把动态特性引入到有限普通集合X内,改进了普通集合X,提出了P-集合(packet sets);P-集合是由内P-集合X■(internal packet set X■)与外P-集合XF(outer packet set XF)构成的集合对;或者(X■,XF)是P-集合。P-集合具有动态特性:内P-集合...把动态特性引入到有限普通集合X内,改进了普通集合X,提出了P-集合(packet sets);P-集合是由内P-集合X■(internal packet set X■)与外P-集合XF(outer packet set XF)构成的集合对;或者(X■,XF)是P-集合。P-集合具有动态特性:内P-集合具有内-动态特性,外P-集合具有外-动态特性。把P-集合(X■,XF)引入到L.A.Zadeh模糊集A中,改进L.A.Zadeh模糊集A,提出P-模糊集(packet fuzzy sets)。P-模糊集是由内P-模糊集A■(internal packetfuzzy set A■)与外P-模糊集AF(outer packet fuzzy set AF)构成的模糊集合对,或者(A■,AF)是P-模糊集。P-模糊集具有动态特性,给出了P-模糊集的若干特征与应用。在一定条件下,P-模糊集(A■,AF)能够回到L.A.Zadeh模糊集A的"原点"。P-模糊集比L.A.Zadeh模糊集具有更大的应用空间。P-模糊集是模糊集理论与应用中的一个新的研究方向。展开更多
In this paper, a robust fractional order fuzzy P ＋ fuzzy I ＋ fuzzy D （FOFP ＋ FOFI ＋ FOFD） controller is presented for a nonlinear and uncertain 2-1ink planar rigid manipulator. It is a nonlinear fuzzy controller...In this paper, a robust fractional order fuzzy P ＋ fuzzy I ＋ fuzzy D （FOFP ＋ FOFI ＋ FOFD） controller is presented for a nonlinear and uncertain 2-1ink planar rigid manipulator. It is a nonlinear fuzzy controller with variable gains that makes it self- adjustable or adaptive in nature. The fractional order operators further make it more robust by providing additional degrees of freedom to the design engineer. The integer order counterpart, fuzzy P ＋ fuzzy I ＋ fuzzy D （FP ＋ FI ＋ FD） controller, for a comparative study, was realized by taking the integer value for the fractional order operators in FOFP ＋ FOFI ＋ FOFD controller. The performances of both the fuzzy controllers are evaluated for reference trajectory tracking and disturbance rejection with and without model uncertainty and measurement noise. Genetic algorithm was used to optimize the parameters of controller under study for minimum integral of absolute error. Simulation results demonstrated that FOFP ＋ FOFI ＋ FOFD controller show much better performance as compared to its counterpart FP ＋ FI ＋ FD controller in servo as well as the regulatory problem and in model uncertainty and noisy environment FOFP ＋ FOFI ＋ FOFD controller demonstrated more robust behavior as compared to the FP ＋ FI ＋ FD controller. For the developed controller bounded-input and bounded-output stability conditions are also developed using Small Gain Theorem.展开更多
文摘把动态特性引入到有限普通集合X内,改进了普通集合X,提出了P-集合(packet sets);P-集合是由内P-集合X■(internal packet set X■)与外P-集合XF(outer packet set XF)构成的集合对;或者(X■,XF)是P-集合。P-集合具有动态特性:内P-集合具有内-动态特性,外P-集合具有外-动态特性。把P-集合(X■,XF)引入到L.A.Zadeh模糊集A中,改进L.A.Zadeh模糊集A,提出P-模糊集(packet fuzzy sets)。P-模糊集是由内P-模糊集A■(internal packetfuzzy set A■)与外P-模糊集AF(outer packet fuzzy set AF)构成的模糊集合对,或者(A■,AF)是P-模糊集。P-模糊集具有动态特性,给出了P-模糊集的若干特征与应用。在一定条件下,P-模糊集(A■,AF)能够回到L.A.Zadeh模糊集A的"原点"。P-模糊集比L.A.Zadeh模糊集具有更大的应用空间。P-模糊集是模糊集理论与应用中的一个新的研究方向。
文摘In this paper, a robust fractional order fuzzy P ＋ fuzzy I ＋ fuzzy D （FOFP ＋ FOFI ＋ FOFD） controller is presented for a nonlinear and uncertain 2-1ink planar rigid manipulator. It is a nonlinear fuzzy controller with variable gains that makes it self- adjustable or adaptive in nature. The fractional order operators further make it more robust by providing additional degrees of freedom to the design engineer. The integer order counterpart, fuzzy P ＋ fuzzy I ＋ fuzzy D （FP ＋ FI ＋ FD） controller, for a comparative study, was realized by taking the integer value for the fractional order operators in FOFP ＋ FOFI ＋ FOFD controller. The performances of both the fuzzy controllers are evaluated for reference trajectory tracking and disturbance rejection with and without model uncertainty and measurement noise. Genetic algorithm was used to optimize the parameters of controller under study for minimum integral of absolute error. Simulation results demonstrated that FOFP ＋ FOFI ＋ FOFD controller show much better performance as compared to its counterpart FP ＋ FI ＋ FD controller in servo as well as the regulatory problem and in model uncertainty and noisy environment FOFP ＋ FOFI ＋ FOFD controller demonstrated more robust behavior as compared to the FP ＋ FI ＋ FD controller. For the developed controller bounded-input and bounded-output stability conditions are also developed using Small Gain Theorem.
