Iterative learning control for a class of discrete-time singular systems

Abstract This paper is concerned with the iterative learning control problem for a class of discrete-time singular systems. According to the characteristics of the systems, a closed-loop PD-type learning algorithm is proposed and the convergence condition of the algorithm is established. It is shown that the algorithm can guarantee the system output converges to the desired trajectory on the whole time interval. Moreover, the presented algorithm is also suitable for discrete-time singular systems with state delay. Finally, the validity of the presented algorithm is verified by two numerical examples

Iterative Learning Control with Forgetting Factor for Linear Distributed Parameter Systems with Uncertainty

Iterative learning control is an intelligent control algorithm which imitates human learning process. Based on this concept, this paper discussed iterative learning control problem for a class parabolic linear distributed parameter systems with uncertainty coefficients. Iterative learning control algorithm with forgetting factor is proposed and the conditions for convergence of algorithm are established. Combining the matrix theory with the basic theory of distributed parameter systems gives rigorous convergence proof of the algorithm. Finally, by using the forward difference scheme of partial differential equation to solve the problems, the simulation results are presented to illustrate the feasibility of the algorithm

On a Novel Tracking Differentiator Design Based on Iterative Learning in a Moving Window

Differential signals are key in control engineering as they anticipate future behavior of process variables and therefore are critical in formulating control laws such as proportional-integral-derivative (PID). The practical challenge, however, is to extract such signals from noisy measurements and this difficulty is addressed first by J. Han in the form of linear and nonlinear tracking differentiator (TD). While improvements were made, TD did not completely resolve the conflict between the noise sensitivity and the accuracy and timeliness of the differentiation. The two approaches proposed in this paper start with the basic linear TD, but apply iterative learning mechanism to the historical data in a moving window (MW), to form two new iterative learning tracking differentiators (IL-TD): one is a parallel IL-TD using an iterative ladder network structure which is implementable in analog circuits; the other a serial IL-TD which is implementable digitally on any computer platform. Both algorithms are validated in simulations which show that the proposed two IL-TDs have better tracking differentiation and de-noise performance compared to the existing linear TD

On the Equivalence between PID-like Controller and LADRC for Second-order Systems

In this paper, the equivalence is established between the linear active disturbance rejection control (LADRC) and the two-degree of freedom (2-DOF) proportional-integral-derivative (PID) with lead-lag compensators. This allows advantage of LADRC, particularly its bandwidth-parameterization strategy, to be incorporated into the run-of-mill PID controllers. Specifically, the competing design objectives in disturbance rejection, tracking, and noise sensitivities can now be handled with ease