Optimization Of Parameters And Performance Of Iterative Learning Control With Forgetting Factor

Iterative learning control with forgetting factor(ILCFF)has been widely studied and applied in systems containing disturbances,which is often used to restrain the disturbances and reduce the system-output fluctuation.However,there are also some problems in the study of ILCFF.First,the traditional concept believes that the introduction of forgetting factor will lead to the increase of the system-output tracking error,but the lack of in-depth research fails to provide theoretical guidance for the application of ILCFF method in different systems.Second,the current three common ILCFF methods only involve the analysis of algorithm convergence and lack of further analysis of the output characteristics of the system,which resulting the suitable ILCFF method can not be judged and selected in the actual use,and restricting the promotion and development of ILCFF.Thirdly,the study of ILCFF usually assumes that the system initial state error does not exist,which is inconsistent with the actual situation and greatly limits the practical application effect of ILCFF method.Therefore,in view of the above problems,this paper combines the optimal control theory with the iterative learning control method,proposes the optimal control gains calculation method of ILCFF method,studies the specific influence of forgetting factor on the output characteristics of the system in the optimal control gains,and obtains the optimal control strategies of different ILCFF methods on this basis.At the same time,aiming at the deficiency of the initial state learning method in the discrete system,the optimal control gains are used to improve the initial state learning method to achieve the stability and rapid convergence of the system output.Finally,aiming at the shortcomings of fixed forgetting factor,two time-varying forgetting factor design methods based on the change rate of system-output error and the expected output of the system are proposed in combination with the optimal control gains to further reduce the system-output error and its fluctuation.The main research contents and results are as follows:1.For a class of discrete linear time-invariant(LTI)systems with non-repetitive perturbations,sufficient and necessary conditions for the convergence of the ILCFF method and the monotone convergence of the system are presented.Based on the optimal control theory,the optimal control gain calculation method of the ILCFF method is proposed.By comparing with the traditional ILC method and its optimal control gains,the influence of the forgetting factor on the optimal control gains is studied,and the relationship between the forgetting factor and the system convergence rate is further analyzed.2.Aiming at the problem that the inhibition mechanism of forgetting factor on various disturbances of the system is not clear yet,the influence of forgetting factor on the system output is studied based on the optimal control gains,the influence mechanism of forgetting factor on the tracking error of the system output is clarified,the ILCFF theory is improved,and the blank of forgetting factor research is filled.At the same time,aiming at the current situation that the accurate mathematical model of the system is difficult to obtain,the convergence rate and output tracking error of ILCFF and ILC under non-optimal control gains are further analyzed.The general conclusion that ILCFF realizes the optimization of the output characteristics of the system is obtained.The simulation results verify the correctness of the relevant inferences.3.In order to solve the problem that the common ILCFF method does not involve the system output characteristics and the control vector effect is unknown,the influence of different ILCFF method control vectors on the system convergence,monotone convergence and optimal control gains in the system with initial state error is analyzed.On this basis,the output characteristics of different ILCFF methods are analyzed and obtained under the optimal control gain,and the optimization strategies of different ILCFF methods are proposed to achieve the optimal output characteristics of the system.The simulation results verify the correctness of different ILCFF methods and their optimization strategies.4.Aiming at the problems of slow convergence rate of the existing initial state learning methods and the convergence error first suppressed and then raised in the discrete system,combining with the calculation method of optimal control gain,an ILCFF method for optimal initial state learning of the discrete system is proposed to realize the fast convergence of the method.At the same time,the influence of the initial state learning method on the optimal control gains and output characteristics of the traditional ILCFF method is studied.On the basis of ensuring convergence,the optimal output characteristics of the method are obtained by changing the algorithm parameters,so as to realize the rapid and effective suppression of the influence of the initial state error in the discrete system and ensure the stability of the system-output error.Simulation results demonstrate the effectiveness of the proposed method.5.In view of the fixed forgetting factor cannot be at the same time to achieve optimum system convergence speed and convergence error,on the basis of existing research summed up the time-varying forgetting factor design principle,and put forward two kinds of different systems according to the results of the pilot study of time-varying optimal ILCFF algorithm: based on the system-output error and its change rate of time-varying optimal ILCFF,and based on system output and error rate of change of time-varying optimal ILCFF.On the basis of ensuring the convergence of the two methods,the feasibility of the time-varying optimal ILCFF method based on the rate of change of system expected output and output error for a class of systems with small expected output is proved by theoretical derivation.The simulation results verify the effectiveness of the above two methods.Finally,the experimental results of DC motor show that the proposed general conclusion of ILCFF based on the optimal control gains is valid,and the introduction of forgetting factor is helpful to accelerate the convergence rate and reduce the system-output error in the platform with small expected output.In summary,the proposed optimal control gains of ILCFF effectively improve the system-output performance in this paper.On this basis,the initial state learning ILCFF method and time-varying ILCFF can further optimize the system convergence rate and reduce the system output error.The simulation and experimental results verify the validity of the proposed ILCFF optimization method and related conclusions.