Iterative Learning Control For Distributed Parameter Systems With Variable Tracking Trajectory

The distributed parameter system has a wide range of application backgrounds in various control fields due to its own spatial and temporal distribution characteristics,such as population growth,chemical processes,vibration processes,nuclear reaction processes,social systems,environmental engineering,etc.Iterative learning control has become one of the main intelligent control algorithms for solving distributed parameter system control problems because of its unique memory and correction characteristics.Any learning algorithm requires an inherent requirement,namely repeatability.However,the repeatability requirements for the controlled system often limit the wide application of iterative learning control to a certain extent,because when the tracking target changes,the iterative learning control algorithm needs to be learned from the beginning,thereby wasting the experience that has been learned before.When the tracking target changes along the iterative axis,the learning control algorithm can make full use of the existing information for adjustment.At present,there are only reports on centralized parameter systems for research in this area,and the related research on distributed parameter systems is still very limited.In this paper,it is of great significance to study the iterative learning control of distributed parameter systems with variable tracking trajectories.The research work of the thesis is as follows:(1)The learning control problem of variable tracking trajectory is applied to a linear distributed parameter system is one of the research focuses of this paper.First,we studied at the desired trajectory with varying number of iterations,comprising proposed a new iterative learning control algorithm desired output trajectory of the controlled system offset characteristic,and the establishment of a linear system in a distributed parameter control algorithm for the new,the actual output trajectory of the system reaches the sufficient condition for complete tracking.Secondly,the stability of the system is analyzed using mathematical formulas such as compression mapping principle and differential inequality.Through numerical simulation experiments,the effectiveness of the given learning control algorithm is verified.(2)Research on iterative learning control of variable tracking trajectories for nonlinear distributed parameter systems.With the help of Lipschitz conditions,the nonlinear distributed parameter system is simplified to obtain an equivalent control system.Furthermore,according to the changing characteristics of the desired trajectory of the system,under the condition of the proposed new algorithm,the sufficient conditions for the output error of the controlled system to converge in the sense of(L,)norm are given.With the help of numerical examples,the effectiveness of the algorithm is further verified.(3)Aiming at the fractional-order linear distributed parameter system,a new Ptype iterative learning control algorithm is used to study the learning control problem of variable tracking trajectory.Considering the difference between a fractional order system and an integer order system,through mathematical tools such as Caputo derivative,Gamma function and fractional order inequality,the algebraic relationship between the system state error and the system output error are estimated respectively,so as to obtain the stability condition of the fractional order system.In addition,using the basic mathematical formulas such as Green's formula and related norm characteristics,the conditions for the effectiveness of the proposed algorithm are given.Finally,considering the situation that the expected output of the system changes with the number of iterations,sufficient conditions for the output error of the system to converge to a certain area is given.The numerical simulation results further verify the effectiveness of the iterative algorithm.