Iterative Learning Controller Design And Application For Singular Systems

Iterative Learning Control(ILC)theory is an important branch of control theory,which is mainly applied to the controlled systems with repetitive movement.ILC uses the error signals caused by the actual output and desired output signals to amend the control signals,to gradually improve and trace performance to get the desired signals.Singular systems,widely used in economic systems,are more general than normal systems.Relatively few researches focus on the ILC for singular systems.Therefore,the study of ILC algorithm and application for singular systems is of certainly significance.The main works are shown as follows:1.For the initial value problem of ILC for discrete singular systems,two different initial conditions are considered.Firstly,the convergence of ILC for singular system with initial state learning is studied.Secondly,based on restricted equivalent form of discrete singular system,the convergence of algorithm with the initial state of bounded disturbance is studied.Finally,the illustrative examples show the effectiveness of the algorithm with two different initial conditions.2.For the fixed initial value problem of ILC for singular systems,two different forms of ILC algorithms are considered.Firstly,a kind of closed-loop D-type algorithm is adopted and proved theoretically that under the given convergence condition the output of the system is uniformly convergent to a signal,which has a fixed deviation when compared with the desired signal.Secondly,for the deviation problem caused by the D-type algorithm,an error correction strategy is designed,that is the closed-loop PD-type algorithm.Finally,the effectiveness of error correction strategy is verified by the simulation results.3.For the convergence rate and the algorithm's influence on the performance of the systems,three different forms of ILC algorithms for singular systems with initial state learning are considered.Firstly,the convergence of PD-type ILC algorithm is studied and the simulation results show that the P-type part affects the performance of the system.Secondly,a D-type algorithm with index gain is designed and the simulation results show that the algorithm can speed up the convergence rate.Thirdly,a PD-type algorithm with index gain is considered,which can not only speed up the convergence of the algorithm,but also can improve the performance of the system.Finally,the effectiveness of the design of algorithms is verified by simulation examples.4.The application of iterative learning control in singular systems is studied.Firstly,a mathematical model of an actual singular system is established and the importance of tracking system desired voltage signal is pointed out.Secondly,considering that the initial value of the voltage signal in the actual system is unequal to desired initial value,different iterative learning controllers are designed according to two different initial conditions.Finally,the effectiveness of the controllers is illustrated by simulation results.