PD-type Iterative Learning Control For Uncertain Spatially Interconnected Systems

Recently,spatially interconnected systems are widely used in power system,computer communication network,automatic highway system and other practical production and life,and its trajectory tracking performance has become a hot research topic.However,due to the coupling of various elements within the spatially interconnected systems,its structure is often complex and there exists uncertainty of the structure model or parameter.In addition,the delay phenomenon is common in practical engineering,which may lead to the instability of the system.Moreover,it is often accompanied by a variety of disturbances,affecting the performance of the system.Therefore,how to realize accurate tracking and performance improvement of spatially interconnected systems in complex environment is an important problem to be settled.By learning the controlled system,iterative learning control uses prior error signal to constantly update the control input,so as to gradually improve the tracking performance of the system and finally realize complete tracking.Compared with the traditional control methods,iterative learning control only requires less prior information and has strong robustness to uncertainty.It is an effective method to solve the tracking control problem of complex spatially interconnected systems.Although some achievements have been made in the iterative learning control for spatially interconnected systems,it is seldom involved in the study of uncertainty,delay,disturbances and so on,which still need to be further studied and improved.In this paper,a feedback based robust iterative learning control design method is proposed for discrete spatially interconnected systems with respect to uncertainty.The main research contents and innovations include:1.A PD-type iterative learning control method based on state feedback is developed for discrete spatially interconnected systems with norm uncertainty.Firstly,the spatially interconnected systems are modeled as an equivalent one-dimensional dynamic system by lifting technique,and then transformed into a general state space model in view of singular system theory.By combining the state error with the tracking error of the previous trial,an iterative learning law is designed to transform the controlled system into an equivalent linear repetitive process model.According to Lyapunov stability analysis theory,sufficient condition in terms of linear matrix inequality(LMI)is established to ensure the robust stability of the resulting system along the trial.An example of active ladder circuits is given to demonstrate the effectiveness and advantages of the proposed method.2.The robust tracking problem of discrete spatially interconnected systems subject to both structured uncertainty and input delay is addressed.Through lifting along the space direction and variable processing,the spatially interconnected systems is transformed into an equivalent uncertain state space model.In order to compensate the influence of input delay,a state observer is constructed to predict the future state of the system.Combined with state observation,a PD-type iterative learning control method is presented to transform the system into a linear repetitive process model with time delay.Based on Lyapunov theory,the LMI condition for robust stability of closed-loop system with time-delay is derived.The suggested method is applied to multi-particle train control system,and the simulation results validate the feasibility and advantages of the method.3.For discrete spatially interconnected systems with polytopic uncertainty and external disturbances,in combination with H_? control theory,a PD-type iterative learning control scheme integrated with real-time output feedback is provided,which can ensure the robust stability of the system along the trial and H_? disturbance attenuation performance in the absence of accurate state measurement,and thus facilitating the practical applications.Using the pre-designed iterative learning gain based on state feedback,a two-stage heuristic method is constructed to iteratively calculate the output feedback gain without additional constraint.Finally,taking the temperature control of metal rod as an example,the effectiveness and superiority of the recommended method are verified.