Iterative Learning Control In Finite Frequency Range For Spatially Interconnected Systems

In recent years,with the progress of industrialization,there have been an increasing number of spatially interconnected systems with huge scale,diverse targets and comprehensive functions.For multi-node spatially interconnected systems with repetitive operation characteristics,related control technologies have received extensive attention from scholars.Iterative learning control can use the previous operating data to correct the control signal of the current state of the system,which has an ideal control effect on systems that repeatedly run within a limited period of time.In actual engineering,spatially interconnected systems often have specific operating frequency bands according to process requirements.At the same time,the structure of spatially interconnected systems is decentralized and the systems are often operated in a complex environment,which inevitably produce problems such as system parameter uncertainty,external disturbances,execution failures and time delays.Therefore,in finite frequency range,the research of iterative learning control schemes that makes the space interconnected system stable and reliable and still maintain the ideal characteristics under severe conditions has a certain value.Based on the theory of repetitive processes,this paper designs iterative learning control laws for spatially interconnected systems.The generalized Kalman–Yakubovich–Povov(KYP)lemma is used to explore the sufficient conditions to make the system stable in finite frequency range.Meanwhile,the linear matrix inequalities(LMI)are used to study the solution of the related control law gain,and to ensure the convergence of the output tracking error of the system.The specific research contents are arranged as follows:(1)For a multi-node spatially interconnected system with norm uncertainties,a robust iterative learning control algorithm in finite frequency range is proposed.Through lifting technology,the multi-dimensional spatial interconnection system is transformed into a class of equivalent systems along the node distribution direction.For the equivalent system,a robust iterative learning control law is designed to transform it into a linear iterative process model.According to the spectral range of the reference trajectory signal,the generalized KYP lemma is used to analyze the frequency-domain stability of the closed-loop system,and the control law design problem is converted into corresponding linear matrix inequalities to solve the problem,which ensures the output tracking error convergence in the time and frequency domains.The control simulation of active ladder circuit verifies the effectiveness of the proposed algorithm.(2)For a multi-node spatially interconnected system,considering the influence of external state disturbance and output disturbance,a H ? robust iterative learning control scheme is designed with a finite frequency range.Firstly,the dimension reduction of multi-dimensional spatially interconnected systems is performed.Secondly,the robust iterative learning control law is designed with the equivalent system to obtain a continuous discrete repeating process model.Then,based on the iterative process theory and the generalized bounded real lemma,sufficient conditions are given to ensure the stability of the closed-loop system in frequency domain and robust H ? control performance.The linear matrix inequalities are used to solve the system control law gain to ensure the ideal convergence of the output tracking error,and the system operation is not affected by external bounded disturbances.Finally,the effectiveness of the proposed algorithm is verified by the control simulation of series inverted pendulum.(3)For a multi-node spatially interconnected system with actuator faults and multi-state delays,considering the polyhedral uncertainty of the system parameters,an iterative learning fault-tolerant control algorithm in finite frequency range is proposed.By selecting the super vector containing space nodes,an equivalent system corresponding to the multi-dimensional fault-delayed spatially interconnected system is obtained.Meanwhile,an iterative learning fault-tolerant control law based on the output information is designed and combined with the controlled system to transform into a linear repeating process model with time delay.According to the output reference trajectory,the system's operating frequency range is obtained.Using the generalized KYP lemma,the sufficient conditions for the stability of the closed-loop system in frequency domain and the design method of the fault-tolerant control law are given in the form of linear matrix inequalities,which ensure that the system outputs have an ideal track performance and fault tolerance of failed systems.The control simulation of the active ladder circuit with time delay validates the feasibility of the proposed algorithm.