2-D System Theory Based Iterative Learning Control Algorithms

Iterative learning control techniques are suitable for control systems which perform repetitive tasks on a finite interval. By the conventional learning algorithms, the information from previous iterations is used to correct the control input, and the tracking performance of such systems is improved gradually. On the basis of the 2-D system theory, this thesis presents a 2-D system theory of the feedback-aided iterative learning control, by which the 2-D error models of the closed-loop systems are given. The method for obtaining the controller gains that make the system undertaken to be convergent is proposed, and the performance analysis about convergence of the learning algorithms is carried out in this thesis.The main work and achievements of this thesis are summarized as follows:1. In order to accelerate the convergence speed and improve system performance, we propose feedback-aided PD-type and D-type iterative learning control algorithms for linear discrete time-invariant systems. A two-dimensional(2-D) system model is derived, and the convergence analysis of the learning algorithm is conducted through the usage of the state transition matrix.2. The feedback aided iterative learning control is constructed by adding a feedback term in open-loop one. Applying the bounded real lemma(BRL), a linear matrix inequality(LMI) is formed. Through solving the LMI, the feedback aided iterative learning control gains can be obtained, which is shown in a numerical study that the faster convergence rate along the iterative axis can be achieved.3. For solving the linear matrix inequalities(LMI), one needs the aid of MATLAB LMI toolbox. An example for illustrating how to use the toolbox to solve the LMI is presented in details. Illustrative examples are provided to verify effectiveness of the feedback aided iterative learning control strategies. The pros and cons of the feedback aided control strategies and open-loop learning algorithms are examined by the numerical results.4. For the discrete-time irregular systems, the design method of open loop iterative learning controllers is summarized, and the design method of the feedback aided iterative learning controllers is put forward. The tracking performance resulted by two kinds of learning control strategies is compared with simulation results, and comparatively, the effectiveness of feedback aided iterative learning controller is demonstrated.5. Utilizing the input and output data obtained from the experiment of a permanent magnet motor, the mathematical model of the motor is given by applying the least square method. According to the feedback aided iterative learning method aforementioned, the linear motor servo controller is designed, and implemented for achieving high-precision position-tracking. The experimental results are present and verify the validity of the learning algorithm.