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    中英文翻译---常规PID和模糊PID算法的分析比较.doc

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    中英文翻译---常规PID和模糊PID算法的分析比较.doc

    毕业设计(论文) 中英文资料 信 电 系 工业电气自动化 专业 03 级 1 班课题名称:基于单片机的模糊PID温度控制系统设计毕业设计(论文)起止时间:2006年 2月15日6月8日(共17周)学生姓名: 学号: 指导教师: 报告日期: 2006年6月8日 常规PID和模糊PID算法的分析比较摘要:模糊PID控制器实际上跟传统的PID控制器有很大联系。区别在于传统的控制器的控制前提必须是熟悉控制对象的模型结构,而模糊控制器因为它的非线性特性,所以控制性能优于传统PID控制器。对于时变系统,如果能够很好地采用模糊控制器进行调节,其控制结果的稳定性和活力性都会有改善。但是,如果调节效果不好,执行器会因为周期振荡影响使用寿命,特别是调节器是阀门的场合,就必须考虑这个问题。为了解决这个问题,出现了很多模糊控制的分析方法。本文提出的方法采用一个固定的初始域,这样相当程度上简化了模糊控制的设定问题以及实现。文中分析了振荡的原因并分析如何抑制这种振荡的各种方法,最后,还给出一种方案,通过减少隶属函数的数量以及改善解模糊化的方法缩短控制信号计算时间,有效的改善了控制的实时性。1 引言模糊控制器的一个主要缺陷就是调整的参数太多。特别是参数设定的时候,因为没有相关的书参考,所以它的给定非常困难。众所周知,优化方法的收敛性跟它的初始化设定有很大关联,如果模糊控制器的初始域是固定的,那么它的控制就明显的简化了。而且我们要控制的参数大多有其实际的物理意义,所以模糊控制器完全可以利用PID算法的控制规律进行近似的调整。也就是说最简单的模糊PID控制器就是同时采用几种基本模糊控制算法(P+I+D或者PI+D),控制过程中它会根据控制要求,做出适当的选择,保证在处理跟踪以抗阶跃干扰问题上,其控制性能接近于任何一种PID控制。假设模糊集的初始域是对称的,两个调节器的参数采用Ziegler-Nichols方法。为了改善上述设计的模糊控制器,我们有必要考模糊控制器的参数问题,有两种方法可以采纳,一种采用手动的方法改变,另一种就是采用一些相关的优化算法。其中遗传算法就是一种。控制器采用的参数不同,其收敛的优化值也会不一样。这些参数包括模糊集的分布,模糊集的个数,映射规则,基本模糊控制器的参数和不同的算法组合等。要注意的是在优化前必须选定模糊推理及解模糊的方法。很明显,优化过程很耗时,更有甚者,有些优化方法要已知系统的精确模型,但是实际过程中难以得到系统的精确模型,所以在大多数情况下,这些优化算法不能直接应用在实际过程。也就是说模型不精确直接影响优化成败。模糊控制的主要思想就是针对那些传递函数未知的或者结构难以辨识的系统进行控制,这也是模糊控制的性能为什么优于传统方法的原因。同时,把模糊控制和传统的PID控制算法结合起来,更能体现这种算法的优点,因为它大大简化实际过程的调整。 图1 隶属函数图 图2映射规则图 参数集的启发式优化法也适用于模糊PI控制器,它采用固定的定义域,其参数的选取和传统的PI控制器都一样。我们采用的控制方法是结合模糊PI算法和PD算法并利用启发式优化法处理参数集,特别要注意这里的调节器出现了两个比例环节,所以它的控制可能不同于传统的PID算法。但是我们调整的参数它们本身具有实际的物理意义,值得一提的是前面所提到的控制可以通过改变采样时间而不改变定义域的范围实现调整。2模糊PI控制器设计控制信号由模糊控制器得到(参考文献2):模糊PI控制器的一种实现过程如图3所示: 图3 模糊PI控制器结构(区域单位化)现在我们假设控制对象的传递函数如下描述,然后通过仿真图比较模糊PI控制器和传统PI控制器的控制性能:采用6中所用的调节方法,我们可得参数,其响应如图4和图5所示。干扰作用于系统的输入,模糊控制器如图3 所示,映射规则如图2 所示,隶属函数如图1所示。 图4 传统PI控制图 图5 模糊PI控制图同理取相同的参数集合,但是采用不用的模糊推理和解模糊化方法进行优化,我们把最大值设为10,即,采用周期,则,输出响应如图5所示,下面的集合已经在3中测试过了,模糊推理方法采用Min-Max 和Prod-Max,解模糊部分采用COG方法,隶属函数采用三角形分布或单值分布,把定义域单位化,然后从七个模糊集中任取三个,进行仿真,如果隶属函数是单值分布,也一样。把传统的PI控制算法和模糊PI控制算法的结果进行比较并讨论。我们发现采用模糊控制的系统输出超调量虽然很小,但是抗干扰能力并不比传统的PI控制器好。 图6 有7个隶属函数的模糊控制 图7有3个隶属函数的模糊PI控制器采用最小-最大模糊推理 参考文献6,看图5,发现给系统的输入端加上幅度为0.05的阶跃干扰,系统输出响应趋向振荡地很厉害。假设这里所有响应采用的集合都是一样的,我们看图6,它的响应曲线没有明显的振荡。但是,我们还不能分析6所提供导致振荡的可能原因,因为这里没有文6提供的模糊控制的所需的实验数据集。我们发现,即使采用遗传优化算法,其控制结果也没有远远胜过模糊PI控制的近似调整结果。但是我们可以通过减少隶属函数的个数达到缩短计算控制量所需时间。可是,减少隶属函数个数的同时,也会伴随着动态性能的降低,但是这种品质的降低完全可以通过适当调节参数来弥补。从仿真结果来看,文献6中的结论没有理论证明。3模糊PD+PI控制器的设计让我们先给出一个模糊控制器,它是由模糊PI和模糊PD控制器并联在一起组合而成。其中,图9是传统的I-PD控制器的输出,它采用Ziegler-Nichols方法()。而模糊PI-PD控制的设定参考文献2 (,模糊推理采用最小-最大法,解模糊采用COG方法,有7个隶属函数)。其中PI和PD的隶属函数的分布以及采用的模糊规则分别如图1、图2所示。唯一的区别在于控制增量的变化,如图11所示,图10是仿真结果,而图12给出了采用不同的三个集合的系统输出,实线表示采用前面文章所用的调整方法,但模糊推理方法采用Prod-Max。虚线表示采用3个隶属函数,最小最大模糊推理、解模糊采用COG(隶属函数为三角形分布)的仿真的结果,点划线表示采用3个隶属函数,最小最大模糊推理、解模糊采用COG(隶属函数为单值分布)的仿真的结果。图13表示系统输入加入0.05的阶跃干扰后对系统的输出影响。采用模糊控制的系统输出或多或少都会有振荡,其原因不仅仅受参数的调节的影响,还有所用的最小最大模糊推理的影响。但是如果采用Prod-Max的模糊推理,解模糊时采用单值法,这种振荡可以大大的抑制。但是造成振荡的另一个可能原因就是推理机构的错误动作。从图14我们发现,如果两个相邻的隶属函数的最值的距离只有0.01(所用的区域已经单位化,如图15所示),在没有其他干预的情况下,就会出现等幅振荡。众所周知,PD控制会有初始误差,PI控制会有振荡。但是如果采用单值隶属函数而不是三角形分布的隶属函数,上述的振荡现象就可以抑制。从图14中可以看出,采用单值隶属函数,在刚开始,系统输出振荡最厉害的时候采用单值隶属函数,等到等幅数振荡输出之后就不采用单值隶属函数(虚线表示),之后采用三角形隶属函数和COG解模糊方法。(两种情况都没有稳定误差)。所以我们可以下结论:即使采用相同的解模糊方法(COG),如果隶属函数不一样,控制结果也会不同的。COMPARATIVE ANALYSIS OF CLASSICAL AND FUZZY PIDCONTROL ALGORITHMSAbstract: A fuzzy PID controllers are physically related to classical PID controller. The settings of classical controllers are based on deep common physical background. Fuzzy controller can embody better behavior comparing with classical linear PID controller because of its non linear characteristics. Well tuned fuzzy controller can be also more stable and more robust for the time varying systems. On the other hand, when the fuzzy controller is tuned badly it can exhibit limit cycle which can decrease lifetime of the actuator. This phenomenon is critical especially when the actuator is valve. Knowing about these problems, more analytical methods of tuning fuzzy controllers can be found. The method with unified universe considerably simplifies the setting and realization of fuzzy controllers. This paper tries to analyze causes of oscillations and it outlines the possibilities how to reduce them. The paper also shows solution how to reduce time needed for computation of control signal by decreasing the number of membership functions and by changing defuzzification method. 1. INTRODUCTIONOne of the main drawbacks of fuzzy controllers is big amount of parameters to be tuned. It is especially difficult to make initial approximate adjustment because there is no cookery book how to do it. Also it is very well known that good convergence of optimum method is strongly dependent on initial settings. The adjustment of fuzzy controllers is considerably simplified when fuzzy controller with a unified universe is used. The parameters to be tune then have their physical meaning and fuzzy controller can be approximately adjusted using known rules for classical controllers. Probably the easiest way how to implement fuzzy PID controller is to create it as a parallel combination of basic fuzzy controllers (P+I+D 4 or PI+D 5). Suitable choice of inference method can ensure behavior which is close to one of classical PID controller for both the tracking problem and the step disturbance rejection. The fuzzy sets are assumed to have initially symmetrical layout and the parameters of both regulators are tuned using for example by Ziegler- Nichols method.To improve behavior of such designed fuzzy controller it is necessary either to manually change the quantities of fuzzy controller or to use some optimum methods which do this operation. One which can be implied are genetic algorithms. Different quantities can be changed to reach the optimum values. These quantities are fuzzy set layout, number of fuzzy sets, rule base mapping, the parameters of basic fuzzy controllers and their various combinations. Note that all the optimum must be always performed according to the chosen inference and defuzzification method. It is apparent that process of optimum can take a lot of time. Moreover this method is contingent on existence of accurate mathematical model of the process because in vast majority of the cases it is not possible to perform any kind of optimum directly on real process. The model usually does not correspond to real system which limits the success of optimum methods. The prime idea of fuzzy control was to apply it at the place where there is no deep knowledge of transfer function of controlled system and where this knowledge can be hardly identified. These are often the cases where the fuzzy control leads to better performance comparing with classical approach. Also for this instance it seems to be advantageous to have physical connection between fuzzy controller and its classical counterpart because it can significantly simplify the adjustment of regulator for real process.The heuristic optimum of parameters settings is also suitable for fuzzy PI controller with unified universe where the parameters are the same as the ones of classical PI controller. The parallel combination of fuzzy PI and PD controllers can be used for heuristic optimum of parameters settings but it should be noted that because of the presence of double proportional part in this regulatorthe adjusted parameters will differ from the ones of classical PID controller. But important thing is that the adjustment of this parameters is still in the same physical meaning. Note that for all previously mentioned controllers it is also possible to employ time transformation (sample time modification) without having to change the scope of universes.2. FUZZY PI CONTROLLER DESIGNThe control signal generated by fuzzy PI controller (according to 2) is A realization of the fuzzy PI controller is shown in Fig. 3.Let us assume plant described by following transfer function to illustrate and to compare behavior of fuzzy PI controller with classical continuous PI controller:Using the tuning method from 6 we obtain parameters K=2.14, TI = 5.8 s. The responses of controlled system using this control algorithm are shown in Fig. 4. The disturbance acts on the input of the system. Fuzzy controller was realized according to Fig. 3 with rule base mapping according to Fig. 2. The membership functions were distributed as shown in Fig.1. The similar settings of parameters K = 2.14, TI = 5 with respect to optimum for different methods of inference and defuzzification methods was used. The scale was settled to M = 10 and sample period was set to T = 0.1 s. The time responses for different inference and defuzzification methods are shown in Fig. 5. The following settings were tested according to 3. The inference method Min-Max and Prod-Max. Defuzzification was done using COG method with singletons or triangles as an output membership functions. The simulations were launched with either three of seven fuzzy sets in all the normalized universes. Also singletons were realized using normalized universe. The singletons were located in vertexes of original fuzzy sets (see Fig. 1). Comparing the results obtained using classical PI and fuzzy PI controllers following discussion can take place. The output of the system has very small overshoot when it is controlled with fuzzy regulator. The disturbance rejection using fuzzy controller is comparable with disturbance rejection of classical PI controller.In the reference 6 in Fig. 5 there was shown that the step disturbance in the input of the system with amplitude 0.05 brings the system to the significant oscillations. The same settings as in this article were used to obtain time responses. As it can be seen in Fig. 6, where there are corresponding time responses, there are no any oscillations visible. However, it was not possible to analyze potential causes of oscillations which were obtained in article 6 due to the lack of detailed settings of fuzzy controller. Significantly better results comparing with approximately adjusted fuzzy PI controller were not obtained even after the optimum using genetic algorithms. It is possible to shorten time required for computing the command by reducing the number of membership functions to three. Reduction of membership functions brings together small degradation of dynamical behavior (Fig. 7). This degradation can be almost eliminated by fine tuning of the parameters. As a result of these simulations we can state that the assertions in paper 6 were not proved.3. FUZZY PD+PI CONTROLLER DESIGNLet us create fuzzy controller as a parallel combination of fuzzy PI and PD controllers. Simulation results obtained using classical I-PD controller are shown in Fig. 9. This controller was adjusted using Ziegler-Nichols method (K = 7.28, TI = 2.8 s, TD = 0.7 s). The initial adjustment of fuzzy PI-PD controller is taken up from reference 2 (KI = KD = 4, TI = 2.2, TD = 2, MI = MD = 10, T = 0.1 s, Min-Max inference method, COG method for defuzzification, 7 membership functions). Membership function layout and rule base for both PI and PD parts are shown in Fig. 1 and Fig. 2 respectively. The only exception is in increment of command which is realized as shown in Fig. 11. Simulation results can be seen in Fig. 10. Fig. 12 shows the time responses with three different settings. Solid line uses the same adjustment as previously described simulation but inference method is Prod-Max. Dash-dot dot line represents the simulation with 3 membership functions, inference Min-Max and defuzzification using triangular membership functions with COG method. Dash-and-dot line shows simulation results with 3 membership functions, inference Min-Max and defuzzification using singletons. When the singletons are used they are placed into the vertex of original fuzzy membership functions.The influence of disturbance with small amplitude of 0.05 which acts at the input of the system is shown in Fig. 13.Fuzzy controller is generally inclinable to oscillation with relatively small amplitude. The origin of this oscillation is not only incorrect tuning of the parameters but also the inference method Min-Max. The oscillations are considerably eliminated when the Prod-Max inference method is employed and singletons for defuzzification are used. Another potential source of oscillations is wrong implementation of inference engine. Shift of the vertex point of middle membership function just for 0.01 on the normalized universe (illustrated in Fig. 15) causes the limit cycles to appear (see results in Fig. 14) without any other external intervention. The initial deviation is caused by PD controller and the oscillations by PI controller. When the singleton membership functions are used instead of triangular ones the described phenomena of oscillations disappear. Following the results in Fig. 14 it can be seen that the singletons as an output membership functions give at the beginning higher oscillation but after the time they disappear (dashed line). Triangular membership functions with COG defuzzification give after short transient response steady limit cycle. Note the nonzero steady state error in both cases. As a consequence we can say that there is a difference between defuzzification using singletons and triangular membership functions even if the COG method is used. 12

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