开关磁阻电机液压机电液伺服系统英文文献和中文翻译(3)
(8) Then the learning rule of open-loop PD ILC can be represented as: 1pdd()() () ()dkkk ketutut ettΓΓ + =+ + (9) where Γp and Γd are the gain parameters of PD ILC; uk(t), uk+1(t) are the control quantities of the kth and (k+1)th at time t; and ek(t) is the error of the kth operation at t. By adopting the above ILC with PD learning rule, when the learning gain is settled, tracking performance and convergence speed are fixed. The research results showed that the required precision was achieved generally only through thousands of iterative learning for the electro-hydraulic servo system [10−11]. The convergence rate of ILC is so slow that it is difficult to be applied to the practical system. 4.2 Algorithm of fuzzy ILC 4.2.1 Principle of fuzzy ILC In order to solve the adaptive ability of ILC and improve convergence speed, a new kind of adaptive fuzzy ILC was put forward by combining ILC and adaptive fuzzy control, which is shown in Fig.3. A fuzzy inference module that can regulate iterative learning gain parameters adaptively is added into the open-loop PD ILC. The fuzzy control module adopts the structure of two inputs and two outputs, in which the inputs are error and change in error coming from ILC at every turn, and the outputs are PD iterative learning gain parameters Γp and Γd. The fuzzy control module accomplishes adjusting the learning rate adaptively based on error and change in error. So the convergence speed of ILC can be accelerated. 4.2.2 Establishment of membership function Fuzzy inference system is established on the basis of fuzzy set theory. At first, the input and output variables are needed to carry out fuzzification processing, which transforms the input and output variables into proper semantic value. In this work, the basic universes of input and output variables are: e∈[−5, 5], e & ∈[−10, 10], Γp∈[0, 5], Γd∈[0, 10]. In order to design easily, the fuzzy universes are united as: e, e & ∈[−1, 1]; Γp, Γd∈[0, 1]. The corresponding fuzzy subsets of input and output variables are: , [NB, NM, NS, ZO, PS, PM, PB] ee = & pd , [SS, MS, MM, BM, BB] ΓΓ = where NB is the abbreviation of negative big, NM is the negative middle, NS is the negative small, ZO is the zero, PS is the positive small, PM is the positive middle, and PB is the positive big; SS is the small, MS is the middle small, MM is the middle, BM is the big middle, and BB is the big. Let NB and PB be trapezoidal membership functions and others be triangular membership functions; let BB be trapezoidal membership functions and others be triangular membership functions. All figures of the membership functions are shown in Figs.4 and 5. 4.2.3 Establishment of fuzzy inference rule A key to implementing iterative learning gain adaptive adjustment during the design of fuzzy PD ILC is to establish exact fuzzy inference rules. So far, the professional knowledge about adaptively regulating learning gain parameters with error and change in error is deficient. In this work, the fuzzy mapping relation between inputs and outputs, shown in Table 1, is concluded through large amount of iterative learning simulation experiments which study influences of the gain parameter on iterative learning convergence rate. 4.2.4 Fuzzy inference and defuzzification The fuzzy inference rule used in Table 1 is as follows: If e is Ai and e & is Bj, then Γp=Cij and Γd=Dij. where Ai, Bj, Cij and Dij are fuzzy subsets of input and output variables, and i, j=1, 2, 3, 4, 5, 6, 7. The Mamdani min and max operators are adopted to carry out fuzzy calculation for fuzzy implication and synthesis respectively. Thus, the result of Γp (Γd is similar) is: 5 Simulation and experimental results The volume control hydraulic press developed in this paper is reconstructed on the basis of common hydraulic press Y−63. The hydraulic system of original press is transformed based on the principle of SRM direct-drive volume control system described in Fig.1.
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