Iterative Learning Control For Irregular Discrete Distributed Parameter Systems

Iterative learning control(ILC)is an important branch of intelligent control with strict mathematical description.ILC can control and regulate the controlled system with repetitive running.The deviation of the actual output and expected trajectory is used to correct the control input of the next running.So that the control performance of system is continuously improved during the iterative process.The significant feature of ILC is the simple algorithm and its own good learning ability.ILC is very suitable for solving the problems of nonlinear,strong coupling,difficult to model and high precision trajectory tracking control requirements.For a lumped parameter system,its state variable is only a single-variable function about time.For distributed parameter systems(DPSs),their state variables are generally binary functions about time and space.Therefore,the learning control of the distributed parameter systems are more complicated than the lumped parameter systems.On the other hand,in practical,regardless of the online analysis of continuous-time system by used of digital computer,or implementing control employing discrete control device,it is necessary to convert the continuous-time system into equivalent discrete-time system.In this dissertation,the ILC of irregular discrete distributed parameter system with no direct transmission channel between the input and output is considered.Several learning algorithms are proposed according to the characteristics of system model.The convergence of tracking error within the fixed time interval is analyzed to ensure the actual output can track the desired trajectory precisely.The research content of this dissertation mainly includes the following aspects.Firstly,the problem of ILC for a class of irregular discrete parabolic distributed parameter systems with initial value learning is studied.In view of the characteristics of the initial value being not fixed and there is no direct transmission channel between input and output for a learning system,a D-type iterative learning control algorithm with initial learning is designed.The sufficient condition of tracking error convergence under the open-loop algorithm is derived through rigorous analysis by using of discrete Gronwall inequality,discrete Green inequality and contraction mapping principle.At the same time,the closed-loop and open-closed-loop control algorithms with initial learning are proposed.Finally,the numerical simulation examples are given to verify the effectiveness of the algorithm designed in this chapter.Secondly,the ILC for a class of high-relative irregular discrete parabolic distributed parameter systems is discussed.Based on the high-relative of the system,a D-type iterative learning control algorithm with relative degree is proposed.The general solution of partial difference equations under appropriate initial and boundary conditions is adopted to dimensionality reduction for the learning system.According to the stability theory of linear system,the necessary and sufficient conditions of the convergence for tracking error are presented.The corresponding numerical simulation example is used to illustrate the effectiveness of the algorithm proposed in this chapter.Finally,the ILC for irregular discrete second-order hyperbolic distributed parameter systems is researched.In order to achieve the accurate tracking of the actual output to the desired trajectory,a D-type learning control algorithm is designed.The sufficient condition for tracking error convergence under the learning algorithm is established.A simulation example is given to validate the effectiveness of the designed algorithm.