基于敏感传递函数的分数阶PI~λ控制器的参数整定
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摘要
讨论一种基于敏感传递函数的分数阶PIλ控制器的参数整定方法.根据敏感传递函数的定义,采用代数方法,对固定的PIλ控制器的积分阶次,在比例增益和积分增益参数平面上,按敏感传递函数的界进行PIλ控制器的参数整定.该敏感传递函数的界与系统的幅值裕度和相角裕度直接相关,给出了系统相对稳定性的信息.仿真实例表明,利用该方法设计的PIλ控制器具有良好的动态性能和鲁棒性.
This paper discusses the parameter tuning method of fractional-order PIλ controllers based on sensitivity transfer function constraint.According to the definition of sensitivity transfer function,in the plane of proportional-integral gains of PIλ controller,for fixed integral-order,the parameters of the controller are tuned by plotting the sensitivity bound obtained via an algebraic derivation. The bound of sensitivity transfer function is directly related to the gain-margin and the phase-margin of the system,which gives the information on the relative stability of the system. Simulation examples prove that the designed PIλ controller can achieve better dynamic performances and robustness.
This paper discusses the parameter tuning method of fractional-order PIλ controllers based on sensitivity transfer function constraint.According to the definition of sensitivity transfer function,in the plane of proportional-integral gains of PIλ controller,for fixed integral-order,the parameters of the controller are tuned by plotting the sensitivity bound obtained via an algebraic derivation. The bound of sensitivity transfer function is directly related to the gain-margin and the phase-margin of the system,which gives the information on the relative stability of the system. Simulation examples prove that the designed PIλ controller can achieve better dynamic performances and robustness.
引文
[1]Podlubny I.Fractional Differential Equations[M].San Diego:Academic Press,1999.
[2]薛定宇,赵春娜.分数阶系统的分数阶PID控制器设计[J].控制理论与应用,2007,24(5):771–776.
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[6]Astrom K J,Panagopoulas H,Hagglund T.Design of PI controllers based on non-convex optimization[J].Automatica,1998,34(5):585–601.
[7]Yaniv O,Nagurka M.Design of PID controllers satisfying gain margin and sensitivity constraints on a set of plants[J].Automatica,2004,40(1):111–116.
[8]Wang D,Zhang J.A graphical tuning of PIλcontrollers for fractional order systems[J].Journal of Control Theory and Applications,2011,9(4):599–603.
[9]蔡国娟.液位控制系统分数阶PIλ控制器设计及实验[D].天津:天津科技大学,2012.
[2]薛定宇,赵春娜.分数阶系统的分数阶PID控制器设计[J].控制理论与应用,2007,24(5):771–776.
[3]Podlubny I.Fractional-order systems and PI Dλμcontrollers[J].IEEE Transactions on Automatic Control,1999,44(1):208–214.
[4]Hamamci S E.An algorithm for stabilization of fractional order time-delay systems using fractional order PID controllers[J].IEEE Transactions on Automatic Control,2007,52(10):1964–1969.
[5]Lou Y,Chen Y Q,Wang C Y,et al.Tuning fractional order proportional integral controllers for fractional order systems[J].Journal of Process Control,2010,20(7):823–832.
[6]Astrom K J,Panagopoulas H,Hagglund T.Design of PI controllers based on non-convex optimization[J].Automatica,1998,34(5):585–601.
[7]Yaniv O,Nagurka M.Design of PID controllers satisfying gain margin and sensitivity constraints on a set of plants[J].Automatica,2004,40(1):111–116.
[8]Wang D,Zhang J.A graphical tuning of PIλcontrollers for fractional order systems[J].Journal of Control Theory and Applications,2011,9(4):599–603.
[9]蔡国娟.液位控制系统分数阶PIλ控制器设计及实验[D].天津:天津科技大学,2012.