Iterative Learning Control For Two Class Of Distributed Parameter Systems

Two class of distributed parameter systems with sensor and actuator are considered.This two kinds of systems have the characteristics of both time evolution and space evolution,which can describe phenomena occurred in the nature and control systems encountered in industrial production more comprehensively and accurately,and have a wide application background.Sensor and actuator have the advantages of low cost,low power,micromation,intelligentialize,flexibility and robustness.Therefore,the study of distributed parameter systems with sensor and actuator has important theoretical significance and application value.In this paper,the trajectory tracking problem of parabolic and hyperbolic distributed parameter systems with sensor/actu-ator is studied by using iterative learning control algorithms.The convergence conditions of output error of the systems are derived strictly in theory,and the effectiveness of the algorithms is verified by numerical simulation.Then,the fault diagnosis of a kind of distributed parameter systems based on sensor/actuator with a process fault is carried out via the iterative learning control theory.The main contributions are as follows:1.For the trajectory tracking problem of linear parabolic distributed parameter systems with sensor and actuator,two iterative learning control algorithms are proposed.The output tracking error convergence of linear parabolic distributed parameter systems with sensor/ac-tuator is strictly analyzed in theory by using Bellman-Gronwall inequality,L₂-norm and the contraction mapping theory,etc.Finally,the effectiveness of the proposed algorithms is veri-fied by numerical simulations.2.For the trajectory tracking problem of a class of nonlinear parabolic distributed param-eter systems based on sensor/actuator with unknown input disturbance and measurement noise,a D-type iterative learning control algorithm is presented to analyze the convergence of system output error.Then,the effectiveness of the proposed iterative learning control algorithm is ver-ified in the Fisher equation and the system model of the temperature change of the catalytic rod in an industrial chemical reactor.Next,the trajectory tracking problem of a class of nonlinear parabolic distributed parameter systems based on sensor and actuator with random data packet loss is studied.The convergence condition of system output error in a mean square sense is ob-tained by designing an intermittent updating P-type iterative learning control algorithm.Finally,the simulation results show the effectiveness of the proposed algorithm.3.For the trajectory tracking problem of hyperbolic distributed parameter systems based on sensor/actuator with Kelvin-Voigt damping and viscous damping,the convergence conditions of output error are obtained via iterative learning control theory.In the theoretical derivation process,the convergence of the systems can be obtained via the contraction mapping theory,L₂-norm,etc.This method avoids the errors caused by models'dimension reduction or dis-cretization of the systems,and thus improves the control performance of the systems.Finally,a cable system with air damping and structural damping is considered to verify the effectiveness of the proposed method.4.For the fault diagnosis problem of nonlinear parabolic distributed parameter systems with a process fault based on sensor and actuator,the original systems can be described as evolution equations by the operator semigroup theory,and then a fault estimator is designed by introducing a virtual fault.A residual signal is generated via the actual output of the system and the output of the fault estimator.According to this residual signal,the iterative learning control methods are used to adjust and control the introduced virtual fault,which makes the virtual fault converge to the actual fault as the number of iterations tends to infinity,so as to achieve the purpose of fault diagnosis.Finally,the Fisher equation is given to verify the validity of the proposed fault diagnosis methods,and a typical chemical industrial process is analyzed.