基于内模控制的模糊pid参数的整定外文文献翻译

基于内模控制的模糊pid参数的整定外文文献翻译内容摘要：

near control performance. At a higher level, the tuning is performed by changing the knowledge base parameters to enhance the control performance. However, it is difficult to tune the knowledge base parameters. Moreover, it is hard to improve the transient response by changing the member the knowledge base conveys a general control policy, it is preferred to keep 8 the member function unchanged and to leave the design and tuning exercises to scaling gains. However, the tuning mechanism of scaling factors and the stability analysis are still difficult tasks due to the plexity of the nonlinear control surface that is generated by fuzzy PID controllers. If the nonlinearity can be suitably utilized, fuzzy PID controllers may pose the potential to achieve better system performance than conventional PID controllers. Some nonanalytical tuning methods were Although the nonlinearity was considered on the basis of gain margin and phase margin specifications, the fuzzy PID controller may produce higher gains than conventional PID controllers due to the nonlinear factor. A high gain could deteriorate the stability of the control The conventional PID controller is easy to implement, and lots of tuning rules are available to cover a wide range of process specifications. Among tuning methods of the conventional PID controller, the internal model control (IMC) based tuning is one of the popular methods in mercial PID software packages because only one tuning parameter is required and better set point response can be An analytical tuning method based on IMC to tune fuzzy PID controllers is proposed in this paper. The fuzzy PID controller is first deposed as a linear PID controller plus an onlinear pensation item. When the nonlinear pensation item is approximated as a process disturbance, the fuzzy PID scaling parameters can then be analytically designed using the IMC scheme. The stability analysis of the fuzzy PID controllers is given on the basis of the Lyapunov stability theory. Finally, the effectiveness of the tuning methodology is demonstrated by simulations. 2 Problem Formulation Conventional PID Controller The conventional PID controller is often described by the following equation:20,21 .dp eKe dte   IP ID KKU =    .d ee dti1ep TTK （ 1） where e is the tracking error, KP is the proportional gain, KI is the integral gain, KD is the derivative gain, and Ti and Td are the integral time constant and the derivative time constant, respectively. The relationships between these control parameters are KI = KP/Ti and KD= KPTd. The transfer function of the PID controller (1) can be expressed as follows:  s 1st1st)s( di ）（ CC KG （ 2） On the rootlocus plane, the PID controller has two zeros ti and td, and one pole at the origin. The condition to have real zeros is that Ti ＞ 4Td. 9 Figure 1 IMC configuration（ a） Figure 2 IMC configuration (b) Principle of IMC The basic IMC principle is shown in Figure 1a, where P is the plant, P˜ is a nominal model of the plant, C is a controller。 r and d are the set point and the disturbance, and y and yk are the outputs of the plant and its nominal model, respectively. The IMC structure is equivalent to the classical singleloop feedback controller shown in Figure 1b. If the singleloop controller CIMC is given by       ss1 ss ~PCCC IMC  （ 3） with     sfsp 1s ~_C （ 4） where P˜ (s)=P˜ (s)P˜ +(s), P˜ (s) is the minimum phase part of the plant model, P˜ +(s) contains any time delays and righthalf plane zeros, and f(s) is a lowpass filter with a steadystate gain of one, which typically has the form:    ncst11sf  （ 5） The tuning parameter tc is the desired closedloop time constant, and n is a positive integer to be determined. Figure Figure 3 FuzzyPID controller structure C ~P P + u d e y y + _ y~~ r _ .eK.eK eK Ki Kd  Rule Base s .e E R u e PIDU MICC P r + + e + + _ + + + u + + d + + y y + + 10 Model of Fuzzy PID Controller The fuzzy PID controller, as shown in Figure 2, is described as follows:   10 p1u KKU PID (6) with  u k 1 BBSA   γ is a nonlinear time varying parameter( 132  ), A and B are half of the spread of each input and out member function, respectively. The fuzzy PID control actually has two levels of The scaling gains (Ke, Kd, K0, and K1) are at the lower level. The tuning of these scaling gains will affect the gains of fuzzy PID The fuzzy PID control actually has two levels of The scaling gains (Ke, Kd, K0, and K1) are at the lower level. The tuning of these scaling gains will affect the gains of fuzzy PID controllers, resulting in the changing of the control performance. As the control actions are fuzzily coupled, the contribution of each Ke, Kd, K0, and K1 to different control actions is still not very clear, which makes the practical design and tuning process rather difficult. 3 Tuning Fuzzy PID Based on the IMC To tune the fuzzy PID controller based on the IMC method,an analytical model of the fuzzy PID controller is obtained first by simple derivation. Then, the parameters of the fuzzy PID controller can be determined on the basis of the IMC principle. Suppose that an industrial process can be modeled by a first order plus delay time (FOPDT) structure that has the transfer function as follows:   LST KP  e1ss~ (7) where K, T, and L are the steadystate gain, the time constant, and the time delay, re。