Abstract—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.    32072
Keywords—Fuzzy control, computer control, feedback regulation;
I. Introduction
  The PID controller is the most common form of feedback. It was an essential element of early governors and it became the standard tool when process control emerged in the 1940s. In process control today, more than 95% of the control loops are of PID type, most loops are actually PI control. PID controllers are today found in all areas where control is used. The controllers come in many different forms. There are standalone systems in boxes for one or a few loops, which are manufactured by the hundred thousands yearly. PID control is an important ingredient of a distributed control system. The controllers are also embedded in many special purpose control systems. PID control is often combined with logic, sequential functions, selectors, and simple function blocks to build the complicated automation systems used for energy production, transportation, and manufacturing. Many sophisticated control strategies, such as model predictive control, are also organized hierarchically. PID control is used at the lowest level; the multivariable controller gives the set points to the controllers at the lower level. The PID controller can thus be said to be the “bread and butter of control engineering. It is an important component in every control engineer’s tool box.
  PID controllers have survived many changes in technology, from mechanics and pneumatics to microprocessors via electronic tubes, transistors, integrated circuits. The microprocessor has had a dramatic influence the PID controller. Practically all PID controllers made today are based on microprocessors. This has given opportunities to provide additional features like automatic tuning, gain scheduling, and continuous adaptation.
II. Algorithm
  We will start by summarizing the key features of the PID controller. The “textbook” version of the PID algorithm is described by:
  where y is the measured process variable, r the reference variable, u is the control signal and e is the control error（e =  − y）. The reference variable is often called the set point. The control signal is thus a sum of three terms: the P-term （which is proportional to the error）, the I-term （which is proportional to the integral of the error）, and the D-term （which is proportional to the derivative of the error）. The controller parameters are proportional gain K, integral time Ti, and derivative time Td. The integral, proportional and derivative part can be interpreted as control actions based on the past, the present and the future as is illustrated in Figure 2.2. The derivative part can also be interpreted as prediction by linear extrapolation as is illustrated in Figure 2.2. The action of the different terms can be illustrated by the following figures which show the response to step changes in the reference value in a typical case.
  Effects of Proportional, Integral and Derivative Action
  Proportional control is illustrated in Figure 2.1. The controller is given by D2.1E with Ti =  and Td=0. The figure shows that there is always a steady state error in proportional control. The error will decrease with increasing gain, but the tendency towards oscillation will also increase. 模糊PID控制算法英文文献和中文翻译:http://www.751com.cn/fanyi/lunwen_28483.html