Research On The Convergence Rate Of Iterative Learning Control

As is known to all, the aim of control is to design controllers that could make control system track the ideal output trajectory under known or unknown disturbance quickly and accurately. As for iterative learning control, there are already much research on its robustness and learning convergence, but few are on the convergence rate of the iterative learning. This article will focus on the convergence rate of iterative learning in nonlinear system which has repeated motion characters and uncertain disturbance in initial state and repeated bounded error in the output, this article will focus on the nonlinear system, main research results are given as follows:(1) For a class of nonlinear systems with repeated output disturbance and a random initial value within a certain range, we give the convergence conditions in the form of spectral radius and prove it using open-plus-closed loop D-type iterative learning control algorithm. Then we analyze the convergence rate according to λ norm theory, contraction mapping, and robust optimal control theory, in the end, we prove the exact results of the theory by comparison of simulation results.(2) For a class of nonlinear systems with repeated output disturbance and a random initial value within a certain range, we give the convergence conditions and its convergence proof using open-plus-closed loop D-type iterative learning control algorithm with forgetting factor, Then, we analyze the convergence speed according to compression, robust optimal control theory and compare it with the open-closed loop D-type iterative learning algorithm. Finally, we prove the results of the theory by comparison of simulation results.(3) For a class of nonlinear systems with repeated output disturbance and a random initial value within a certain range, we give the convergence conditions and its convergence proof using second or M (M>3) order open-plus-closed loop D-type iterative learning control algorithm with forgetting factor. Then, we analyze the convergence speed according to compression, robust optimal control theory and compare it with the previous control algorithm. Finally, we prove the exact results of the theory by comparison of simulation results.(4) Using the production of unsaturated polyester resin, a typical batch process as the object of study, we collect the reaction kettle temperature data on site, and fit the temperature curve to determine the ideal temperature control curve. Then we give a model based on the physics mechanism of the temperature of materials in a continuous stirred tank reactor, control the continuously stirred tank reactor temperature with a open-plus-closed loop D-type iterative learning control algorithm with forgetting factor, and compare the convergence rate of the iterative learning matrix derived according to this thesis and that of the literature [71] and [72]. The research has been validated with the comparison of the simulation results.