无模型自适应控制方法的改进设计与仿真
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摘要
面对工程实际问题和工程应用对控制方法要求的不断提高,基于数学模型的控制理论和方法的局限性日益明显,要求新的控制方法必须满足被控对象的一系列要求,它应对模型要求低,具有自适应功能、克服大时滞功能等。因此,不基于被控对象数学模型的控制方法一无模型自适应控制MFAC(Model Free Adaptive Control)成为实际工程中自动控制发展的一个重要方向。无模型自适应控制是一种新的控制方法,是指控制器的设计仅利用被控系统的I/O数据,且控制器中不包含被控过程数学模型的任何信息的控制理论与方法。本文将对无模型自适应控制进行深入研究。
首先,本文对基本无模型控制器的控制原理、收敛性、合理性及适用性进行了详细的分析。
其次,为了进一步提高无模型自适应控制器的控制性能,针对基本无模型自适应控制方法存在的不足进行了改进,提出带有单输出跟踪微分器的无模型自适应控制器(TD-MFAC)。跟踪微分器具有很好的滤波性能,能够很好的将输出信号从噪声中分离出来,合理的提取微分信号,得到原始信号的最佳逼近。因此,将跟踪微分器引入到基本无模型自适应控制器中以增强无模型自适应控制器的抗干扰性。仿真结果表明,与基本无模型自适应控制器相比,TD-MFAC具有良好的抗干扰性能。
此外,本文还将基本无模型自适应控制方法与常规PID控制方法做了深入的分析比较,仿真结果表明,基本无模型自适应控制方法在跟踪性能、适应性、克服大时滞能力方面都明显优于常规PID控制方法。
Classical control theory and modern control theory is based on the system model, such as PID control, predictive control, fuzzy control, neural network control and so on. However, these control methods have some defects, for example, there are so many parameters to determine, and these methods do not have a satisfactory effect when dealing with the large time-delay system. So, the control methods based on model are facing the high requirement of practical problems in engineering and engineering application. The new control methods should meet the requirements of controlled objects, such as imprecise model, adaptability, overcoming the large time-delay system and so on. Model free adaptive control (MFAC) which does not base on the mathematical model of the controlled object is another important aspect of automation. MFAC is control object oriented, it is a functional combination control method which does not consider the mathematical model of the controlled system first.
Model-free adaptive (MFA) control, as its name suggests, is an adaptive control method that does not require process models. There are not any information of controlled process in the controller, only the I/O data of the controlled system should be available when designing the controller. It is the products of the integration of modeling and controling, a nonlinear controller designed by the approach of functions combination. Unlike the traditional control methods which consider the mathematical model of the controlled object first, MFAC combinates the modeling and feedback control, real-time modeling and real-time feedback control correction online. It has been widely used recently.
This paper makes research on the basic model-free adaptive control method and proposes the improved method which combinates the single output tracking differentiator with the basic MFAC. The new controller makes full use of the filter characteristics of the tracking differentiator and improves the anti-interference performance of the MFAC. Specific studies are as follows:
1、The basic theory of model-free control method. Introducing several major branches of model-free control theory, such as model-free fuzzy control, expert control, neural network model-free control, learning control, auto-disturbance rejection control and model-free adaptive control.
2、The basic theory of model-free adaptive control method. Analyzing the related theory of model-free adaptive control method. First, introducing the concept of universal model and its expression. Second, deriving model-free adaptive control law and the estimated algorithm of the pseudo-partial derivative which is the unknown factor of the control law. Finally, getting the model-free adaptive control program.
3、Designing the model-free adaptive controller. Mainly making research on model-free adaptive controller. First, analyzing the convergence and rationality of MFAC with the mathematical methods. Second, Explaining why the model-free adaptive controller can be applied to a wide class of nonlinear systems without modeling, finally, presenting the model-free adaptive control program and making simulation comparison with PID control method. The simulation results show the model-free adaptive control method is better than PID control method in the aspacts of tracking, adaptability and overcoming the large time-delay obviously. Reaching the following conclusions: First of all, model-free adaptive controller is like a black box, second of all, model-free adaptive control can handle non-linear discrete-time systems.
4、The improved design of model-free adaptive control method. Making improvement on the basic model model-free adaptive control method to further enhance the control quality of model-free adaptive controller. MFAC with single output tracking differentiator (TD-MFAC) is proposed which combinating the basic model-free adaptive controller and the single output tracking differentiator. The improved controller which combinates the filter characteristics of the single output tracking differentiator enhances the anti-jamming ability of model-free adaptive control method. Finally, making the compared simulation with the basic model-free adaptive controller. The simulation results show that TD-MFAC has the unique advantage which is suitable for dealing with the controlled system with interference.
首先,本文对基本无模型控制器的控制原理、收敛性、合理性及适用性进行了详细的分析。
其次,为了进一步提高无模型自适应控制器的控制性能,针对基本无模型自适应控制方法存在的不足进行了改进,提出带有单输出跟踪微分器的无模型自适应控制器(TD-MFAC)。跟踪微分器具有很好的滤波性能,能够很好的将输出信号从噪声中分离出来,合理的提取微分信号,得到原始信号的最佳逼近。因此,将跟踪微分器引入到基本无模型自适应控制器中以增强无模型自适应控制器的抗干扰性。仿真结果表明,与基本无模型自适应控制器相比,TD-MFAC具有良好的抗干扰性能。
此外,本文还将基本无模型自适应控制方法与常规PID控制方法做了深入的分析比较,仿真结果表明,基本无模型自适应控制方法在跟踪性能、适应性、克服大时滞能力方面都明显优于常规PID控制方法。
Classical control theory and modern control theory is based on the system model, such as PID control, predictive control, fuzzy control, neural network control and so on. However, these control methods have some defects, for example, there are so many parameters to determine, and these methods do not have a satisfactory effect when dealing with the large time-delay system. So, the control methods based on model are facing the high requirement of practical problems in engineering and engineering application. The new control methods should meet the requirements of controlled objects, such as imprecise model, adaptability, overcoming the large time-delay system and so on. Model free adaptive control (MFAC) which does not base on the mathematical model of the controlled object is another important aspect of automation. MFAC is control object oriented, it is a functional combination control method which does not consider the mathematical model of the controlled system first.
Model-free adaptive (MFA) control, as its name suggests, is an adaptive control method that does not require process models. There are not any information of controlled process in the controller, only the I/O data of the controlled system should be available when designing the controller. It is the products of the integration of modeling and controling, a nonlinear controller designed by the approach of functions combination. Unlike the traditional control methods which consider the mathematical model of the controlled object first, MFAC combinates the modeling and feedback control, real-time modeling and real-time feedback control correction online. It has been widely used recently.
This paper makes research on the basic model-free adaptive control method and proposes the improved method which combinates the single output tracking differentiator with the basic MFAC. The new controller makes full use of the filter characteristics of the tracking differentiator and improves the anti-interference performance of the MFAC. Specific studies are as follows:
1、The basic theory of model-free control method. Introducing several major branches of model-free control theory, such as model-free fuzzy control, expert control, neural network model-free control, learning control, auto-disturbance rejection control and model-free adaptive control.
2、The basic theory of model-free adaptive control method. Analyzing the related theory of model-free adaptive control method. First, introducing the concept of universal model and its expression. Second, deriving model-free adaptive control law and the estimated algorithm of the pseudo-partial derivative which is the unknown factor of the control law. Finally, getting the model-free adaptive control program.
3、Designing the model-free adaptive controller. Mainly making research on model-free adaptive controller. First, analyzing the convergence and rationality of MFAC with the mathematical methods. Second, Explaining why the model-free adaptive controller can be applied to a wide class of nonlinear systems without modeling, finally, presenting the model-free adaptive control program and making simulation comparison with PID control method. The simulation results show the model-free adaptive control method is better than PID control method in the aspacts of tracking, adaptability and overcoming the large time-delay obviously. Reaching the following conclusions: First of all, model-free adaptive controller is like a black box, second of all, model-free adaptive control can handle non-linear discrete-time systems.
4、The improved design of model-free adaptive control method. Making improvement on the basic model model-free adaptive control method to further enhance the control quality of model-free adaptive controller. MFAC with single output tracking differentiator (TD-MFAC) is proposed which combinating the basic model-free adaptive controller and the single output tracking differentiator. The improved controller which combinates the filter characteristics of the single output tracking differentiator enhances the anti-jamming ability of model-free adaptive control method. Finally, making the compared simulation with the basic model-free adaptive controller. The simulation results show that TD-MFAC has the unique advantage which is suitable for dealing with the controlled system with interference.
引文
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[2]Cheng,G.S.Model-Free Adaptive(MFA)Control.IEEE Computing and Control Engneering [J].Engineering Europe,2004,15(3):28-33.
[3]Kharitonov V,Mondie S,Collado J.Exponential Estimates for Neutral Time-delay Systems An LMI Approach[J].IEEE Transactions on Automatic Control,2005,50(5):666-670.
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[5]Tim Barry,Liuping Wang.A Model-free Predictive Controller with Laguerre Polynomials[C].Melbourne,Australia:The 5th Asian Control Conference,2004.
[6]蒋爱平,李秀英,韩志刚.从PID到无模型控制器[J].控制工程,2005,1(23):217-220.
[7]Cheng George,Shu-Xing.Model-free adaptive process control[J/OL].1999.http://www.wipo.int/portal/index.html.en.
[8]Cheng George,Shu-Xing.Model-free adaptive control of quality variables[J/lOL].2004.http://www.patentstorm.us/patents/7016743/description.html.
[9]Cheng George.Model-free adaptive control of turbidity in water coagulation process[J].Control Engineering Europe,2004,21(5):5-10.
[10]Cheng George,Shu-Xing.Robust model-flee adaptive control[J/OL].2004.http://www.freepatents online.com/6684112.html.
[11]Jing X J,Wang Y C.Exponential Stability of Uncertain Time-delayed Systems[C].Melbourne,Australia:The 5th Asian Control Conference(ASCC2004),2004.
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[14]韩志刚.无模型控制器理论与应用的进展[J].自动化技术与应用,2004,23(2):1-6.
[15]薛荆岩.无模型控制方法在复杂大时滞系统控制中的应用研究[J].自动化技术与应用,2004,23(4):1-6.
[16]Harris,S.Model-Free Adaptive Control Improves Productivity and Efficiency[J].Control,2004,6(8):102-108.
[17]Cheng G.Model-free coking furnace adaptive control[J].Hydrocarbon Processing,1999,78(12):73 -76.
[18]韩志刚,王德进.无模型控制器[J].黑龙江大学自然科学学报,1994,11(4):29-35.
[19]韩志刚.无模型控制器的设计问题[J].控制工程,2002,9(3):19-22.
[20]韩志刚.动态系统时变参数的辨识[J].自动化学报,1984,10(4):330-337.
[21]韩志刚.关于建模与自适应控制的一体化途径[J].自动化学报,2004,30(3):380-389.
[22]胡致强.一类多重时滞非线性系统无模型学习自适应控制[J].哈尔滨工业大学学报,2001,33(2):261-264.
[23]韩志刚,徐明新.无模型控制律的一般形式及其在石化工业中的应用[J].黑龙江大学自然科学学报,2001,18(3):24-29.
[24]韩志刚.无模型控制器的应用[J].控制工程,2002,9(4):22-25.
[25]薛荆岩,巫红,韩志刚.无模型控制方法在复杂大时滞系统中的应用研究[J].控制理论与应用,2004,23(4):1-6.
[26]韩志刚,徐明新.无模型自适应控制器的一般形式及其在石化工业中的应用[J].黑龙江大学自然科学学报,200l,18(3):24-30.
[27]侯忠生,韩志刚.非线性系统参数估计及与之对偶的自适应控制[J].自动化学报,1995,21(1):122-125.
[28]王德进,王玲,韩志刚.无模型自适应控制器的设计问题[J].控制与决策,1997,12(2):136-141.
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