Finite Frequency Domain Iterative Learning Control For Uncertain Systems With State Delay

In some chemical intermittent processes such as injection molding machine injection speed control,it is usually necessary to perform some repetitive operations within a limited running time.In recent years,how to use the information of the repeated operation of the system to improve system performance has attracted widespread attention.Iterative learning control is one of the methods to effectively solve this kind of control problem.The control input is continuously optimized through the error information of the previous trial to achieve the control purpose of high-precision tracking.Aiming at the common state delay system in actual production,this paper further considers the influence of the model uncertainty in operation on the system tracking performance,establishes the state delay uncertainty model and expands the design of the system iterative learning controller and system stability problem research.This paper mainly study the design of iterative learning controllers for uncertain systems with state delay in finite frequency domain.Usually the system works in a certain frequency range and when discussing the stability of the system,a reasonable use of the frequency characteristics of the system will help improve the performance of the system and reduce the conservativeness of the system.Therefore,the research on uncertain systems with state delay in the frequency domain has certain theoretical and practical significance.Based on the linear repetitive process model and the theoretical framework of repetitive process stability,this paper discusses the stability of the system in the limited frequency domain based on the generalized Kalman-Yakubovich-Popov(KYP)lemma and the error monotonic convergence condition of the system under the constraint of linear matrix inequality is given.The main research contents are as follows(1)For a class of multiple state delays systems subjected to polytopic uncertainty,a PD-type iterative learning controller is designed in the finite frequency domain.By defining the tracking error of the system and designing the PD-type control law,the tracking error transfer function of the system along the batch direction is obtained.The system is equivalently converted into a set of parallel repetitive process models to achieve the purpose of discussing the stability of the system in the finite frequency domain.Based on the stability related results of the repetitive process,the linear matrix inequalities for the monotonic convergence of the nominal system and the uncertain system are respectively given.Finally,the effectiveness of the proposed PD-type algorithm is verified through numerical simulation and comparison with P and D-type algorithms.(2)For a class of state delay uncertain systems with non-repetitive disturbances,an iterative learning control law is designed combining state feedback and P-type control.Considering the effects of repetitive disturbances and non-repetitive disturbances separately,iterative learning controllers are designed in the frequency domain.Based on the generalized KYP lemma,the stability conditions of the state delay system with repetitive disturbances is discussed.Based on the lifting technology and the robust technology to achieve the control purpose designed in the finite frequency domain,the sufficient conditions for the system to meet the robust attenuation suppression index and the monotonic convergence of the tracking error are given.Finally,the effectiveness of the proposed algorithm is verified by controlling the injection speed of the injection molding machine.(3)For a class of state delay systems with uncertainty,a high-order iterative learning controller is proposed.The iterative learning control law is composed of state feedback and tracking error information from multiple previous trials.At this time,the system is a non-unit storage model and through lifting technology the system is transformed into a unit storage repetitive process model.Based on the generalized KYP lemma,the purpose of stability analysis in the frequency domain is achieved and sufficient conditions for the error monotonic convergence of the nominal system and the uncertain system with time delay are given.Finally,use the injection molding process as a model to design different orders of iterative learning controllers and analyze the performance of the system when different control law orders are used.