A.Shiriaev,J.W.Perram,and C.Canudas-de Wit,Constructive tool for orbital stabilization of underactuated nonlinear systems:virtual constraints approach,IEEE Transactions on Automatic Control,50(8):1164–1176,2005.
[20]A.Shiriaev,A.Robertsson,J.Perram,and A.Sandberg,Periodic motion planning for virtually constrained euler-lagrange systems,Systems and Control Letters,55:900–907,2006.
[21]A.S.Shiriaev,L.B.Freidovich,and S.V.Gusev,Transverse linearization for controlled mechanical systems with several passive degrees of freedom,IEEE Transactions on Automatic Control,55(4):893–906,2010.
[22]J.Ghommam,F.Mnif,and N.Derbel,Global stabilisation and tracking control of underactuated surface vessels,IET Control Theory and Applications,4(1):71–88,2010.
[23]K.D.Do,Global tracking control of underactuated odins in three-dimensional space,International Journal of Control,86:183–196,2013.
[24]J.Y.Hung,W.Gao,and J.C.Hung,Variable structure control:a survey,IEEE Transactions on Industrial Electronics,40(1):2–22,1993.
[25]C.Edwards,and S.K.Spurgeon,Sliding Mode Control,Theory and Applications,Taylor and Francis,N.Y.1998.
[26]V.Sankaranarayanan,and A.D.Mahindrakar,Control of a class of underactuated mechanical systems using sliding modes,IEEE Transactions on Robotics,25(2):459–467,2009.
[27]R.Xu,and¨U.zgüner,Sliding mode control of a class of underactuated systems,Automatica,44:233–241,2008.
[28]Y.F.Chen,and A.C.Huang,Controller design for a class of underactuated mechanical systems,IET Control Theory and Applications,6(1):103–110,2012.
[29]J.X.Xu,Z.Q.Guo,and T.H.Lee,Design and implementation of integral sliding-mode control on an underactuated twowheeled mobile robot,IEEE Transactions on Industrial Electronics,61:3671–3681,2014.
[30]Z.Q.Guo,J.X.Xu,and T.H.Lee,Design and implementation of a new sliding mode controller on an underactuated wheeled inverted pendulum,Journal of the Franklin Institute,351:2261–2282,2014.
[31]M.Reyhanoglu,A.van der Schaft,N.H.Mc Clamroch,and I.Kolmanovsky,Dynamics and control of a class of underactuated mechanical systems,IEEE Transactions on Automatic Control,44(9):1663–1671,1999.
[32]R.Jafari,F.B.Mathis,R.Mukherjee,and H.Khalil,Enlarging the region of attraction of equilibria of underactuated systems using impulsive inputs,IEEE Transactions on Control Systems Technology,24(1):334–340,2016.
[33]J.Moreno-Valenzuela,C.Aguilar-Avelar,S.A.PugaGuzman,and V.Santib′a?nez,Adaptive neural network control for the trajectory tracking of the Furuta pendulum,IEEE Transactions on Cybernetics,46(12):3439–3452,2016.
[34]N.Sun,Y.Wu,Y.Fang,H.Chen,and B.Lu,Nonlinear continuous global stabilization control for underactuated RTAC systems:design,analysis,and experimentation,IEEE/ASME Transactions on Mechatronics,,22(2):1104–1115,2017.
[35]P.S.Thakar,P.K.Trivedi,B.Bandyopadhyay,and P.S.Gandhi,A new nonlinear control for asymptotic stabilization of a class of underactuated systems:an implementation to slosh-container problem,IEEE/ASME Transactions on Mechatronics,22(2):1082–1092,2017.
[36]Z.Wang,L.B.Freidovich,and H.Zhang,Periodic motion planning and control for underactuated mechanical systems,International Journal of Control,Doi:10.1080/00207179.2017.1314022.
[37]S.Boyd,L.E.Ghaoui,E.Feron,and V.Balakrishnan,Linear Matrix Inequalities in System and Control Theory,SIAM,Philadelphia,PA,1994.
[38]J.J.E.Slotine,and W.Li,Applied Nonlinear Control.Prentice Hall,New Jersey,1991.
[39]G.Tao,Adaptive Control Design and Analysis,John Wiley and Sons,New Jersey,2003.