Research Of Initial State For Iterative Learning Control

Iterative learning control is proposed in order to achieve bounded error in tracking theexpectations orbit in the tracking systems, and it is widely used in the controlled system withrepetitive motion. The initial state is an important research content of iterative learningcontrol.The initial state has very important implication on the convergence of iterativelearning control. The research of initial state is significance to the iterative learning controland the application of the algorithm in practical engineering projects.This research work doneby the following:1. An iterative learning control of variable gain is propsed,based on iterative learningcontrol theory，which increases iterative learning rule of initial state of system. By using theoperator theory,it is proved that the output of system can track the expected trajectorycompletely after the iterative learning of the nonlinear system with initial state offset.Theconvergence is strictly proved mathematically,and the convergent condition for the spectralradius form of the algorithm is given. Compared with the invariable gain iterative learningcontrol in system of injection molding machine. The simulation in the system of injectionmolding machine speed controlling results show the effectiveness of the algorithm.2. For a class of nonlinear systems, a new learning control algorithm is proposed, whichbased on the open-loop D-type iterative learning control rule with arbitrary initial stateconditions. A special time interval is designed with the characteristic of the more iterations,the less time interval.State error is modified in the interval to make the system tracking errorconverge to the bound, which is effected by the system uncertainties and disturbances,unrelated to initial state error. The tracking error caused by the sensor fault is inhibited byselecting proper control gain based on the theory of λ norm. Meanwhile, the proof ofuniform convergence and bounded error is given. The simulation in the system of injectionmolding machine speed controlling results show the effectiveness of the algorithm.3. For a class of nonlinear systems with state and control time delay, which with theinitial deviation and disturbances of output error. A closed-loop PD-type iterative learningcontrol algorithm with forgetting factor is proposed, and increased iterative learning rule ofinitial state of system. Based on the λ norm theory and the Bellman-Gronwall inequality,the necessary and sufficient conditions for the existence of the learning gain is discussed. Thealgorithm eliminates the effect of initial state error and the convergence of the controlalgorithm is analyzed to ensure the batch error of the closed-loop tracking system isbounded.The simulation of mechianical arm tracking control system results show theeffectiveness of the algorithm.