Research On Iterative Learning Control Algorithm For Nonlinear System

Iterative learning control be able to completely eliminate the repeated errors of the controlled system and achieve the desired output trajectory tracking in theory. However, in actural operation, non-repeating errors exist inevitably, for example, measurement errors, random disturbances and so on. Iterative learning control can not do anything to non-repeatable errors. with the increase of the number of iterations, non-repeatable errors continue to augment. Non-repeating errors accumulated so large that the transient response of the controlled system fluctuates sharply, even beyond the permissible values of the system. Then, it results in a serious deterioration in the performance of the control system. On the other hand, several conditions are needed for iterative learning control to achieve the elimination of the repeated error in the controlled system, the first is the initial value problem, which requires the controlled system has the same initial state as the desired trajectory. The second is the convergence problem for nonlinear controlled system, in order to ensure convergence to the desired control input, it is always assume that the desired control is in existence, and the controlled system must meet Lipschiz continuous conditions. These assumptions limit the scope of application of the iterative learning control. Aim to the problems above for iterative learning control, this paper will combinate iterative learning control method and predictive control method to provide some novel strategy to deal with the non-repeated errors in iterative learning control for nonlinear systems, meanwhile, in Hilbert space, we make use of the operator theory to fomulate iterative learning control algirithm for systems which cannt meet the Lipschiz continuous conditions.The main contents and innovations are as follows:Aim to remove the aperiodic errors in the iterative learning control for nonlinear systems, a predictive control method is developed to despel the aperiodic errors at each sampling time during a iterative process. Because the continuous nonlinear system can be discreted, so the text of the control strategy is designed for discrete systems. Because the iterative learning control law is designed off-line, predictive control scheme is the focus that we pay attention to in the control design. Assuming that the controlled system has a number of sampling points during each repeated operation process, at each sampling point, it must implement different learning control law. The control law is different in the output errors, and these different errors are obtained through the implementation of predictive control at each sample point. It also gives the convergence and stability of predictive iterative predictive control algorithm proposed in this paper.As for the question that classical nonlinear iterative learning control system must meets the Lipschiz continuous conditions, a new iterative learning control law called two-step iterative learning control is presented. The proposed iterative learning control law can be applied to the controlled systems which donot meet the conditions of continuous Lipschiz and achieve convergence. It greatly expands the scope of application of the iterative learning control.During the process of iterative learning control, it is required to measure the system output signal.Then we obtain the difference between the ideal output and the actual measured systen output. The control input signal in the next iterative is updated by the controlled system output error. Therefore, the measurement errors occur inevitably,and affect the performance of the control systemseverely.Aim at the measurement error, this paper put forward the predicted variable gain iterative learning control strategies. Taking advantage of a variable gain eliminates the negative impact caused by the presence of measurement error, and this method is applied to the permanent magnet synchronous motor system to eliminate torque ripple.In the published literature on iterative learning control, most of the iterative learning control strategies are proposed in finite-dimensional space.The iterative learning control in infinite-dimensional space rarely raised. Moreover, the iterative learning control algorithm proposed always assumes that the desired control input is in existence in advance, but in practice, we do not know whether there is the control input. In this paper, a iterative learning control method in the infinite-dimensional space is proposed, and it shows how to determine that whether there is a desired control input for controlled system. The contribution of the method is greatly reducing the subjectivity of desired control input, and enriching and developing the theory of iterative learning control.In order to solve problems in VSC-HVDC circulating current suppressing control which include decoupling completely and imperfectly compensating for nonlinear problems, a iterative learning control methord is proposed based on error model predictive control. Firstly, the discrete mathematical model of VSC-HVDC is obtained according to Euler’s formula from continous model of the controlled system, and then it establish the discrete model of tracking errors which can eliminate repetitive disturbance.secondly, Kalman filter estimates the current state value and eliminate random error by predictive control to achieve the completely tracking of ideal system output. Predictive control method itself has computation intensive, when combined with a modular multi-level converter, it leads to greater online computational problem.To solve these problems, according to the mean inequality, it deduce the optimal grouping method to solve the optimal target value of prediction cost function. Furthermore, the optimal grouping method can be extend to solve many multi-predictive control which greatly reducing the online computation of predictive control and improve the control performance of the system.