Calculation of Robust and Optimal Fractional PID Controllers for Time Delay Systems with Gain Margin and Phase Margin Specifications
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- 英文论文题名：Calculation of Robust and Optimal Fractional PID Controllers for Time Delay Systems with Gain Margin and Phase Margin Specifications
- 论文作者：Yuan-Jay Wang ; Shao-Tang Huang ; Kun-Han You
- 英文论文作者：Yuan-Jay Wang ; Shao-Tang Huang ; Kun-Han You ; Department of Electrical Engineering ; Tungnan University
- 年：2017
- 作者机构：Department of Electrical Engineering,Tungnan University;
- 英文论文关键词：Fractional order ; stability equation ; IAE ; ISE ; time delay ; robust PID controller ; gain margin ; phase margin
- 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（B）
- 英文会议录名称：Proceedings of the 36th Chinese Control Conference（B）
- 语种：英文
- 分类号：TP273
- 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：6
- 文件大小：166k
- 原文格式：D
- 会议级别：全国
摘要
This paper proposes a novel method to graphically compute all feasible gain and phase margin specifications-oriented robust and optimal fractional PID controllers to stabilize time delay processes(TD) of any order. The gain-phase margin tester method is utilized to guarantee the concerned systems certain robust safety margins and test the constant gain margin boundary, constant phase margin boundary, and stability boundary in the parameter plane. The overlapping region of these plotted boundaries, which represents all feasible robust stabilizing PID controllers and allows the considered TD processes to retain pre-specified safety margins, is graphically determined as the gain and phase margin specifications-oriented region(GPMSOR). The variations of the GPMSOR and the stability region with respect to the variations of the noninteger orders of the integral and derivative terms have been investigated. According this, it is possible to slightly enlarge the GPMSOR by altering the noninterger order of the integral and derivative terms. This modifications in GPMSOR through altering the noninteger orders of the integral and derivative terms allows us to find the robust and optimal PID controller gain set for the considered TD systems. In other words, the selected fractional order PID controllers from the GPMSOR not only retain the prescribed GM and PM specifications but minimize the integral of the absolute error(IAE) or the integral of the squared error(ISE) performance criterion. Finally, an illustrative example cited from the literature with computer simulations is provided to demonstrate the effectiveness and confirm the validity of the proposed methodology.
This paper proposes a novel method to graphically compute all feasible gain and phase margin specifications-oriented robust and optimal fractional PID controllers to stabilize time delay processes(TD) of any order. The gain-phase margin tester method is utilized to guarantee the concerned systems certain robust safety margins and test the constant gain margin boundary, constant phase margin boundary, and stability boundary in the parameter plane. The overlapping region of these plotted boundaries, which represents all feasible robust stabilizing PID controllers and allows the considered TD processes to retain pre-specified safety margins, is graphically determined as the gain and phase margin specifications-oriented region(GPMSOR). The variations of the GPMSOR and the stability region with respect to the variations of the noninteger orders of the integral and derivative terms have been investigated. According this, it is possible to slightly enlarge the GPMSOR by altering the noninterger order of the integral and derivative terms. This modifications in GPMSOR through altering the noninteger orders of the integral and derivative terms allows us to find the robust and optimal PID controller gain set for the considered TD systems. In other words, the selected fractional order PID controllers from the GPMSOR not only retain the prescribed GM and PM specifications but minimize the integral of the absolute error(IAE) or the integral of the squared error(ISE) performance criterion. Finally, an illustrative example cited from the literature with computer simulations is provided to demonstrate the effectiveness and confirm the validity of the proposed methodology.
This paper proposes a novel method to graphically compute all feasible gain and phase margin specifications-oriented robust and optimal fractional PID controllers to stabilize time delay processes(TD) of any order. The gain-phase margin tester method is utilized to guarantee the concerned systems certain robust safety margins and test the constant gain margin boundary, constant phase margin boundary, and stability boundary in the parameter plane. The overlapping region of these plotted boundaries, which represents all feasible robust stabilizing PID controllers and allows the considered TD processes to retain pre-specified safety margins, is graphically determined as the gain and phase margin specifications-oriented region(GPMSOR). The variations of the GPMSOR and the stability region with respect to the variations of the noninteger orders of the integral and derivative terms have been investigated. According this, it is possible to slightly enlarge the GPMSOR by altering the noninterger order of the integral and derivative terms. This modifications in GPMSOR through altering the noninteger orders of the integral and derivative terms allows us to find the robust and optimal PID controller gain set for the considered TD systems. In other words, the selected fractional order PID controllers from the GPMSOR not only retain the prescribed GM and PM specifications but minimize the integral of the absolute error(IAE) or the integral of the squared error(ISE) performance criterion. Finally, an illustrative example cited from the literature with computer simulations is provided to demonstrate the effectiveness and confirm the validity of the proposed methodology.
引文
[1]B.N.Narahari Achar,J.W.Hanneken,T.Clarke,“Response characteristics of a fractional oscillator,”Physica A,Vol.309,pp.275-288,2002.
[2]J.C.Wang,“Realizations of generalized warburg impedance with RC ladder networks and transmission lines,”J.of Electrochem.Soc.,Vol.134,No.8,pp.1915-1920,1987.
[3]R.L.Magin,Fractional calculus in bioengineering,Begell House Publishers Inc.,2006.
[4]K.Astrom and T.Hagglund,“The future of PID control,”Control Engineering Practice,Vol.9,No.11,pp.1163-1175,2001.
[5]I.Podlubny,“Fractional-order systems and PIλDμ–controllers,”,IEEE Trans.on Automatic Control,Vol.44,pp.208-214,1999.
[6]Y.C.Cheng and C.Huang,“Stabilization of unstable first-order time delay systems using fractional-order PD controllers,”Journal of the Chinese Institute of Engineers,Vol.29,No.2,pp.241-249,2006.
[7]A.Ruszewski,“Stability regions of closed loop system with time delay inertial plant of fractional order and fractional order PI controller,”Bulletin of the Polish Academy of Sciences Technical Sciences,Vol.56,No.4,pp.329-332,2008.
[8]S.E.Hamamci,P.Kanthabhabha,K.Vaithiyanathan,“Computation of All Stabilizing First Order Controllers for Fractional-Order Systems,”Proceedings of the 27 Chinese Control Conference,July 16-18,pp.123-128,2008.
[9]Y.J.Huang and Y.J.Wang,“Robust PID tuning strategy for uncertain plants based on the Kharitonov theorem,”ISA Transactions,Vol.39,No.4,pp.419-431,2000.
[10]Y.J.Huang and Y.J.Wang,“Robust PID controller design for non-minimum phase time delay systems,”ISA Transactions,Vol.40,No.1,pp.31-39,2001.
[11]Y.J.Wang,“Graphical computation of gain and phase margin specifications-oriented robust PID controllers for uncertain systems with time-varying delay,”J.of Process Control,Vol.21,Issue 4,pp.475-488,Apr.2010.
[12]C.H.Chang and K.W.Han,“Gain margins and phase margins for control systems with adjustable parameters,”AIAA J.of Guidance,Control,and Dynamics,Vol.13,No.3,pp.404-408,1990.
[13]G.H.Lii,C.H.Chung,and K.W.Han,“Analysis of robust control systems using stability equations,”J.of Control Systems and Technology,Vol.1,No.1,pp.83-89,1993.
[14]J.S.Yang,“Parameter plane control design for a two-tank chemical reactor systems,”J.of the Franklin Institute,Vol.331B-1,Issue 1,pp.61-76,1994.
[15]A.Tepljakov,E.Petlenkov,and J.Belikov,“FOMCON:a MATLAB toolbox for fractional-order system identification and control,”International Journal of Microelectronics and Computer Science,Vol.2,No.2,pp.51–62,2011.
[16]A.Tepljakov.(2012)FOMCON:Fractional-order Modeling and Control.http://www.fomcon.net/.
[17]S.E.Hamaci and N.Tan,“Design of PI controllers for achieveing time and frequency domain specificaions simultaneously,”ISA Transactions,Vol.45,No.4,pp.529-543,October 2006.
[18]G.K.I.Mann,B.G.Hu,and R.G.Gosine,“Time-domain based design and analysis of new PID tuning rules,”IEE Proc.-Control Theory Appl.,Vol.148,No.3,pp.251-261,May 2001.
[2]J.C.Wang,“Realizations of generalized warburg impedance with RC ladder networks and transmission lines,”J.of Electrochem.Soc.,Vol.134,No.8,pp.1915-1920,1987.
[3]R.L.Magin,Fractional calculus in bioengineering,Begell House Publishers Inc.,2006.
[4]K.Astrom and T.Hagglund,“The future of PID control,”Control Engineering Practice,Vol.9,No.11,pp.1163-1175,2001.
[5]I.Podlubny,“Fractional-order systems and PIλDμ–controllers,”,IEEE Trans.on Automatic Control,Vol.44,pp.208-214,1999.
[6]Y.C.Cheng and C.Huang,“Stabilization of unstable first-order time delay systems using fractional-order PD controllers,”Journal of the Chinese Institute of Engineers,Vol.29,No.2,pp.241-249,2006.
[7]A.Ruszewski,“Stability regions of closed loop system with time delay inertial plant of fractional order and fractional order PI controller,”Bulletin of the Polish Academy of Sciences Technical Sciences,Vol.56,No.4,pp.329-332,2008.
[8]S.E.Hamamci,P.Kanthabhabha,K.Vaithiyanathan,“Computation of All Stabilizing First Order Controllers for Fractional-Order Systems,”Proceedings of the 27 Chinese Control Conference,July 16-18,pp.123-128,2008.
[9]Y.J.Huang and Y.J.Wang,“Robust PID tuning strategy for uncertain plants based on the Kharitonov theorem,”ISA Transactions,Vol.39,No.4,pp.419-431,2000.
[10]Y.J.Huang and Y.J.Wang,“Robust PID controller design for non-minimum phase time delay systems,”ISA Transactions,Vol.40,No.1,pp.31-39,2001.
[11]Y.J.Wang,“Graphical computation of gain and phase margin specifications-oriented robust PID controllers for uncertain systems with time-varying delay,”J.of Process Control,Vol.21,Issue 4,pp.475-488,Apr.2010.
[12]C.H.Chang and K.W.Han,“Gain margins and phase margins for control systems with adjustable parameters,”AIAA J.of Guidance,Control,and Dynamics,Vol.13,No.3,pp.404-408,1990.
[13]G.H.Lii,C.H.Chung,and K.W.Han,“Analysis of robust control systems using stability equations,”J.of Control Systems and Technology,Vol.1,No.1,pp.83-89,1993.
[14]J.S.Yang,“Parameter plane control design for a two-tank chemical reactor systems,”J.of the Franklin Institute,Vol.331B-1,Issue 1,pp.61-76,1994.
[15]A.Tepljakov,E.Petlenkov,and J.Belikov,“FOMCON:a MATLAB toolbox for fractional-order system identification and control,”International Journal of Microelectronics and Computer Science,Vol.2,No.2,pp.51–62,2011.
[16]A.Tepljakov.(2012)FOMCON:Fractional-order Modeling and Control.http://www.fomcon.net/.
[17]S.E.Hamaci and N.Tan,“Design of PI controllers for achieveing time and frequency domain specificaions simultaneously,”ISA Transactions,Vol.45,No.4,pp.529-543,October 2006.
[18]G.K.I.Mann,B.G.Hu,and R.G.Gosine,“Time-domain based design and analysis of new PID tuning rules,”IEE Proc.-Control Theory Appl.,Vol.148,No.3,pp.251-261,May 2001.