Initial Value Problem Of Iterative Learning Control

Iterative learning control (ILC for short) is an important branch of the intelligent control. It is used to deal with controlled plants which have repetitive characteristic. It can track fully desired trajectory over a finite time interval. Many researchers have paid much attention to iterative learning control in recent years because of its simplicity and effectiveness. This dissertation researches on the initial value problems based on operator theory.(1) The fixed initial value problem is researched. This dissertation uses the open-loop D-type learning algorithm and gives the convergence condition of spectral radius form. Then the convergence of the learning algorithm is proved based on operator theory.(2) The problem of initial value that varies within a certain scope is researched. This dissertation uses the open-loop D-type learning algorithm and gives the convergence condition of spectral radius form. Then the convergence of the learning algorithm is proved based on operator theory.(3) The arbitrary value problem is researched. This dissertation uses the algorithm that the control input and the initial value learn at the same time and gives the convergence condition of spectral radius form. Then the convergence of the learning algorithm is proved based on operator theory.(4) The validity of the learning algorithm and convergence condition is tested by simulation. The results of simulation also illustrate the convergence condition of spectral radius form is weaker than the convergence condition of norm form.(5) For the time-delay phenomenon exits widely in practice, the convergence problems for a class of linear time-invariant systems and nonlinear systems with control time-delay in the case of arbitrary initial value are researched. This dissertation gives the simulation examples for the batch process control plants with control time-delay. The result of simulation shows that the iterative learning control method can get good effect.