模糊控制理论外文文献翻译
【机械类文献翻译】对移动式遥控装置的智能控制—使用2型模糊理论
附件1：外文资料翻译译文对移动式遥控装置的智能控制——使用2型模糊理论摘要：我们针对单轮移动式遥控装置的动态模型开发出一种追踪控制器，这种追踪控制器是建立在模糊理论的基础上将运动控制器和力矩控制器整合起来的装置。
用计算机模拟来确定追踪控制器的工作情况和它对不同航向的实际用途。
关键词：智能控制、2型模糊理论、移动式遥控装置I. 介绍由于受运动学强制约束，移动遥控装置是非完整的系统。
描述此约束的恒等式不能够明确的反映出遥控装置在局部及整体坐标系中的关系。
因此，包括它们在内的控制问题吸引了去年控制领域的注意力。
不同的方法被用来解决运动控制的问题。
Kanayama等人针对一个非完整的交通工具提出了一个稳定的追踪控制方案，这种方案使用了Lyapunov功能。
Lee等人用还原法和饱和约束来解决追踪控制。
此外，大多数被报道过的设计依赖于智能控制方式如模糊逻辑控制和神经式网络。
然而上述提到的发表中大多数都集中在移动式遥控装置的运动模块，即这些模块是受速度控制的。
而很少有发表关注到不完整的动力系统，即受力和扭矩控制的模块：布洛克。
在2005年12月15日被视为标准并且在2006年3月5日被公认的手稿。
这一著作在某种程度上受到DGEST——一个在Grant 493.05-P下的研究所的支持。
研究者们同样也受到了来自CONACYT——给予他们研究成果的奖学金的支持。
在这篇论文中我展现了一台追踪单轮移动式遥控装置的控制器，这台追踪控制器用了一种控制条件如移动遥控装置的速度达到了有效速度，还用了一种模糊理论控制器如给实际遥控装置提供了必要扭矩。
这篇论文的其余部分的结构如下：第二部分和第三部分对问题作了简洁描述，包括了单轮车移动遥控装置的运动和动力模块和对追踪控制器的介绍。
第四部分用追踪控制器列举了些模拟结果。
第五部分做出了结论。
II. 疑难问题陈述A 移动控制装置这个被看作单轮移动控制器的模型（见图1），它是由两个同轴驱动轮和一个自由前轮组成。
自动化 外文翻译 外文文献 英文文献 锅炉蒸汽温度模糊神经网络的广义预测控制
目录Part 1 PID type fuzzy controller and parameters adaptive method1 Part 2 Application of self adaptation fuzzy-PID control for main steamtemperature control system in power station错误！未定义书签。
Part 3 Neuro-fuzzy generalized predictive control of boiler steam temperature .............................................................. (13)Part 4 为Part3译文：锅炉蒸汽温度模糊神经网络的广义预测控制22Part 1 PID type fuzzy controller andParameters adaptivemethodWu zhi QIAO, Masaharu MizumotoAbstract: The authors of this paper try to analyze the dynamic behavior of the product-sum crisp type fuzzy controller, revealing that this type of fuzzy controller behaves approximately like a PD controller that may yield steady-state error for the control system. By relating to the conventional PID control theory, we propose a new fuzzy controller structure, namely PID type fuzzy controller which retains the characteristics similar to the conventional PID controller. In order to improve further the performance of the fuzzy controller, we work out a method to tune the parameters of the PID type fuzzy controller on line, producing a parameter adaptive fuzzy controller. Simulation experiments are made to demonstrate the fine performance of these novel fuzzy controller structures.Keywords: Fuzzy controller; PID control; Adaptive control1. IntroductionAmong various inference methods used in the fuzzy controller found in literatures , the most widely used ones in practice are the Mamdani method proposed by Mamdani and his associates who adopted the Min-max compositional rule of inference based on an interpretation of a control rule as a conjunction of the antecedent and consequent, and the product-sum method proposed by Mizumoto who suggested to introduce the product and arithmetic mean aggregation operators to replace the logical AND (minimum) and OR (maximum) calculations in the Min-max compositional rule of inference.In the algorithm of a fuzzy controller, the fuzzy function calculation isalso a complicated and time consuming task. Tagagi and Sugeno proposed a crisp type model in which the consequent parts of the fuzzy control rules are crisp functional representation or crisp real numbers in the simplified case instead of fuzzy sets . With this model of crisp real number output, the fuzzy set of the inference consequence will be a discrete fuzzy set with a finite number of points, this can greatly simplify the fuzzy function algorithm.Both the Min-max method and the product-sum method are often applied with the crisp output model in a mixed manner. Especially the mixed product-sum crisp model has a fine performance and the simplest algorithm that is very easy to be implemented in hardware system and converted into a fuzzy neural network model. In this paper, we will take account of the product-sum crisp type fuzzy controller.2. PID type fuzzy controller structureAs illustrated in previous sections, the PD function approximately behaves like a parameter time-varying PD controller. Since the mathematical models of most industrial process systems are of type, obviously there would exist an steady-state error if they are controlled by this kind of fuzzy controller. This characteristic has been stated in the brief review of the PID controller in the previous section.If we want to eliminate the steady-state error of the control system, we can imagine to substitute the input (the change rate of error or the derivative of error) of the fuzzy controller with the integration of error. This will result the fuzzy controller behaving like a parameter time-varying PI controller, thus the steady-state error is expelled by the integration action. However, a PI type fuzzy controller will have a slow rise time if the P parameters are chosen small, and have a large overshoot if the P or I parameters are chosen large. So there may be the time when one wants to introduce not only the integration control but the derivative control to the fuzzy control system, because the derivative control can reduce the overshoot of the system's response so as to improve thecontrol performance. Of course this can be realized by designing a fuzzy controller with three inputs, error, the change rate of error and the integration of error. However, these methods will be hard to implement in practice because of the difficulty in constructing fuzzy control rules. Usually fuzzy control rules are constructed by summarizing the manual control experience of an operator who has been controlling the industrial process skillfully and successfully. The operator intuitively regulates the executor to control the process by watching the error and the change rate of the error between the system's output and the set-point value. It is not the practice for the operator to observe the integration of error. Moreover, adding one input variable will greatly increase the number of control rules, the constructing of fuzzy control rules are even more difficult task and it needs more computation efforts. Hence we may want to design a fuzzy controller that possesses the fine characteristics of the PID controller by using only the error and the change rate of error as its inputs.One way is to have an integrator serially connected to the output of the fuzzy controller as shown in Fig. 1. In Fig. 1,1K and 2K are scaling factors for e and ~ respectively, and fl is the integral constant. In the proceeding text, for convenience, we did not consider the scaling factors. Here in Fig. 2, when we look at the neighborhood of NODE point in the e - ~ plane, it follows from (1) that the control input to the plant can be approximated by(1)Hence the fuzzy controller becomes a parameter time-varying PI controller, its equivalent proportional control and integral control components are BK2D and ilK1 P respectively. We call this fuzzy controller as the PI type fuzzy controller (PI fc). We can hope that in a PI type fuzzy control system, the steady-state error becomes zero. To verify the property of the PI type fuzzy controller, we carry out some simulation experiments. Before presenting the simulation, we give a description of the simulation model. In the fuzzy control system shown in Fig. 3, the plant model is a second-order and type system with the following transfer function:)1)(1()(21++=s T s T K s G (2) Where K = 16, 1T = 1, and 2T = 0.5. In our simulation experiments, we use the discrete simulation method, the results would be slightly different from that of a continuous system, the sampling time of the system is set to be 0.1 s. For the fuzzy controller, the fuzzy subsets of e and d are defined as shown in Fig. 4. Their coresThe fuzzy control rules are represented as Table 1. Fig. 5 demonstrates the simulation result of step response of the fuzzy control system with a Pl fc. We can see that the steady-state error of the control system becomes zero, but when the integration factor fl is small, the system's response is slow, and when it is too large, there is a high overshoot and serious oscillation. Therefore, wemay want to introduce the derivative control law into the fuzzy controller to overcome the overshoot and instability. We propose a controller structure that simply connects the PD type and the PI type fuzzy controller together in parallel. We have the equivalent structure of that by connecting a PI device with the basic fuzzy controller serially as shown in Fig.6. Where ~ is the weight on PD type fuzzy controller and fi is that on PI type fuzzy controller, the larger a/fi means more emphasis on the derivative control and less emphasis on the integration control, and vice versa. It follows from (7) that the output of the fuzzy controller is(3)3. The parameter adaptive methodThus the fuzzy controller behaves like a time-varying PID controller, its equivalent proportional control, integral control and derivative control components are respectively. We call this new controller structure a PID type fuzzy controller (PID fc). Figs. 7 and 8 are the simulation results of the system's step response of such control system. The influence of ~ and fl to the system performance is illustrated. When ~ > 0 and/3 = 0, meaning that the fuzzy controller behaves like PD fc, there exist a steady-state error. When ~ = 0 and fl > 0, meaning that the fuzzy controller behaves like a PI fc, the steady-state error of the system is eliminated but there is a large overshoot and serious oscillation.When ~ > 0 and 13 > 0 the fuzzy controller becomes a PID fc, the overshoot is substantially reduced. It is possible to get a comparatively good performance by carefully choosing the value of αandβ.4. ConclusionsWe have studied the input-output behavior of the product-sum crisp type fuzzy controller, revealing that this type of fuzzy controller behaves approximately like a parameter time-varying PD controller. Therefore, the analysis and designing of a fuzzy control system can take advantage of the conventional PID control theory. According to the coventional PID control theory, we have been able to propose some improvement methods for the crisp type fuzzy controller.It has been illustrated that the PD type fuzzy controller yields a steady-state error for the type system, the PI type fuzzy controller can eliminate the steady-state error. We proposed a controller structure, that combines the features of both PD type and PI type fuzzy controller, obtaining a PID type fuzzy controller which allows the control system to have a fast rise and a small overshoot as well as a short settling time.To improve further the performance of the proposed PID type fuzzy controller, the authors designed a parameter adaptive fuzzy controller. The PID type fuzzy controller can be decomposed into the equivalent proportionalcontrol, integral control and the derivative control components. The proposed parameter adaptive fuzzy controller decreases the equivalent integral control component of the fuzzy controller gradually with the system response process time, so as to increase the damping of the system when the system is about to settle down, meanwhile keeps the proportional control component unchanged so as to guarantee quick reaction against the system's error. With the parameter adaptive fuzzy controller, the oscillation of the system is strongly restrained and the settling time is shortened considerably.We have presented the simulation results to demonstrate the fine performance of the proposed PID type fuzzy controller and the parameter adaptive fuzzy controller structure.Part 2 Application of self adaptationfuzzy-PID control for main steam temperature control system inpower stationZHI-BIN LIAbstract: In light of the large delay, strong inertia, and uncertainty characteristics of main steam temperature process, a self adaptation fuzzy-PID serial control system is presented, which not only contains the anti-disturbance performance of serial control, but also combines the good dynamic performance of fuzzy control. The simulation results show that this control system has more quickly response, better precision and strongeranti-disturbance ability．Keywords：Main steam temperature；Self adaptation；Fuzzy control；Serial control1. IntroductionThe boiler superheaters of modem thermal power station run under the condition of high temperature and high pressure, and the superheater’s temperature is highest in the steam channels．so it has important effect to the running of the whole thermal power station．If the temperature is too high, it will be probably burnt out. If the temperature is too low ,the efficiency will be reduced So the main steam temperature mast be strictly controlled near the given value．Fig l shows the boiler main steam temperature system structure.Fig.1 boiler main steam temperature systemIt can be concluded from Fig l that a good main steam temperature control system not only has adequately quickly response to flue disturbance and load fluctuation, but also has strong control ability to desuperheating water disturbance. The general control scheme is serial PID control or double loop control system with derivative. But when the work condition and external disturbance change large, the performance will become instable. This paper presents a self adaptation fuzzy-PID serial control system. which not only contains the anti-disturbance performance of serial control, but also combines the good dynamic character and quickly response of fuzzy control．1. Design of Control SystemThe general regulation adopts serial PID control system with load feedforward ．which assures that the main steam temperature is near the given value 540℃in most condition ．If parameter of PID control changeless and the work condition and external disturbance change large, the performance will become in stable ．The fuzzy control is fit for controlling non-linear and uncertain process. The general fuzzy controller takes error E and error change ratio EC as input variables ．actually it is a non-linear PD controller, so it has the good dynamic performance ．But the steady error is still in existence. In linear system theory, integral can eliminate the steady error. So if fuzzy control is combined with PI control, not only contains the anti-disturbance performance of serial control, but also has the good dynamic performance and quickly response.In order to improve fuzzy control self adaptation ability, Prof ．Long Sheng-Zhao and Wang Pei-zhuang take the located in bringing forward a new idea which can modify the control regulation online ．This regulation is:]1,0[,)1(∈-+=αααEC E UThis control regulation depends on only one parameter α.Once αis fixed ．the weight of E and EC will be fixed and the self adaptation ability will be very small ．It was improved by Prof. Li Dong-hui and the new regulation is as follow;]1,0[,,,3,)1(2,)1(1,)1(0,)1({321033221100∈±=-+±=-+±=-+=-+=ααααααααααααE EC E E EC E E EC E E EC E UBecause it is very difficult to find a self of optimum parameter, a new method is presented by Prof ．Zhou Xian-Lan, the regulation is as follow:)0(),exp(12>--=k ke αBut this algorithm still can not eliminate the steady error ．This paper combines this algorithm with PI control ，the performance is improved ．2. Simulation of Control System3.1 Dynamic character of controlled objectPapers should be limited to 6 pages Papers longer than 6 pages will be subject to extra fees based on their length ．Fig .2 main steam temperature control system structureFig 2 shows the main steam temperature control system structure ，)(),(21s W s W δδare main controller and auxiliary controller,)(),(21s W s W o o are characters of the leading and inertia sections,)(),(21s W s W H Hare measure unit.3.2 Simulation of the general serial PID control system The simulation of the general serial PID control system is operated by MATLAB, the simulation modal is as Fig.3.Setp1 and Setp2 are the given value disturbance and superheating water disturb & rice .PID Controller1 and PID Controller2 are main controller and auxiliary controller ．The parameter value which comes from references is as follow ：667.37,074.0,33.31)(25)(111111122===++===D I p D I p p k k k s k sk k s W k s W δδFig.3. the general PID control system simulation modal3.3 Simulation of self adaptation fuzzy-PID control system SpacingThe simulation modal is as Fig 4.Auxiliary controlleris:25)(22==p k s W δ.Main controller is Fuzzy-PI structure, and the PI controller is:074.0,33.31)(11111==+=I p I p k k s k k s W δFuzzy controller is realized by S-function, and the code is as fig.5.Fig.4. the fuzzy PID control system simulation modalFig 5 the S-function code of fuzzy control3.4 Comparison of the simulationGiven the same given value disturbance and the superheating water disturbance，we compare the response of fuzzy-PID control system with PID serial control system. The simulation results are as fig.6-7.From Fig6-7,we can conclude that the self adaptation fuzzy-PID control system has the more quickly response, smaller excess and strongeranti-disturbance．4. Conclusion(1)Because it combines the advantage of PID controller and fuzzy controller, theself adaptation fuzzy-PID control system has better performance than the general PID serial control system.(2)The parameter can self adjust according to the error E value. so this kind of controller can harmonize quickly response with system stability．Part 3 Neuro-fuzzy generalized predictive controlof boiler steam temperatureXiangjie LIU, Jizhen LIU, Ping GUANAbstract: Power plants are nonlinear and uncertain complex systems. Reliable control of superheated steam temperature is necessary to ensure high efficiency and high load-following capability in the operation of modern power plant. A nonlinear generalized predictive controller based on neuro-fuzzy network (NFGPC) is proposed in this paper. The proposed nonlinear controller is applied to control the superheated steam temperature of a 200MW power plant. From the experiments on the plant and the simulation of the plant, much better performance than the traditional controller is obtained.Keywords: Neuro-fuzzy networks; Generalized predictive control;Superheated steam temperature1. IntroductionContinuous process in power plant and power station are complex systems characterized by nonlinearity, uncertainty and load disturbance. The superheater is an important part of the steam generation process in the boiler-turbine system, where steam is superheated before entering the turbine that drives the generator. Controlling superheated steam temperature is not only technically challenging, but also economically important.From Fig.1,the steam generated from the boiler drum passes through the low-temperature superheater before it enters the radiant-type platen superheater. Water is sprayed onto the steam to control the superheated steam temperature in both the low and high temperature superheaters. Proper control of the superheated steam temperature is extremely important to ensure the overall efficiency and safety of the power plant. It is undesirable that the steam temperature is too high, as it can damage the superheater and the high pressure turbine, or too low, as it will lower the efficiency of the power plant. It is also important to reduce the temperature fluctuations inside the superheater, as it helps to minimize mechanical stress that causes micro-cracks in the unit, in order to prolong the life of the unit and to reducemaintenance costs. As the GPC is derived by minimizing these fluctuations, it is amongst the controllers that are most suitable for achieving this goal.The multivariable multi-step adaptive regulator has been applied to control the superheated steam temperature in a 150 t/h boiler, and generalized predictive control was proposed to control the steam temperature.A nonlinear long-range predictive controller based on neural networks is developed into control the main steam temperature and pressure, and the reheated steam temperature at several operating levels. The control of the main steam pressure and temperature based on a nonlinear model that consists of nonlinear static constants and linear dynamics is presented in that.Fig.1 The boiler and superheater steam generation process Fuzzy logic is capable of incorporating human experiences via the fuzzy rules. Nevertheless, the design of fuzzy logic controllers is somehow time consuming, as the fuzzy rules are often obtained by trials and errors. In contrast, neural networks not only have the ability to approximate non-linear functions with arbitrary accuracy, they can also be trained from experimental data. The neuro-fuzzy networks developed recently have the advantages of model transparency of fuzzy logic and learning capability of neural networks. The NFN is have been used to develop self-tuning control, and is therefore a useful tool for developing nonlinear predictive control. Since NFN is can be considered as a network that consists of several local re-gions, each of which contains a local linear model, nonlinear predictive control based on NFN can be devised with the network incorporating all the local generalized predictivecontrollers (GPC) designed using the respective local linear models. Following this approach, the nonlinear generalized predictive controllers based on the NFN, or simply, the neuro-fuzzy generalized predictive controllers (NFG-PCs)are derived here. The proposed controller is then applied to control the superheated steam temperature of the 200MW power unit. Experimental data obtained from the plant are used to train the NFN model, and from which local GPC that form part of the NFGPC is then designed. The proposed controller is tested first on the simulation of the process, before applying it to control the power plant.2. Neuro-fuzzy network modellingConsider the following general single-input single-output nonlinear dynamic system:),1(),...,(),(),...,1([)(''+-----=uy n d t u d t u n t y t y f t y ∆+--/)()](),...,1('t e n t e t e e (1)where f[.]is a smooth nonlinear function such that a Taylor series expansion exists, e(t)is a zero mean white noise andΔis the differencing operator,''',,e u y n n n and d are respectively the known orders and time delay of the system. Let the local linear model of the nonlinear system (1) at the operating point )(t o be given by the following Controlled Auto-Regressive Integrated Moving Average (CARIMA) model:)()()()()()(111t e z C t u z B z t y z A d ----+∆= (2) Where )()(),()(1111----∆=z andC z B z A z A are polynomials in 1-z , the backward shift operator. Note that the coefficients of these polynomials are a function of the operating point )(t o .The nonlinear system (1) is partitioned into several operating regions, such that each region can be approximated by a local linear model. Since NFN is a class of associative memory networks with knowledge stored locally, they can be applied to model this class of nonlinear systems. Aschematic diagram of the NFN is shown in Fig.2.B-spline functions are used as the membership functions in the NFN for the following reasons. First, B-spline functions can be readily specified by the order of the basis function and the number of inner knots. Second, they are defined on a bounded support, and the output of the basis function is always positive, i.e.,],[,0)(j k j j k x x λλμ-∉=and ],[,0)(j k j j k x x λλμ-∈>.Third, the basis functions form a partition of unity, i.e.,.][,1)(m i n ,∑∈≡j m a mj k x x x x μ(3) And fourth, the output of the basis functions can be obtained by a recurrence equation.Fig. 2 neuro-fuzzy network The membership functions of the fuzzy variables derived from the fuzzy rules can be obtained by the tensor product of the univariate basis functions. As an example, consider the NFN shown in Fig.2, which consists of the following fuzzy rules:IF operating condition i (1x is positive small, ... , and n x is negative large),THEN the output is given by the local CARIMA model i:...)()(ˆ...)1(ˆ)(ˆ01+-∆+-++-=d t u b n t y a t y a t yi i a i in i i i a )(...)()(c i in i b i in n t e c t e n d t u b c b -+++--∆+ (4) or)()()()()(ˆ)(111t e z C t u z B z t yz A i i i i d i i ----+∆= (5)Where )()(),(111---z andC z B z A i i i are polynomials in the backward shiftoperator 1-z , and d is the dead time of the plant,)(t u i is the control, and )(t e i is a zero mean independent random variable with a variance of 2δ. The multivariate basis function )(k i x a is obtained by the tensor products of the univariate basis functions,p i x A a nk k i k i ,...,2,1,)(1==∏=μ (6)where n is the dimension of the input vector x , and p , the total number of weights in the NFN, is given by,∏=+=nk i i k R p 1)( (7)Where i k and i R are the order of the basis function and the number of inner knots respectively. The properties of the univariate B-spline basis functions described previously also apply to the multivariate basis function, which is defined on the hyper-rectangles. The output of the NFN is,∑∑∑=====p i i i p i ip i i i a y aa yy 111ˆˆˆ (8) 3. Neuro-fuzzy modelling and predictive control of superheatedsteam temperatureLet θbe the superheated steam temperature, and θμ, the flow of spray water to the high temperature superheater. The response of θcan be approximated by a second order model:s pe s T s T K s s G τθμθ-++==)1)(1()()(21 (9)The linear models, however, only a local model for the selected operating point. Since load is the unique antecedent variable, it is used to select the division between the local regions in the NFN. Based on this approach, the load is divided into five regions as shown in Fig.3,using also the experience of the operators, who regard a load of 200MW as high,180MW as medium high,160MW as medium,140MW as medium low and 120MW as low. For a sampling interval of 30s , the estimated linear local models )(1-z A used in the NFN are shown in Table 1.Fig. 3 Membership function for local modelsTable 1 Local CARIMA models in neuro-fuzzy modelCascade control scheme is widely used to control the superheated steam temperature. Feed forward control, with the steam flow and the gas temperature as inputs, can be applied to provide a faster response to large variations in these two variables. In practice, the feed forward paths areactivated only when there are significant changes in these variables. The control scheme also prevents the faster dynamics of the plant, i.e., the spray water valve and the water/steam mixing, from affecting the slower dynamics of the plant, i.e., the high temperature superheater. With the global nonlinear NFN model in Table 1, the proposed NFGPC scheme is shown in Fig.4.Fig. 4 NFGPC control of superheated steam temperature with feed-for-wardcontrol.As a further illustration, the power plant is simulated using the NFN model given in Table 1,and is controlled respectively by the NFGPC, the conventional linear GPC controller, and the cascaded PI controller while the load changes from 160MW to 200MW.The conventional linear GPC controller is the local controller designed for the“medium”operating region. The results are shown in Fig.5,showing that, as expected, the best performance is obtained from the NFGPC as it is designed based on a more accurate process model. This is followed by the conventional linear GPC controller. The performance of the conventional cascade PI controller is the worst, indicating that it is unable to control satisfactory the superheated steam temperature under large load changes. This may be the reason for controlling the power plant manually when there are large load changes.Fig.5 comparison of the NFGPC, conventional linear GPC, and cascade PIcontroller.4. ConclusionsThe modeling and control of a 200 MW power plant using the neuro-fuzzy approach is presented in this paper. The NFN consists of five local CARIMA models. The out-put of the network is the interpolation of the local models using memberships given by the B-spline basis functions. The proposed NFGPC is similarly constructed, which is designed from the CARIMA models in the NFN. The NFGPC is most suitable for processes with smooth nonlinearity, such that its full operating range can be partitioned into several local linear operating regions. The proposed NFGPC therefore provides a useful alternative for controlling this class of nonlinear power plants, which are formerly difficult to be controlled using traditional methods.。
控制类毕业设计中英文翻译资料--模煳逻辑
模糊逻辑-分析和控制复杂系统的新途径--托马斯索沃尔欢迎进入模糊逻辑的精彩世界，你可以用新科学有力地实现一些东西。
在你的技术与管理技能的领域中，增加了基于模糊逻辑分析和控制的能力，你就可以实现除此之外的其他人与物无法做到的事情。
以下就是模糊逻辑的基础知识：随着系统复杂性的增加，对系统精确的阐述变得越来越难，最终变得无法阐述。
于是，终于到达了一个只有靠人类发明的模糊逻辑才能解决的复杂程度。
模糊逻辑用于系统的分析和控制设计，因为它可以缩短工程发展的时间；有时，在一些高度复杂的系统中，这是唯一可以解决问题的方法。
虽然，我们经常认为控制是和控制一个物理系统有关系的，但是，扎德博士最初设计这个概念的时候本意并非如此。
实际上，模糊逻辑适用于生物，经济，市场营销和其他大而复杂的系统。
模糊这个词最早出现在扎德博士于1962年在一个工程学权威刊物上发表论文中。
1963年，扎德博士成为加州大学伯克利分校电气工程学院院长。
那就意味着达到了电气工程领域的顶尖。
扎德博士认为模糊控制是那时的热点，不是以后的热点，更不应该受到轻视。
目前已经有了成千上万基于模糊逻辑的产品，从聚焦照相机到可以根据衣服脏度自我控制洗涤方式的洗衣机等。
如果你在美国，你会很容易找到基于模糊的系统。
想一想，当通用汽车告诉大众，她生产的汽车其反刹车是根据模糊逻辑而造成的时候，那会对其销售造成多么大的影响。
以下的章节包括：1)介绍处于商业等各个领域的人们他们如果从模糊逻辑演变而来的利益中得到好处，以及帮助大家理解模糊逻辑是怎么工作的。
2)提供模糊逻辑是怎么工作的一种指导，只有人们知道了这一点，才能运用它用于做一些对自己有利的事情。
这本书就是一个指导，因此尽管你不是电气领域的专家，你也可以运用模糊逻辑。
需要指出的是有一些针对模糊逻辑的相反观点和批评。
一个人应该学会观察反面的各个观点，从而得出自己的观点。
我个人认为，身为被表扬以及因写关于模糊逻辑论文而受到赞赏的作者，他会认为，在这个领域中的这种批评有点过激。
fuzzy control 外文翻译
C H A P T E R2Fuzzy Control:The BasicsA few strong instincts and a few plain rules sufficeus.–Ralph Waldo Emerson2.1OverviewThe primary goal of control engineering is to distill and apply knowledge about how to control a process so that the resulting control system will reliably and safely achieve high-performance operation.In this chapter we show how fuzzy logic provides a methodology for representing and implementing our knowledge about how best to control a process.We begin in Section2.2with a“gentle”(tutorial)introduction,where we focus on the construction and basic mechanics of operation of a two-input one-output fuzzy controller with the most commonly used fuzzy operations.Building on our understanding of the two-input one-output fuzzy controller,in Section2.3we pro-vide a mathematical characterization of general fuzzy systems with many inputs and outputs,and general fuzzification,inference,and defuzzification strategies.In Section2.4we illustrate some typical steps in the fuzzy control design process via a simple inverted pendulum control problem.We explain how to write a computer program that will simulate the actions of a fuzzy controller in Section2.5.More-over,we discuss various issues encountered in implementing fuzzy controllers in Section2.6.Then,in Chapter3,after providing an overview of some design methodologies for fuzzy controllers and computer-aided design(CAD)packages for fuzzy system construction,we present several design case studies for fuzzy control systems.It is these case studies that the reader willfind most useful in learning thefiner2324Chapter2/Fuzzy Control:The Basicspoints about the fuzzy controller’s operation and design.Indeed,the best way toreally learn fuzzy control is to design your own fuzzy controller for one of theplants studied in this or the next chapter,and simulate the fuzzy control system toevaluate its performance.Initially,we recommend coding this fuzzy controller in ahigh-level language such as C,Matlab,or ter,after you have acquiredafirm understanding of the fuzzy controller’s operation,you can take shortcuts byusing a(or designing your own)CAD package for fuzzy control systems.After completing this chapter,the reader should be able to design and simulatea fuzzy control system.This will move the reader a long way toward implementationof fuzzy controllers since we provide pointers on how to overcome certain practicalproblems encountered in fuzzy control system design and implementation(e.g.,coding the fuzzy controller to operate in real-time,even with large rule-bases).This chapter provides a foundation on which the remainder of the book rests.After our case studies in direct fuzzy controller design in Chapter3,we will usethe basic definition of the fuzzy control system and study its fundamental dynamicproperties,including stability,in Chapter 4.We will use the same plants,andothers,to illustrate the techniques for fuzzy identification,fuzzy adaptive control,and fuzzy supervisory control in Chapters5,6,and7,respectively.It is thereforeimportant for the reader to have afirm grasp of the concepts in this and the nextchapter before moving on to these more advanced chapters.Before skipping any sections or chapters of this book,we recommend that the reader study the chapter summaries at the end of each chapter.In these summarieswe will highlight all the major concepts,approaches,and techniques that are coveredin the chapter.These summaries also serve to remind the reader what should belearned in each chapter.2.2Fuzzy Control:A Tutorial IntroductionA block diagram of a fuzzy control system is shown in Figure2.1.The fuzzy con-troller1is composed of the following four elements:1.A rule-base(a set of If-Then rules),which contains a fuzzy logic quantificationof the expert’s linguistic description of how to achieve good control.2.An inference mechanism(also called an“inference engine”or“fuzzy inference”module),which emulates the expert’s decision making in interpreting and ap-plying knowledge about how best to control the plant.3.A fuzzification interface,which converts controller inputs into information thatthe inference mechanism can easily use to activate and apply rules.4.A defuzzification interface,which converts the conclusions of the inferencemechanism into actual inputs for the process.1.Sometimes a fuzzy controller is called a“fuzzy logic controller”(FLC)or even a“fuzzylinguistic controller”since,as we will see,it uses fuzzy logic in the quantification of linguisticdescriptions.In this book we will avoid these phrases and simply use“fuzzy controller.”2.2Fuzzy Control:A Tutorial Introduction 25FIGURE 2.1Fuzzy controller.We introduce each of the components of the fuzzy controller for a simple prob-lem of balancing an inverted pendulum on a cart,as shown in Figure 2.2.Here,y denotes the angle that the pendulum makes with the vertical (in radians),l is the half-pendulum length (in meters),and u is the force input that moves the cart (in Newtons).We will use r to denote the desired angular position of the pendulum.The goal is to balance the pendulum in the upright position (i.e.,r =0)when it initially starts with some nonzero angle offthe vertical (i.e.,y =0).This is a very simple and academic nonlinear control problem,and many good techniques already existfor its solution.Indeed,for this standard configuration,a simple PID controller works well even in implementation.In the remainder of this section,we will use the inverted pendulum as a con-venient problem to illustrate the design and basic mechanics of the operation of a fuzzy control system.We will also use this problem in Section 2.4to discuss much more general issues in fuzzy control system design that the reader will find useful for more challenging applications (e.g.,the ones in the next chapter).FIGURE 2.2Inverted pendulumon a cart.26Chapter2/Fuzzy Control:The Basics2.2.1Choosing Fuzzy Controller Inputs and OutputsConsider a human-in-the-loop whose responsibility is to control the pendulum,asshown in Figure2.3.The fuzzy controller is to be designed to automate how ahuman expert who is successful at this task would control the system.First,theexpert tells us(the designers of the fuzzy controller)what information she or hewill use as inputs to the decision-making process.Suppose that for the invertedpendulum,the expert(this could be you!)says that she or he will usee(t)=r(t)−y(t)andde(t)dtas the variables on which to base decisions.Certainly,there are many other choices(e.g.,the integral of the error e could also be used)but this choice makes goodintuitive sense.Next,we must identify the controlled variable.For the invertedpendulum,we are allowed to control only the force that moves the cart,so thechoice here is simple.FIGURE2.3Human controlling aninverted pendulum on a cart.For more complex applications,the choice of the inputs to the controller and outputs of the controller(inputs to the plant)can be more difficult.Essentially,youwant to make sure that the controller will have the proper information availableto be able to make good decisions and have proper control inputs to be able tosteer the system in the directions needed to be able to achieve high-performanceoperation.Practically speaking,access to information and the ability to effectivelycontrol the system often cost money.If the designer believes that proper informationis not available for making control decisions,he or she may have to invest in anothersensor that can provide a measurement of another system variable.Alternatively,the designer may implement somefiltering or other processing of the plant outputs.In addition,if the designer determines that the current actuators will not allowfor the precise control of the process,he or she may need to invest in designingand implementing an actuator that can properly affect the process.Hence,while insome academic problems you may be given the plant inputs and outputs,in manypractical situations you may have someflexibility in their choice.These choices2.2Fuzzy Control:A Tutorial Introduction27 affect what information is available for making on-line decisions about the controlof a process and hence affect how we design a fuzzy controller.Once the fuzzy controller inputs and outputs are chosen,you must determinewhat the reference inputs are.For the inverted pendulum,the choice of the referenceinput r=0is clear.In some situations,however,you may want to choose r assome nonzero constant to balance the pendulum in the off-vertical position.To dothis,the controller must maintain the cart at a constant acceleration so that the pendulum will not fall.After all the inputs and outputs are defined for the fuzzy controller,we canspecify the fuzzy control system.The fuzzy control system for the inverted pendu-lum,with our choice of inputs and outputs,is shown in Figure2.4.Now,within this framework we seek to obtain a description of how to control the process.We see thenthat the choice of the inputs and outputs of the controller places certain constraintson the remainder of the fuzzy control design process.If the proper information isnot provided to the fuzzy controller,there will be little hope for being able to designa good rule-base or inference mechanism.Moreover,even if the proper informationis available to make control decisions,this will be of little use if the controller isnot able to properly affect the process variables via the process inputs.It must be understood that the choice of the controller inputs and outputs is a fundamentally important part of the control design process.We will revisit this issue several times throughout the remainder of this chapter(and book).FIGURE2.4Fuzzy controller for an inverted pendulum on a cart.2.2.2Putting Control Knowledge into Rule-BasesSuppose that the human expert shown in Figure2.3provides a description of howbest to control the plant in some natural language(e.g.,English).We seek to takethis“linguistic”description and load it into the fuzzy controller,as indicated bythe arrow in Figure2.4.28Chapter2/Fuzzy Control:The BasicsLinguistic DescriptionsThe linguistic description provided by the expert can generally be broken intoseveral parts.There will be“linguistic variables”that describe each of the time-varying fuzzy controller inputs and outputs.For the inverted pendulum,“error”describes e(t)“change-in-error”describes ddt e(t)“force”describes u(t)Note that we use quotes to emphasize that certain words or phrases are linguistic descriptions,and that we have added the time index to,for example,e(t),to em-phasize that generally e varies with time.There are many possible choices for the linguistic descriptions for variables.Some designers like to choose them so that they are quite descriptive for documentation purposes.However,this can sometimes lead to long descriptions.Others seek to keep the linguistic descriptions as short as pos-sible(e.g.,using“e(t)”as the linguistic variable for e(t)),yet accurate enough so that they adequately represent the variables.Regardless,the choice of the linguistic variable has no impact on the way that the fuzzy controller operates;it is simply a notation that helps to facilitate the construction of the fuzzy controller via fuzzy logic.Just as e(t)takes on a value of,for example,0.1at t=2(e(2)=0.1),linguistic variables assume“linguistic values.”That is,the values that linguistic variables take on over time change dynamically.Suppose for the pendulum example that “error,”“change-in-error,”and“force”take on the following values:“neglarge”“negsmall”“zero”“possmall”“poslarge”Note that we are using“negsmall”as an abbreviation for“negative small in size”and so on for the other variables.Such abbreviations help keep the linguistic de-scriptions short yet precise.For an even shorter description we could use integers:“−2”to represent“neglarge”“−1”to represent“negsmall”“0”to represent“zero”“1”to represent“possmall”“2”to represent“poslarge”This is a particularly appealing choice for the linguistic values since the descriptions are short and nicely represent that the variable we are concerned with has a numeric quality.We are not,for example,associating“−1”with any particular number of radians of error;the use of the numbers for linguistic descriptions simply quantifies the sign of the error(in the usual way)and indicates the size in relation to the2.2Fuzzy Control:A Tutorial Introduction29 other linguistic values.We shallfind the use of this type of linguistic value quite convenient and hence will give it the special name,“linguistic-numeric value.”The linguistic variables and values provide a language for the expert to expressher or his ideas about the control decision-making process in the context of the framework established by our choice of fuzzy controller inputs and outputs.Recallthat for the inverted pendulum r=0and e=r−y so thate=−yandd dt e=−ddtysince ddt r=0.First,we will study how we can quantify certain dynamic behaviorswith linguistics.In the next subsection we will study how to quantify knowledge about how to control the pendulum using linguistic descriptions.For the inverted pendulum each of the following statements quantifies a different configuration of the pendulum(refer back to Figure2.2on page25):•The statement“error is poslarge”can represent the situation where the pendulum is at a significant angle to the left of the vertical.•The statement“error is negsmall”can represent the situation where the pendulum is just slightly to the right of the vertical,but not too close to the vertical to justify quantifying it as“zero”and not too far away to justify quantifying it as “neglarge.”•The statement“error is zero”can represent the situation where the pendulum is very near the vertical position(a linguistic quantification is not precise,hence we are willing to accept any value of the error around e(t)=0as being quantified linguistically by“zero”since this can be considered a better quantification than “possmall”or“negsmall”).•The statement“error is poslarge and change-in-error is possmall”can representthe situation where the pendulum is to the left of the vertical and,since ddt y<0,the pendulum is moving away from the upright position(note that in this case the pendulum is moving counterclockwise).•The statement“error is negsmall and change-in-error is possmall”can represent the situation where the pendulum is slightly to the right of the vertical and,sinced dt y<0,the pendulum is moving toward the upright position(note that in thiscase the pendulum is also moving counterclockwise).It is important for the reader to study each of the cases above to understand how the expert’s linguistics quantify the dynamics of the pendulum(actually,each partially quantifies the pendulum’s state).30Chapter2/Fuzzy Control:The BasicsOverall,we see that to quantify the dynamics of the process we need to have a good understanding of the physics of the underlying process we are trying to control.While for the pendulum problem,the task of coming to a good understanding ofthe dynamics is relatively easy,this is not the case for many physical processes.Quantifying the process dynamics with linguistics is not always easy,and certainlya better understanding of the process dynamics generally leads to a better linguisticquantification.Often,this will naturally lead to a better fuzzy controller providedthat you can adequately measure the system dynamics so that the fuzzy controllercan make the right decisions at the proper time.RulesNext,we will use the above linguistic quantification to specify a set of rules(arule-base)that captures the expert’s knowledge about how to control the plant.Inparticular,for the inverted pendulum in the three positions shown in Figure2.5,we have the following rules(notice that we drop the quotes since the whole rule islinguistic):1.If error is neglarge and change-in-error is neglarge Then force is poslargeThis rule quantifies the situation in Figure2.5(a)where the pendulum has alarge positive angle and is moving clockwise;hence it is clear that we shouldapply a strong positive force(to the right)so that we can try to start thependulum moving in the proper direction.2.If error is zero and change-in-error is possmall Then force is negsmallThis rule quantifies the situation in Figure2.5(b)where the pendulum hasnearly a zero angle with the vertical(a linguistic quantification of zero does notimply that e(t)=0exactly)and is moving counterclockwise;hence we shouldapply a small negative force(to the left)to counteract the movement so that itmoves toward zero(a positive force could result in the pendulum overshootingthe desired position).3.If error is poslarge and change-in-error is negsmall Then force is negsmallThis rule quantifies the situation in Figure2.5(c)where the pendulum is far tothe left of the vertical and is moving clockwise;hence we should apply a smallnegative force(to the left)to assist the movement,but not a big one since thependulum is already moving in the proper direction.Each of the three rules listed above is a“linguistic rule”since it is formed solely from linguistic variables and values.Since linguistic values are not preciserepresentations of the underlying quantities that they describe,linguistic rules arenot precise either.They are simply abstract ideas about how to achieve good controlthat could mean somewhat different things to different people.They are,however,at2.2Fuzzy Control:A Tutorial Introduction31(a)(b)(c)FIGURE2.5Inverted pendulum in various positions.a level of abstraction that humans are often comfortable with in terms of specifyinghow to control a process.The general form of the linguistic rules listed above isIf premise Then consequentAs you can see from the three rules listed above,the premises(which are sometimescalled“antecedents”)are associated with the fuzzy controller inputs and are onthe left-hand-side of the rules.The consequents(sometimes called“actions”)are associated with the fuzzy controller outputs and are on the right-hand-side of therules.Notice that each premise(or consequent)can be composed of the conjunctionof several“terms”(e.g.,in rule3above“error is poslarge and change-in-error is negsmall”is a premise that is the conjunction of two terms).The number of fuzzy controller inputs and outputs places an upper limit on the number of elementsin the premises and consequents.Note that there does not need to be a premise (consequent)term for each input(output)in each rule,although often there is.Rule-BasesUsing the above approach,we could continue to write down rules for the pendulumproblem for all possible cases(the reader should do this for practice,at least fora few more rules).Note that since we only specify afinite number of linguisticvariables and linguistic values,there is only afinite number of possible rules.Forthe pendulum problem,with two inputs andfive linguistic values for each of these,there are at most52=25possible rules(all possible combinations of premiselinguistic values for two inputs).A convenient way to list all possible rules for the case where there are not toomany inputs to the fuzzy controller(less than or equal to two or three)is to use atabular representation.A tabular representation of one possible set of rules for theinverted pendulum is shown in Table2.1.Notice that the body of the table lists thelinguistic-numeric consequents of the rules,and the left column and top row of thetable contain the linguistic-numeric premise terms.Then,for instance,the(2,−1)position(where the“2”represents the row having“2”for a numeric-linguistic valueand the“−1”represents the column having“−1”for a numeric-linguistic value)has a−1(“negsmall”)in the body of the table and represents the rule32Chapter2/Fuzzy Control:The BasicsIf error is poslarge and change-in-error is negsmall Then force is negsmall which is rule3above.Table2.1represents abstract knowledge that the expert hasabout how to control the pendulum given the error and its derivative as inputs.TABLE2.1Rule Table for the Inverted Pendulum“force”“change-in-error”˙eu−2−1012−222210“error”−12210−1e0210−1−2110−1−2−220−1−2−2−2The reader should convince him-or herself that the other rules are also valid and take special note of the pattern of rule consequents that appears in the body of thetable:Notice the diagonal of zeros and viewing the body of the table as a matrixwe see that it has a certain symmetry to it.This symmetry that emerges whenthe rules are tabulated is no accident and is actually a representation of abstractknowledge about how to control the pendulum;it arises due to a symmetry in thesystem’s dynamics.We will actually see later that similar patterns will be foundwhen constructing rule-bases for more challenging applications,and we will showhow to exploit this symmetry in implementing fuzzy controllers.2.2.3Fuzzy Quantification of KnowledgeUp to this point we have only quantified,in an abstract way,the knowledge thatthe human expert has about how to control the plant.Next,we will show how touse fuzzy logic to fully quantify the meaning of linguistic descriptions so that wemay automate,in the fuzzy controller,the control rules specified by the expert.Membership FunctionsFirst,we quantify the meaning of the linguistic values using“membership func-tions.”Consider,for example,Figure2.6.This is a plot of a functionμversus e(t)that takes on special meaning.The functionμquantifies the certainty2that e(t)can be classified linguistically as“possmall.”To understand the way that a mem-bership function works,it is best to perform a case analysis where we show how tointerpret it for various values of e(t):2.The reader should not confuse the term“certainty”with“probability”or“likelihood.”Themembership function is not a probability density function,and there is no underlying probabilityspace.By“certainty”we mean“degree of truth.”The membership function does not quantifyrandom behavior;it simply makes more accurate(less fuzzy)the meaning of linguisticdescriptions.2.2Fuzzy Control:A Tutorial Introduction33•If e(t)=−π/2thenμ(−π/2)=0,indicating that we are certain that e(t)=−π/2is not“possmall.”•If e(t)=π/8thenμ(π/8)=0.5,indicating that we are halfway certain thate(t)=π/8is“possmall”(we are only halfway certain since it could also be“zero”with some degree of certainty—this value is in a“gray area”in terms oflinguistic interpretation).•If e(t)=π/4thenμ(π/4)=1.0,indicating that we are absolutely certain thate(t)=π/4is what we mean by“possmall.”•If e(t)=πthenμ(π)=0,indicating that we are certain that e(t)=πis not “possmall”(actually,it is“poslarge”).FIGURE2.6Membership function forlinguistic value“possmall.”The membership function quantifies,in a continuous manner,whether values ofe(t)belong to(are members of)the set of values that are“possmall,”and hence itquantifies the meaning of the linguistic statement“error is possmall.”This is why itis called a membership function.It is important to recognize that the membershipfunction in Figure2.6is only one possible definition of the meaning of“error is possmall”;you could use a bell-shaped function,a trapezoid,or many others.For instance,consider the membership functions shown in Figure2.7.For some application someone may be able to argue that we are absolutely certain that anyvalue of e(t)nearπ4is still“possmall”and only when you get sufficiently far fromπ4do we lose our confidence that it is“possmall.”One way to characterize this un-derstanding of the meaning of“possmall”is via the trapezoid-shaped membership function in Figure2.7(a).For other applications you may think of membership in the set of“possmall”values as being dictated by the Gaussian-shaped member-ship function(not to be confused with the Gaussian probability density function) shown in Figure2.7(b).For still other applications you may not readily acceptvalues far away fromπ4as being“possmall,”so you may use the membership func-tion in Figure2.7(c)to represent this.Finally,while we often think of symmetric characterizations of the meaning of linguistic values,we are not restricted to these34Chapter 2/Fuzzy Control:The Basicssymmetric representations.For instance,in Figure 2.7(d)we represent that we be-lieve that as e (t )moves to the left of π4we are very quick to reduce our confidencethat it is “possmall,”but if we move to the right of π4our confidence that e (t )is“possmall,”diminishes at a slower rate.(a) Trapezoid.(b) Gaussian.(c) Sharp peak.(d) Skewed triangle.FIGURE 2.7A few membership function choices for representing “error ispossmall.”In summary,we see that depending on the application and the designer (ex-pert),many different choices of membership functions are possible.We will further discuss other ways to define membership functions in Section 2.3.2on page 55.It is important to note here,however,that for the most part the definition of a member-ship function is subjective rather than objective.That is,we simply quantify it in a manner that makes sense to us,but others may quantify it in a different manner.The set of values that is described by μas being “positive small”is called a “fuzzy set.”Let A denote this fuzzy set.Notice that from Figure 2.6we are absolutely certain that e (t )=π4is an element of A ,but we are less certain thate (t )=π16is an element of A .Membership in the set,as specified by the membership function,is fuzzy;hence we use the term “fuzzy set.”We will give a more precise description of a fuzzy set in Section 2.3.2on page 55.A “crisp”(as contrasted to “fuzzy”)quantification of “possmall”can also be specified,but via the membership function shown in Figure 2.8.This membership function is simply an alternative representation for the interval on the real line π/8≤e (t )≤3π/8,and it indicates that this interval of numbers represents “poss-mall.”Clearly,this characterization of crisp sets is simply another way to represent a normal interval (set)of real numbers.While the vertical axis in Figure 2.6represents certainty,the horizontal axis is also given a special name.It is called the “universe of discourse”for the input e (t )since it provides the range of values of e (t )that can be quantified with linguistics2.2Fuzzy Control:A Tutorial Introduction35FIGURE2.8Membership function for acrisp set.and fuzzy sets.In conventional terminology,a universe of discourse for an input oroutput of a fuzzy system is simply the range of values the inputs and outputs cantake on.Now that we know how to specify the meaning of a linguistic value via a mem-bership function(and hence a fuzzy set),we can easily specify the membershipfunctions for all15linguistic values(five for each input andfive for the output)of our inverted pendulum example.See Figure2.9for one choice of membership functions.Notice that(for our later convenience)we list both the linguistic values andthe linguistic-numeric values associated with each membership function.Hence,we see that the membership function in Figure2.6for“possmall”is embeddedamong several others that describe other sizes of values(so that,for instance,the membership function to the right of the one for“possmall”is the one that represents“error is poslarge”).Note that other similarly shaped membership functions makesense(e.g.,bell-shaped membership functions).We will discuss the multitude ofchoices that are possible for membership functions in Section2.3.2on page55.The membership functions at the outer edges in Figure2.9deserve specialattention.For the inputs e(t)and ddt e(t)we see that the outermost membershipfunctions“saturate”at a value of one.This makes intuitive sense as at some point the human expert would just group all large values together in a linguistic de-scription such as“poslarge.”The membership functions at the outermost edges appropriately characterize this phenomenon since they characterize“greater than”(for the right side)and“less than”(for the left side).Study Figure2.9and convince yourself of this.For the output u,the membership functions at the outermost edges cannot be saturated for the fuzzy system to be properly defined(more details on this point will be provided in Section2.2.6on page44and Section2.3.5on page65).The basic reason for this is that in decision-making processes of the type we study,we seek to take actions that specify an exact value for the process input.We do not generally indicate to a process actuator,“any value bigger than,say,10,is acceptable.”It is important to have a clear picture in your mind of how the values of the membership functions change as,for example,e(t)changes its value over time. For instance,as e(t)changes from−π/2toπ/2we see that various membership。
模糊控制理论概要介绍一
模糊控制理论概要介绍(一)２．1概述XX模糊控制(fuｚzy coｎtrol），也称模糊逻辑控制(fuzzy logiｃcontｒol),是一种以模糊集合，模糊逻辑和模糊运算为基础的计算机先进控制技术。
随着数字技术的飞速，过程越来越多地使用计算机，如ＤＣＳ、PLC等作为过程自动化的硬件平台。
这不仅大大提高了企业的自动化水平，而且实施模糊控制、神经网络控制和专家控制等只能控制策略以及基于模型的其他先进控制策略带来了很大的方便。
XX2.１。
1 模糊控制理论的起源模糊控制理论是在L.Ａ。
Zadｅh教授于1９６5年创立的模糊集合理论的数学基础上起来的，主要包括模糊集合理论、模糊逻辑、模糊推理和模糊控制等方面的内容。
XX1965年, L。
A． Zadｅh在其“Ｆuzzy Setｓ"中首次提出模糊性的重要概念——隶属度函数,从而突破了19世纪末德国数学家G.Conｔor创立的经典集合理论的局限性。
借助于隶属度函数可以表达一个模糊概念从“完全不属于"到“完全隶属于”的过度,从而能对所有的模糊概念进行定量表示。
隶属度函数的提出奠定了模糊系统理论的数学基础.XX1966年，P．N。
Mａrinoｓ发表了有关模糊逻辑的研究报告。
这一报告真正标志着模糊逻辑的诞生。
模糊逻辑和经典的二值逻辑的不同之处在于:模糊逻辑是一种连续逻辑。
一个模糊命题是一个可以确定隶属度的句子，它的直值可取区间中的任何数。
很明显，模糊逻辑是二值逻辑的扩展，而二值逻辑知识模糊逻辑的特例.模糊逻辑具有更加普遍的实际意义,它弃了二值逻辑的简单的肯定或否定,把客观逻辑世界看成是具有连续隶属度登记变化的，它允许一个命题亦次亦彼，存在着部分肯定和部分否定，只不过隶属程度不同而已。
这就为计算机模仿人的思维方式来处理普遍存在的语言信息提供了可能，因而具有划时代的现实意义。
XX2．2。
２模糊控制理论的及现状1974年,Ｚａdeh进一步研究了模糊逻辑推理。
模糊神经网络外文翻译文献
模糊神经网络外文翻译文献(文档含中英文对照即英文原文和中文翻译)原文：Neuro-fuzzy generalized predictive control ofboiler steam temperatureXiangjie LIU, Jizhen LIU, Ping GUANABSTRACTPower plants are nonlinear and uncertain complex systems. Reliablecontrol of superheated steam temperature is necessary to ensure high efficiency and high load-following capability in the operation of modern power plant. A nonlinear generalized predictive controller based on neuro-fuzzy network (NFGPC) is proposed in this paper. The proposed nonlinear controller is applied to control the superheated steam temperature of a 200MW power plant. From the experiments on the plant and the simulation of the plant, much better performance than the traditional controller is obtained.Keywords:Neuro-fuzzy networks; Generalized predictive control; Superheated steam temperature1. IntroductionContinuous process in power plant and power station are complex systems characterized by nonlinearity, uncertainty and load disturbance. The superheater is an important part of the steam generation process in the boiler-turbine system, where steam is superheated before entering the turbine that drives the generator. Controlling superheated steam temperature is not only technically challenging, but also economically important.From Fig.1,the steam generated from the boiler drum passes through the low-temperature superheater before it enters the radiant-type platen superheater. Water is sprayed onto the steam to control the superheated steam temperature in both the low and high temperature superheaters. Proper control of the superheated steam temperature is extremely important to ensure theoverall efficiency and safety of the power plant. It is undesirable that the steam temperature is too high, as it can damage the superheater and the high pressure turbine, or too low, as it will lower the efficiency of the power plant. It is also important to reduce the temperature fluctuations inside the superheater, as it helps to minimize mechanical stress that causes micro-cracks in the unit, in order to prolong the life of the unit and to reduce maintenance costs. As the GPC is derived by minimizing these fluctuations, it is amongst the controllers that are most suitable for achieving this goal.The multivariable multi-step adaptive regulator has been applied to control the superheated steam temperature in a 150 t/h boiler, and generalized predictive control was proposed to control the steam temperature. A nonlinear long-range predictive controller based on neural networks is developed into control the main steam temperature and pressure, and the reheated steam temperature at several operating levels. The control of the main steam pressure and temperature based on a nonlinear model that consists of nonlinear static constants and linear dynamics is presented in that.Fig.1 The boiler and superheater steam generation processFuzzy logic is capable of incorporating human experiences via the fuzzy rules. Nevertheless, the design of fuzzy logic controllers is somehow time consuming, as the fuzzy rules are often obtained by trials and errors. In contrast, neural networks not only have the ability to approximate non-linear functions with arbitrary accuracy, they can also be trained from experimental data. The neuro-fuzzy networks developed recently have the advantages of model transparency of fuzzy logic and learning capability of neural networks. The NFN is have been used to develop self-tuning control, and is therefore a useful tool for developing nonlinear predictive control. Since NFN is can be considered as a network that consists of several local re-gions, each of which contains a local linear model, nonlinear predictive control based on NFN can be devised with the network incorporating all the local generalized predictive controllers (GPC) designed using the respective local linear models. Following this approach, the nonlinear generalized predictive controllers based on the NFN, or simply, the neuro-fuzzy generalized predictive controllers (NFG-PCs)are derived here. The proposed controller is then applied to control the superheated steam temperature of the 200MW power unit. Experimental data obtained from the plant are used to train the NFN model, and from which local GPC that form part of the NFGPC is then designed. The proposed controller is tested first on the simulation of the process, before applying it to control the power plant.2. Neuro-fuzzy network modellingConsider the following general single-input single-output nonlinear dynamic system:),1(),...,(),(),...,1([)(''+-----=u y n d t u d t u n t y t y f t y∆+--/)()](),...,1('t e n t e t e e (1)where f[.]is a smooth nonlinear function such that a Taylor series expansion exists, e(t)is a zero mean white noise and Δis the differencing operator,''',,e u y n n n and d are respectively the known orders and time delay ofthe system. Let the local linear model of the nonlinear system (1) at the operating point )(t o be given by the following Controlled Auto-Regressive Integrated Moving Average (CARIMA) model:)()()()()()(111t e z C t u z B z t y z A d ----+∆= (2) Where)()(),()(1111----∆=z andC z B z A z A are polynomials in 1-z , the backward shift operator. Note that the coefficients of these polynomials are a function of the operating point )(t o .The nonlinear system (1) is partitioned into several operating regions, such that each region can be approximated by a local linear model. Since NFN is a class of associative memory networks with knowledge stored locally, they can be applied to model this class of nonlinear systems. A schematic diagram of the NFN is shown in Fig.2.B-spline functions are used as the membership functions in the NFN for the following reasons. First,B-spline functions can be readily specified by the order of the basis function and the number of inner knots. Second, they are defined on a bounded support, andthe output of the basis function is always positive, i.e.,],[,0)(j k j j k x x λλμ-∉=and ],[,0)(j k j j k x x λλμ-∈>.Third, the basis functions form a partition of unity, i.e.,.][,1)(min,∑∈≡jmam j k x x x x μ (3)And fourth, the output of the basis functions can be obtained by a recurrence equation.Fig. 2 neuro-fuzzy network The membership functions of the fuzzy variables derived from the fuzzy rules can be obtained by the tensor product of the univariate basis functions. As an example, consider the NFN shown in Fig.2, which consists of the following fuzzy rules:IF operating condition i (1x is positive small, ... , and n x is negative large),THEN the output is given by the local CARIMA model i:...)()(ˆ...)1(ˆ)(ˆ01+-∆+-++-=d t u b n t y a t y a t y i i a i in i i i a )(...)()(c i in i b i in n t e c t e n d t u b cb -+++--∆+ (4)or)()()()()(ˆ)(111t e z C t u z B z t yz A i i i i d i i ----+∆= (5) Where )()(),(111---z andC z B z A i i i are polynomials in the backward shift operator 1-z , and d is the dead time of the plant,)(t u i is the control, and )(t e i isa zero mean independent random variable with a variance of 2δ. Themultivariate basis function )(k i x a is obtained by the tensor products of the univariate basis functions,p i x A a nk k i k i ,...,2,1,)(1==∏=μ(6)where n is the dimension of the input vector x, and p, the total number of weights in the NFN, is given by,∏=+=nk i i k R p 1)((7)Where i k and i R are the order of the basis function and the number of inner knots respectively. The properties of the univariate B-spline basis functions described previously also apply to the multivariate basis function, which is defined on the hyper-rectangles. The output of the NFN is,∑∑∑=====p i i i p i ip i i i a y aa y y 111ˆˆˆ (8)译文：锅炉蒸汽温度模糊神经网络的广义预测控制Xiangjie LIU, Jizhen LIU, Ping GUAN摘要发电厂是非线性和不确定性的复杂系统。
控制类毕业设计中英文翻译资料--模糊逻辑
模糊逻辑-分析和控制复杂系统的新途径--托马斯索沃尔欢迎进入模糊逻辑的精彩世界，你可以用新科学有力地实现一些东西。
在你的技术与管理技能的领域中，增加了基于模糊逻辑分析和控制的能力，你就可以实现除此之外的其他人与物无法做到的事情。
以下就是模糊逻辑的基础知识：随着系统复杂性的增加，对系统精确的阐述变得越来越难，最终变得无法阐述。
于是，终于到达了一个只有靠人类发明的模糊逻辑才能解决的复杂程度。
模糊逻辑用于系统的分析和控制设计，因为它可以缩短工程发展的时间；有时，在一些高度复杂的系统中，这是唯一可以解决问题的方法。
虽然，我们经常认为控制是和控制一个物理系统有关系的，但是，扎德博士最初设计这个概念的时候本意并非如此。
实际上，模糊逻辑适用于生物，经济，市场营销和其他大而复杂的系统。
模糊这个词最早出现在扎德博士于1962年在一个工程学权威刊物上发表论文中。
1963年，扎德博士成为加州大学伯克利分校电气工程学院院长。
那就意味着达到了电气工程领域的顶尖。
扎德博士认为模糊控制是那时的热点，不是以后的热点，更不应该受到轻视。
目前已经有了成千上万基于模糊逻辑的产品，从聚焦照相机到可以根据衣服脏度自我控制洗涤方式的洗衣机等。
如果你在美国，你会很容易找到基于模糊的系统。
想一想，当通用汽车告诉大众，她生产的汽车其反刹车是根据模糊逻辑而造成的时候，那会对其销售造成多么大的影响。
以下的章节包括：1)介绍处于商业等各个领域的人们他们如果从模糊逻辑演变而来的利益中得到好处，以及帮助大家理解模糊逻辑是怎么工作的。
2)提供模糊逻辑是怎么工作的一种指导，只有人们知道了这一点，才能运用它用于做一些对自己有利的事情。
这本书就是一个指导，因此尽管你不是电气领域的专家，你也可以运用模糊逻辑。
需要指出的是有一些针对模糊逻辑的相反观点和批评。
一个人应该学会观察反面的各个观点，从而得出自己的观点。
我个人认为，身为被表扬以及因写关于模糊逻辑论文而受到赞赏的作者，他会认为，在这个领域中的这种批评有点过激。
四级倒立摆的变论域自适应模糊控制英文翻译
四级倒立摆的变论域自适应模糊控制摘要 采用变论域自适应模糊控制理论研究四级倒立摆控制问题。
首先，给出四级倒立摆运动的数学模型并验证了它的可控性；然后根据变论域自适应模糊控制理论设计了四级倒立摆的控制器。
最后展示了仿真结果。
此外，还给出一级、二级和三级倒立摆的硬件(即实物系统)实验结果。
关键词：四级倒立摆；变论域；自适应模糊控制倒立摆仿真或实物控制实验是控制领域中用来检验某种控制理论或方法的典型案例。
一级倒立摆的背景源于火箭发射助推器；二级倒立摆与双足机器人控制有关；三级倒立摆应当说由一、二级倒立摆演绎而来，背景相当复杂。
一级倒立摆控制的仿真或实物系统已广泛用于教学；二级倒立摆控制的仿真或实物系统已见于某些实验室中；三级倒立摆控制的仿真或实物系统实现是世界公认难题，不过1993年有人发表了三级倒立摆控制的仿真实验结果，1995年又有人公布了三级倒立摆控制的实物实验结果。
事实上，这些结果几乎都使用了模糊控制或近似推理或某种拟人推理，然而控制的稳定性并不十分理想。
至于四级倒立摆的控制问题，由于难度相当大且三级倒立摆的控制问题尚不令人满意，故在世界范围内还是个空白。
本文采用变论域自适应模糊控制实现了四级倒立摆控制的仿真实验，不但具有良好的稳定性和鲁棒性，还可使倒立摆小车行走到指定的位置(即定位功能)。
1．四级倒立摆的物理模型 1.1 四级倒立摆的结构与记号四级倒立摆主要由小车、摆1~4组成，它们之间自由链结，将其置于坐标系后如图1所示。
规定顺时针方向转角和力矩均为正。
此外，约定以下记号：u 为外界作用力，x 为小车位移，i θ为摆i 与竖直方向的夹角，i O ，i G 分别为摆i 的链结点与质心的位置，0m 为小车的质量，i m 为摆i 的质量，i J 为摆i 绕i G 的转动惯量，i l 为i O 到摆i 质心iG 的距离，i L 为摆i 的长度，0f 为小车与导轨间滑动摩擦系数，i f 为摆i 绕i O 转动的摩擦阻力矩系数(i =1，2，3，4)。
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1 模糊控制理论
概述 模糊逻辑广泛适用于机械控制。这个词本身激发一个一定的怀疑,试探相当于“仓促的逻辑”或“虚假的逻辑”,但“模糊”不是指一个部分缺乏严格性的方法,而这样的事实,即逻辑涉及能处理的概念,不能被表达为“对”或“否”,而是因为“部分真实”。虽然遗传算法和神经网络可以执行一样模糊逻辑在很多情况下,模糊逻辑的优点是解决这个问题的方法,能够被铸造方面接线员能了解,以便他们的经验,可用于设计的控制器。这让它更容易完成机械化已成功由人执行。 历史以及应用
模糊逻辑首先被提出是有Lotfi在加州大学伯克利分校在1965年的一篇论文。他阐述了他的观点在1973年的一篇论文的概念,介绍了语言变量”,在这篇文章中相当于一个变量定义为一个模糊集合。其他研究打乱了,第二次工业应用中,水泥窑建在丹麦,即将到来的在线1975。 模糊系统在很大程度上在美国被忽略了,因为他们更多关注的是人工智能，一个被过分吹嘘的领域，尤其是在1980年中期年代,导致在诚信缺失的商业领域。 然而日本人对这个却没有偏见和忽略，模糊系统引发日立的Seiji Yasunobu和Soji Yasunobu Miyamoto的兴趣。,他于1985年的模拟,证明了模糊控制系统对仙台铁路的控制的优越性。他们的想法是被接受了,并将模糊系统用来控制加速、制动、和停车，当线于1987年开业。 1987年另一项促进模糊系统的兴趣。在一个国际会议在东京的模糊研究那一年,Yamakawa论证立摆“实验。这是一个经典的控制问题,在这一过程中,车辆努力保持杆安装在顶部用铰链正直来回移动。 这次展示给观察者家们留下了深刻的印象,以及后来的实验,他登上一Yamakawa酒杯包含水或甚至一只活老鼠的顶部的钟摆。该系统在两种情况下,保持稳定。Yamakawa最终继续组织自己的fuzzy-systems研究实验室帮助利用自己的专利在田地里的时候。 2
展示之后,日本工程师开发出了大范围的模糊系统用于工业领域和消费领域的应用。1988年,日本建立了国际模糊工程实验室,建立合作安排48公司进行模糊控制的研究。 松下吸尘器使用微控制器运行模糊算法去控制传感器和调整吸尘力。日立洗衣机用模糊控制器Load-Weight,Fabric-Mix和尘土传感器及自动设定洗涤周期来最佳利用电能、水和洗涤剂。 佳能研制出的一种上相机使用电荷耦合器件(CCD)测量中的图像清晰的六个区域其视野和使用提供的信息来决定是否这个影像在焦点上(清晰)。它也可以追踪变化的速率在镜头运动的重点,以及它的速度以防止控制超调。相机的模糊控制系统采用12输入,6个输入了解解现行清晰所提供的数据和其他6个输入测量CCD镜头的变化率的运动。输出的位置是镜头。模糊控制系统应用13条规则,需要1.1 千字节记忆信息。 另外一个例子是,三菱工业空调设计采用25加热规则和25冷却规则。温度传感器提供输入,输出一个控制逆变器,一个压缩机气阀,风扇电机。和以前的设计相比,新设计的模糊控制器增加五次加热冷却速度,降低能耗24%,增加温度稳定性的一个因素两个,使用较少的传感器。 日本人对模糊逻辑的人情是反映在很广泛的应用范围上,他们一直在研究或实现:例如个性和笔迹识别光学模糊系统,机器人,声控机器人直升飞机。 模糊系统的相关研究工作也在美国和欧洲进行着。美国环境保护署分析了模糊控制节能电动机,美国国家航空和宇宙航行局研究了模糊控制自动太空对接。仿真结果表明,模糊控制系统可大大降低燃料消耗。如波音公司、通用汽车、艾伦-布拉德利、克莱斯勒、伊顿,和漩涡了模糊逻辑用于低功率冰箱、改善汽车变速箱。在1995年美泰克公司推出的一个“聪明” 基于模糊控制器洗碗机，“一站式感应模块”包括热敏电阻器,用来温度测量;电导率传感器,用来测量离子洗涤剂水平存在于洗;分散和浊度传感器用来检测透射光测量失禁的洗涤,以及一个磁致伸缩传感器来读取旋转速率。这个系统确定最优洗周期任何载荷,获得最佳的结果用最少的能源、洗涤剂、和水。 研究和开发还继续模糊应用软件,作为反对固件设计,包括模糊专家系统模糊逻辑与整合神经网络和所谓的自适应遗传软件系统,其最终目的是建立“自主学习”模糊控制系统。 3
模糊集 输入变量在一个模糊控制系统是集映射到一般由类似的隶属度函数,称为“模糊集”。转换的过程中,一个干脆利落的输入值模糊值称为“模糊化”。 一个控制系统也有各种不同的类型开关或“开关”,连同它的模拟输入输入,而这样的开关输入当然总有一个真实的价值等于要么1或0,但该方案能对付他们,简单的模糊函数,要么发生一个值或另一个。 赋予了“映射输入变量的隶属函数和进入真理价值,单片机然后做出决定为采取何种行动基于一套“规则”,每一组的形式。 在一个例子里,有两个输入变量是“刹车温度”和“速度”,定义为模糊集值。输出变量,“制动压力” ,也定义为一个模糊集,有价值观像“静” 、“稍微增大” “略微下降”,等等。 这条规则本身很莫名其妙,因为它看起来好像可以使用，会干扰到与模糊,但要记住,这个决定是基于一套规则。 所有的规则都调用申请,使用模糊隶属度函数和诚实得到输入值,确定结果的规则。这个结果将被映射成一个隶属函数和控制输出变量的真值。 这些结果相结合,给出了具体的(“脆”)的答案,实际的制动压力,一个过程被称为解模糊化，结合了模糊操作规则 "推理“描述”模糊专家系统”。 传统的控制系统是基于数学模型的控制系统,描述了使用一个或更多微分方程确定系统回应其输入。这类系统通常被作为“PID控制器”他们是产品的数十年的发展建设和理论分析,是非常有效的。 如果PID和其他传统的控制系统是如此的先进,何必还要模糊控制吗?它有一些优点。在许多情况下,数学模型的控制过程可能不存在,或太“贵”的认识论的计算机处理能力和内存,与系统的基于经验规则可能更有效。 此外,模糊逻辑都适合低成本实现基于廉价的传感器、低分辨率模拟/数字转换器,或8位单片机芯片one-chip 4比特。这种系统可以很容易地通过增加新的规则升级来提高性能或添加新功能。在许多情况下,模糊控制可以用来改善现有的传统控制器系统通过增加了额外的情报电流控制方法。 模糊控的细节
模糊控制器是很简单的理念上。它们是由一个输入阶段,一个处理阶段,一个输 4
出阶段。地图传感器输入级或其他输入,比如开关等等,到合适的隶属函数和真理的价值。每一个适当的加工阶段调用规则和产生的结果对每个人来说,然后结合结果的规则。最后,将结果输出阶段相结合的具体控制输出回他的价值。 最常见的形状是三角形的隶属度函数,尽管梯形和贝尔曲线也使用,但其形状通常比数量更重要曲线及其位置。从三人至七人通常是适当的覆盖曲线所需要的范围的一个输入值,或“宇宙的话语“在模糊术语。 作为讨论之前,加工阶段是基于规则的集合的形式逻辑IF - THEN报表,那里的部分叫做“之前”和后来的部分被称为“随之”。典型的模糊控制系统具有几十个规则。 这条规则的价值采用真理“温”的输入,真值的“冷”,产生的结果,在模糊集的“加热器“输出,“高”的价值。这个结果是用来与其他规则的结果,最终产生脆复合输出。很明显,越是真理价值的“冷”,真值越高,“高”,但这并不一定就意味着输出本身会被设置为“高”,因为这是唯一准则在许多。在某些情况下,隶属函数可以修正“篱笆”相当于形容词。模糊限制语包括“关于“常见,“近”、“接近”、“大约”、“很”、“稍微”、“太”、“非常”、“有点”。这些操作可能有明确的定义,虽然可能有很大差别的定义不同的实现。“非常”,因为一个典型的例子,广场隶属函数;因为会员价值总是小于1,这减少了隶属函数。“非常”立方体价值观提供更大的缩小,而“有点“扩大功能以平方根的计算。 在实践中,模糊规则集,通常有几个来路综合利用模糊运算,如,或者,不,虽然再次定义每每变化,在一个受欢迎的定义,只是利用最小重量的雏形,而或采用最大值。还有一个不经营者一个隶属函数减去从1到给“补充性”功能。 有几种方法可以定义一个规则的结果,而是一种最常见的和最简单的是“极大极小“推理法,给出了输出隶属函数的真值所产生的前提。 规则可以解决并联在硬件或软件。顺序结果所有的规则，其中的几个方法。在理论上有几十个,每个都有各种各样的优点和缺点。 “质心”的方法很受欢迎,在“的质心”的结果提供了清新的价值。另一个方法是“高度”方法,它以价值的主要因素。方法更利于统治质心与输出最大的区域,而高程法显然更利于规则和最大的输出值。 模糊控制系统的设计是基于经验方法,基本上一个系统的方法试误。大致过程如下: 5
1.文件系统的操作规范和输入与输出。 2.文档模糊集的输入。 3.文件规则集。 4.确定解模糊化方法确定。 5.运行测试套件验证通过制度,调整细节的要求。 6.完整的文件,发布给生产。 逻辑解释模糊控制
尽管有几个困难出现给一个严谨的逻辑解释If - Then规则。作为一个例子,解释一个规则,因为如果(温度是“冷”),那么(加热器是“高”)由第一阶表达式冷)(x→高)(y和假设r是一个输入这样冷)(r是假的。然后公式冷)(r→高)(t是适用于任何一个师,因此任何不正确的控制提供了一种给r。很明显,如果我们考虑系统的先例的规则类定义一个分区这样一个自相矛盾的现象不会出现。在任何情况下它有时是不考虑两个变量x和y在一条规则没有某种功能的依赖。严谨的逻辑正当化中给出的模糊控制Hajek的书,被描绘成一个模糊控制理论的基本Hajek逻辑。在2005 Gerla模糊控制逻辑方法,提出了一种基于以下的想法。f模糊函数表示的系统与模糊控制相结合,即:给定输入r,),()(yrfys是模糊集合可能的输出。然后给出一个可能的输出的t,我们把),(trf为真理程度的表示。更多的是任何系统的If - Then规则可转化为一个模糊的程序,在这种情况下模糊函数f模糊谓词的解释很好),(yx在相关的最小模糊Herbrand模型。以这样一种方式成为一个章模糊控制的模糊逻辑编程。学习过程成为一个问题属于归纳逻辑理论。