压电执行器的建模与控制方法研究
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摘要
压电执行器越来越广泛地应用在了纳米定位技术当中,然而它的非线性却影响了它的使用。虽然通过控制方法可以在一定程度上减小由非线性引起的误差,但是大多控制方法都有多个参数需要确定,这给压电的应用带来了不便。本篇论文正是以压电执行器为背景,以PID控制器为前提,来研究控制器的优化设计方法。本文的主线是压电建模——PID优化——结果分析。
在建模时,分别研究了压电执行器的静态以及动态建模方法,并以PPA80L为研究对象,为其建立静态模型和动态模型。静态模型主要是描述压电执行器的磁滞现象,因此静态模型也称为磁滞模型。通用的磁滞模型有Preisach、Prandtl– Ishlinskii、Bouc– Wen和Wiener四种,在本文中均给出了详细的讲解。动态模型是从牛顿第二定律入手建立的,它可以方便地导出压电执行器的传递函数,便于分析和使用,具有很强的实用性。
由于PID控制器的参数很难确定,所以在本文中提出了PID控制器的优化设计方法。优化时,首先是优化算法的选择。本文的优化算法采用的是基于速度最优的粒子群优化算法(VEPSO),它具有算法思路简单、优化速度快、不易进入局部最优区域等优点。其次是评价函数的选择。评价函数是优化能否取得成功的一个先决条件,因为它将直接鼓励着最优解的走向。本文采用的评价函数是根据典型二阶环节在阻尼系数为0.707时的时域特性建立的,它具有评价性能好,易于使用等优点。由于是第一次提出,所以使用了14个由极限参数的构成的控制对象进行了对比测试,结果最终表明本文提出的评价函数比传统的ITAE和ISTSE评价函数在评价效果上要好得多,在使用范围上要广得多。
确定了优化算法和评价函数之后,最后对压电执行器的PID控制器进行了优化设计。无论是从最终的仿真曲线,还是PID参数上,均证明了本文提出的压电执行器的PID优化设计方案是可行的。
Piezoelectric actuators are widely used in the nano– positioning technology, but its usage is influenced by its nonlinear property. Although through control method can reduce the nonlinear error to some extent, mostly control method has more parameters needed to be confirming that gives the difficulties to the application of piezoelectric. Based on the piezoelectric actuators and PID controller, this paper gives the controller design method on optimization. The outline is piezoelectric actuator modeling, PID optimize design and analysis.
During modeling, static modeling and dynamic modeling are established for piezoelectric actuators PPA80L respectively. Static model also called hysteresis model because it is mainly describe the hysteresis phenomenon. Universal hysteresis model is Preisach, Prandtl– Ishlinskii, Bouc– Wen and Wiener models, which details are given out. Dynamic model is established from Newton`s second law. It can be easily convert to transfer function and easy to analysis.
Due to the parameters of PID controller are difficult to be confirmed, this paper proposes a PID controller design which use optimization method. At first is the optimize algorithm chooses. In this paper, choose the Particle Swarm Optimization Algorithm which has more advantages like simple in algorithm thinking, fast in optimize speed, not easily go to local optimal regional, etc.. The second is the fitness function chooses. Fitness function is important in optimize process because which directly encourages the direction of the optimal solution. In this paper, the fitness function is established from the time domain features of the typical second order models whose damping coefficient is 0.707. To get the evaluate effect, using 14 objects to test and the consequences show that the fitness function has very good evaluate effect compare to ITAE and ISTSE.
After choose the optimization algorithm and the fitness function, give the PID controller optimization design for piezoelectric actuators. The result clearly shows that the PID controller optimization method proposed in this paper is feasible.
在建模时,分别研究了压电执行器的静态以及动态建模方法,并以PPA80L为研究对象,为其建立静态模型和动态模型。静态模型主要是描述压电执行器的磁滞现象,因此静态模型也称为磁滞模型。通用的磁滞模型有Preisach、Prandtl– Ishlinskii、Bouc– Wen和Wiener四种,在本文中均给出了详细的讲解。动态模型是从牛顿第二定律入手建立的,它可以方便地导出压电执行器的传递函数,便于分析和使用,具有很强的实用性。
由于PID控制器的参数很难确定,所以在本文中提出了PID控制器的优化设计方法。优化时,首先是优化算法的选择。本文的优化算法采用的是基于速度最优的粒子群优化算法(VEPSO),它具有算法思路简单、优化速度快、不易进入局部最优区域等优点。其次是评价函数的选择。评价函数是优化能否取得成功的一个先决条件,因为它将直接鼓励着最优解的走向。本文采用的评价函数是根据典型二阶环节在阻尼系数为0.707时的时域特性建立的,它具有评价性能好,易于使用等优点。由于是第一次提出,所以使用了14个由极限参数的构成的控制对象进行了对比测试,结果最终表明本文提出的评价函数比传统的ITAE和ISTSE评价函数在评价效果上要好得多,在使用范围上要广得多。
确定了优化算法和评价函数之后,最后对压电执行器的PID控制器进行了优化设计。无论是从最终的仿真曲线,还是PID参数上,均证明了本文提出的压电执行器的PID优化设计方案是可行的。
Piezoelectric actuators are widely used in the nano– positioning technology, but its usage is influenced by its nonlinear property. Although through control method can reduce the nonlinear error to some extent, mostly control method has more parameters needed to be confirming that gives the difficulties to the application of piezoelectric. Based on the piezoelectric actuators and PID controller, this paper gives the controller design method on optimization. The outline is piezoelectric actuator modeling, PID optimize design and analysis.
During modeling, static modeling and dynamic modeling are established for piezoelectric actuators PPA80L respectively. Static model also called hysteresis model because it is mainly describe the hysteresis phenomenon. Universal hysteresis model is Preisach, Prandtl– Ishlinskii, Bouc– Wen and Wiener models, which details are given out. Dynamic model is established from Newton`s second law. It can be easily convert to transfer function and easy to analysis.
Due to the parameters of PID controller are difficult to be confirmed, this paper proposes a PID controller design which use optimization method. At first is the optimize algorithm chooses. In this paper, choose the Particle Swarm Optimization Algorithm which has more advantages like simple in algorithm thinking, fast in optimize speed, not easily go to local optimal regional, etc.. The second is the fitness function chooses. Fitness function is important in optimize process because which directly encourages the direction of the optimal solution. In this paper, the fitness function is established from the time domain features of the typical second order models whose damping coefficient is 0.707. To get the evaluate effect, using 14 objects to test and the consequences show that the fitness function has very good evaluate effect compare to ITAE and ISTSE.
After choose the optimization algorithm and the fitness function, give the PID controller optimization design for piezoelectric actuators. The result clearly shows that the PID controller optimization method proposed in this paper is feasible.
引文
[1] Santosh Devasia, Evangelos Elefthriou, S. O. Reza Moheimani. A Surey of Control Issues In Nanopositioning. IEEE TRANSACTIONS ON CONTROL SYSTEMS TECHNOLOGY, VOL. 15, NO. 5, SEPTENBER 2007: 802–803.
[2]徐丽香,黎旺显. CD、VCD、DVD原理选购维修.西安电子科技大学出版社,1999年8月: 197–198.
[3] Santosh Devasia, Evangelos Elefthriou, S. O. Reza Moheimani. A Surey of Control Issues In Nanopositioning. IEEE TRANSACTIONS ON CONTROL SYSTEMS TECHNOLOGY, VOL. 15, NO. 5, SEPTENBER 2007: 803–804.
[4] Wikipedia. Inchworm motor. http://en.wikipedia.org/wiki/Inchworm_motor.
[5]上羽贞行,富川义郞著,杨志刚,郑学伦译.超声波马达-理论与应用.上海:上海科学技术出版社,1988.
[6]温建明.平面惯性压电叠堆移动机构的研究.吉林大学博士学位论文,2009: 3–4.
[7]何勍，王宏祥，于威.一种新型高频低幅振动给料装置的研究.机械科学与技术,第26卷,第6期,2007年6月: 758–760.
[8]温建明.平面惯性压电叠堆移动机构的研究.吉林大学博士学位论文,2009: 43–44.
[9]温建明,马继杰,程光明,曾平,阚君武.平面三自由度惯性压电叠堆移动机构研究.中国机械工程,第21卷第18期,2010年9月: 2172–2175.
[10] J. Minase, T. -F. Lu, B. Cazzolato, S. Grainger. A review, supported by experimental results, of voltage, charge and capacitor insertion method fro driving piezoelectric actuators. DOI: 10. 1016 / j. precisioneng. 2010.03.006: 693–695.
[11]程德福,王君,凌振宝.传感器原理及应用.机械工业出版社,2007年12月: 85–90.
[12]张新刚,王泽忠,徐春丽. Preisach理论及其在铁心磁化过程建模中的应用.高电压技术,第31卷第9期,2005年9月: 1–2.
[13]赵国生.磁滞数学模型及考虑磁滞时磁场数值计算.黄河水利出版社,2004年1月: 15–18.
[14]魏燕定,陶惠峰.压电执行器迟滞特性的Preisach模型研究.压电与声光,第26卷第5期,2004年8月: 1–4.
[15]李黎,刘向东,侯朝桢.压电陶瓷执行器Preisach模型的分类排序实现.压电与声光,第29卷第5期,2007年10月: 2–4.
[16] K. Kuhnen, H. Janocha. Inverse feedforward controller for complex hysteretic nonlinearities in smart-material systems: 7–21.
[17] K. Kuhnen, H. Janocha. Complex hysteresis modeling of a broad class of hysteretic actuator nonlinearities: 2–4.
[18] Qingqing Wang, Chun Yisu. Robust adaptive control of a class of nonlinear systems including actuator hysteresis with Prandtl-Ishlinskii presentations. automatica. DOI: 10.1016 / j, 2006. 01. 018: 2–3.
[19] K.Kuhnen, H. Janocha. Adaptive inverse control of piezoelectric actuators with hysteresis operators: 2–2.
[20] Mohammed Ismail, Faycal Ikhouane, Jose Rodellar. The Hysteresis Bouc-Wen Model, a Survey. Arch Comput Methods Eng (2009) 16: 161-188, DOI 10. 1007 / s1183– 009– 9031– 8: 161–170.
[21] Faycal Ikhouane, Jorge E. Hurtado. Variation of the hysteresis loop with the Bouc-Wen model parameters. Nonlinear Dyn (2007) 48: 361-380, DOI: 10. 1007 / s11071– 006– 9091– 3: 1–3.
[22] Faycal Ikhouane, Victor Manosa, Jose Rodellar. Dynamic properties of the hysteretic Bouc-Wen Model. Systems & Control Letters 56 (2007) 197– 205, DOI 10. 1016 / j. sysconle. 2006. 09. 001: 2–3.
[23] Samo Gerksic, Dani Juricic, Stanko Strmcnik, Drago Matko. Wiener model based nonlinear predictive control. International Journal of Systems Science, 31:2, 189– 202, DOI: 10. 1080 / 002077200291307: 2–4.
[24] Abdelkader Chaari, Sofien Rejeb, Faycal Ben Hmida, Hassani Messaoud, Moncef Gossa. Interative identification of Wiener model using hysteresis memory-less nonlinearity. International Journal of Sciences and Techniques of Automatic control & computer engineering, IJ-STA, Volume 2, N 1, July 2008: 430–441.
[25] Yucai Zhu. Estimation of an N– L– N Hammerstein– Wiener Model. 15th Triennial World Congress, Barcelona, Spain: 1–4.
[26] N. Lhermet, O. Delas, F. Claeyssen. Magnetostrictive pump with piezo active valves for more electrical aircraft. ACTUATOR 2006, 10th International Conference on New Actuators, 14– 16 June 2006, Bremen, Germany: 1.
[27] J. Kennedy and R. Eberhart, Particle swarm optimization. Preceeding of IEEE International Conference on Neural Networks, 1995.
[28] Ioan Cristian Trelea. The particle swarm optimization algorithm: convergence analysis and parameter selection. Information Processing Letters 85(2003):319–321.
[29] J. J. Liang, A. K. Qin. Comprehensive learning Particle Swarm Optimizer for Global Optimization of Multinodal Functions. IEEE TRANSACTIONS ON EVOLUTINARY COMPUTATION, VOL. 10, NO. 3, JUNE 2006: 2–4.
[30] R. C. Eberhart, Y. Shi. Comparing inertia weights and constriction factors in particle swarm optimization. Proceeding of the IEEE Congress and Evolutionary Computation, San Diego, USA, 2000: 84–88.
[31] F. van den Bergh, A. P. Englbrecht. A study of particle swarm optimization particle trajectories. Information Science 176(2006) 937-971, DOI: 10.1016/j. ins. 2005.02.003: 5–31.
[32] K. J. Astrom, T. Hagglund. Benchmark Systems for PID Control: 2.
[33]胡寿松.自动控制原理(第四版).科学出版社,2001年2月: 78–79.
[34] Robert H. Bishop. Modern Control Systems Analysis and Design Using MATLAB and Simulink. Tsinghua University Press, 2003年12月第1次印刷: 216–229.
[35] Robert H. Bishop. Modern Control Systems Analysis and Design Using MATLAB and Simulink. Tsinghua University Press, 2003年12月第1次印刷: 121–138.
[36] Ibtissem Chiha, Noureddine Liouane and Pierre Borne. Multi– Objective Ant Colony Optimization to tuning PID controller: 2–3.
[37] Frank D. Grabam, Ricbard C. Latbrop. Synthesis of― optinum‖transient response– criteria and standard forms. WADC TECHNICAL REPORT NO: 6–9.
[38] Asanga Ratnawera, Saman K. Halgamuge, Harry C. Watson. Self– Organizing Hierarchical Particle Swarm Optimizer With Time-Varying Acceleration Coefficients. IEEE TRANSACTIONS ON EVOLUTIONARY COMPUTATION, VOL. 8, NO. 3, JUNE 2004: 5–8.
[39] Daniel Parrott and Xiaodong Li. Locating and Tracking Multiple Dynamic Optima by a Particle Swarm Model Using Speciation. IEEE TRANSACTIONS ON EVOLUTIONARY COMPUTATION, VOL. 10, NO. 4, AUGUST 2006: 8–10.
[40] Maurice Clerc and James Kenndy. The Particle Swarm– Explosion, Stability, and Convergence in a Multidimensional Complex Space. IEEE TRANSACTIONS ON EVOLUTIONARY COMPUTATION, VOL. 6, NO, 1, FEBRUARY 2002: 14–16.
[41] Frans van den Bergh and Andries P. engelbrecht. A Cooperative Approach to Particle Swarm Optimization. IEEE TRANSACTION ON EVOLUTINARY COMPUTATION, VOL. 8, NO. 3, JUNE 2004: 7–10.
[42] Ralf salomon. Reevaluating Genetic Algorithm Performance under Coordinate Rotation of Benchmark Function. Elsevier Science, BioSystems 39(3): 4–7.
[43] P. N. Sugenthan, N. Hansen, J. J. Liang,et.. Problem Definitions and Evaluation Criteria for the CEC 2005 Special Session on Real-Parameter Optimization:1–50.
[2]徐丽香,黎旺显. CD、VCD、DVD原理选购维修.西安电子科技大学出版社,1999年8月: 197–198.
[3] Santosh Devasia, Evangelos Elefthriou, S. O. Reza Moheimani. A Surey of Control Issues In Nanopositioning. IEEE TRANSACTIONS ON CONTROL SYSTEMS TECHNOLOGY, VOL. 15, NO. 5, SEPTENBER 2007: 803–804.
[4] Wikipedia. Inchworm motor. http://en.wikipedia.org/wiki/Inchworm_motor.
[5]上羽贞行,富川义郞著,杨志刚,郑学伦译.超声波马达-理论与应用.上海:上海科学技术出版社,1988.
[6]温建明.平面惯性压电叠堆移动机构的研究.吉林大学博士学位论文,2009: 3–4.
[7]何勍，王宏祥，于威.一种新型高频低幅振动给料装置的研究.机械科学与技术,第26卷,第6期,2007年6月: 758–760.
[8]温建明.平面惯性压电叠堆移动机构的研究.吉林大学博士学位论文,2009: 43–44.
[9]温建明,马继杰,程光明,曾平,阚君武.平面三自由度惯性压电叠堆移动机构研究.中国机械工程,第21卷第18期,2010年9月: 2172–2175.
[10] J. Minase, T. -F. Lu, B. Cazzolato, S. Grainger. A review, supported by experimental results, of voltage, charge and capacitor insertion method fro driving piezoelectric actuators. DOI: 10. 1016 / j. precisioneng. 2010.03.006: 693–695.
[11]程德福,王君,凌振宝.传感器原理及应用.机械工业出版社,2007年12月: 85–90.
[12]张新刚,王泽忠,徐春丽. Preisach理论及其在铁心磁化过程建模中的应用.高电压技术,第31卷第9期,2005年9月: 1–2.
[13]赵国生.磁滞数学模型及考虑磁滞时磁场数值计算.黄河水利出版社,2004年1月: 15–18.
[14]魏燕定,陶惠峰.压电执行器迟滞特性的Preisach模型研究.压电与声光,第26卷第5期,2004年8月: 1–4.
[15]李黎,刘向东,侯朝桢.压电陶瓷执行器Preisach模型的分类排序实现.压电与声光,第29卷第5期,2007年10月: 2–4.
[16] K. Kuhnen, H. Janocha. Inverse feedforward controller for complex hysteretic nonlinearities in smart-material systems: 7–21.
[17] K. Kuhnen, H. Janocha. Complex hysteresis modeling of a broad class of hysteretic actuator nonlinearities: 2–4.
[18] Qingqing Wang, Chun Yisu. Robust adaptive control of a class of nonlinear systems including actuator hysteresis with Prandtl-Ishlinskii presentations. automatica. DOI: 10.1016 / j, 2006. 01. 018: 2–3.
[19] K.Kuhnen, H. Janocha. Adaptive inverse control of piezoelectric actuators with hysteresis operators: 2–2.
[20] Mohammed Ismail, Faycal Ikhouane, Jose Rodellar. The Hysteresis Bouc-Wen Model, a Survey. Arch Comput Methods Eng (2009) 16: 161-188, DOI 10. 1007 / s1183– 009– 9031– 8: 161–170.
[21] Faycal Ikhouane, Jorge E. Hurtado. Variation of the hysteresis loop with the Bouc-Wen model parameters. Nonlinear Dyn (2007) 48: 361-380, DOI: 10. 1007 / s11071– 006– 9091– 3: 1–3.
[22] Faycal Ikhouane, Victor Manosa, Jose Rodellar. Dynamic properties of the hysteretic Bouc-Wen Model. Systems & Control Letters 56 (2007) 197– 205, DOI 10. 1016 / j. sysconle. 2006. 09. 001: 2–3.
[23] Samo Gerksic, Dani Juricic, Stanko Strmcnik, Drago Matko. Wiener model based nonlinear predictive control. International Journal of Systems Science, 31:2, 189– 202, DOI: 10. 1080 / 002077200291307: 2–4.
[24] Abdelkader Chaari, Sofien Rejeb, Faycal Ben Hmida, Hassani Messaoud, Moncef Gossa. Interative identification of Wiener model using hysteresis memory-less nonlinearity. International Journal of Sciences and Techniques of Automatic control & computer engineering, IJ-STA, Volume 2, N 1, July 2008: 430–441.
[25] Yucai Zhu. Estimation of an N– L– N Hammerstein– Wiener Model. 15th Triennial World Congress, Barcelona, Spain: 1–4.
[26] N. Lhermet, O. Delas, F. Claeyssen. Magnetostrictive pump with piezo active valves for more electrical aircraft. ACTUATOR 2006, 10th International Conference on New Actuators, 14– 16 June 2006, Bremen, Germany: 1.
[27] J. Kennedy and R. Eberhart, Particle swarm optimization. Preceeding of IEEE International Conference on Neural Networks, 1995.
[28] Ioan Cristian Trelea. The particle swarm optimization algorithm: convergence analysis and parameter selection. Information Processing Letters 85(2003):319–321.
[29] J. J. Liang, A. K. Qin. Comprehensive learning Particle Swarm Optimizer for Global Optimization of Multinodal Functions. IEEE TRANSACTIONS ON EVOLUTINARY COMPUTATION, VOL. 10, NO. 3, JUNE 2006: 2–4.
[30] R. C. Eberhart, Y. Shi. Comparing inertia weights and constriction factors in particle swarm optimization. Proceeding of the IEEE Congress and Evolutionary Computation, San Diego, USA, 2000: 84–88.
[31] F. van den Bergh, A. P. Englbrecht. A study of particle swarm optimization particle trajectories. Information Science 176(2006) 937-971, DOI: 10.1016/j. ins. 2005.02.003: 5–31.
[32] K. J. Astrom, T. Hagglund. Benchmark Systems for PID Control: 2.
[33]胡寿松.自动控制原理(第四版).科学出版社,2001年2月: 78–79.
[34] Robert H. Bishop. Modern Control Systems Analysis and Design Using MATLAB and Simulink. Tsinghua University Press, 2003年12月第1次印刷: 216–229.
[35] Robert H. Bishop. Modern Control Systems Analysis and Design Using MATLAB and Simulink. Tsinghua University Press, 2003年12月第1次印刷: 121–138.
[36] Ibtissem Chiha, Noureddine Liouane and Pierre Borne. Multi– Objective Ant Colony Optimization to tuning PID controller: 2–3.
[37] Frank D. Grabam, Ricbard C. Latbrop. Synthesis of― optinum‖transient response– criteria and standard forms. WADC TECHNICAL REPORT NO: 6–9.
[38] Asanga Ratnawera, Saman K. Halgamuge, Harry C. Watson. Self– Organizing Hierarchical Particle Swarm Optimizer With Time-Varying Acceleration Coefficients. IEEE TRANSACTIONS ON EVOLUTIONARY COMPUTATION, VOL. 8, NO. 3, JUNE 2004: 5–8.
[39] Daniel Parrott and Xiaodong Li. Locating and Tracking Multiple Dynamic Optima by a Particle Swarm Model Using Speciation. IEEE TRANSACTIONS ON EVOLUTIONARY COMPUTATION, VOL. 10, NO. 4, AUGUST 2006: 8–10.
[40] Maurice Clerc and James Kenndy. The Particle Swarm– Explosion, Stability, and Convergence in a Multidimensional Complex Space. IEEE TRANSACTIONS ON EVOLUTIONARY COMPUTATION, VOL. 6, NO, 1, FEBRUARY 2002: 14–16.
[41] Frans van den Bergh and Andries P. engelbrecht. A Cooperative Approach to Particle Swarm Optimization. IEEE TRANSACTION ON EVOLUTINARY COMPUTATION, VOL. 8, NO. 3, JUNE 2004: 7–10.
[42] Ralf salomon. Reevaluating Genetic Algorithm Performance under Coordinate Rotation of Benchmark Function. Elsevier Science, BioSystems 39(3): 4–7.
[43] P. N. Sugenthan, N. Hansen, J. J. Liang,et.. Problem Definitions and Evaluation Criteria for the CEC 2005 Special Session on Real-Parameter Optimization:1–50.