Discrete Iterative Learning Control Research Articles

Grinding method of noncircular glass ornaments based on successive approximation and discrete cross-coupling iterative learning control

In order to solve the problem of complicated calculation and large counter error of curve fitting method in industrial processing of noncircular glass ornaments, this paper proposes a grinding point searching algorithm. The successive approximation is used to find the grinding point of the workpiece contour and the grinding wheel. The proposed algorithm does not require complicated formula derivation and calculation and has good counter accuracy. According to the discrete characteristics of point-cloud data, a discrete cross-coupling iterative learning control algorithm is proposed to suppress the contour processing control error. Based on the norm theory, the convergence analysis and convergence conditions of the algorithm are presented. The effectiveness of the proposed algorithms is verified by experiments.

D-type iterative learning control for a class of parabolic partial difference systems

In this paper, an iterative learning control problem is addressed for a class of parabolic partial difference systems. Several discrete D-type iterative learning control algorithms with initial state learning are proposed for the systems which have no direct channel between the input and output as well as the initial state value being unfixed in the learning process. Based on fundamental mathematical analysis tools and the discrete Gronwall inequality, sufficient conditions for tracking error convergence in the iterative domain for open-loop, closed-loop and open-closed-loop iterative learning control are established and proven respectively. Numerical simulations verify the effectiveness of the theoretical results.

Adaptive Iterative Learning Control for Freeway Traffic Flow Systems Using Improved Bacterial Foraging Optimized Desired Traffic Densities Planning

In this paper, we propose a discrete fuzzy-neural adaptive iterative learning control (AILC) for freeway traffic flow systems with random initial resetting errors, iteration-varying desired traffic densities, and random bounded off-ramp traffic volumes using traffic densities, space mean speeds, and on-ramp waiting queues design. It is assumed that the system nonlinear functions and input gains are unknown for controller design. An adaptive fuzzy-neural network controller and an adaptive robust controller are applied to compensate for the unknown system nonlinearities and input gains, respectively. Moreover, to deal with the disturbances from random bounded off-ramp traffic volumes, a dead-zone like auxiliary error with a time-varying boundary layer is introduced as a bounding parameter. This proposed auxiliary error is also utilized to construct the adaptive laws without using the bound of the input gain. The traffic density tracking error is shown to converge along the axis of learning iteration to a residual set whose level of magnitude depends on the width of boundary layer. Besides, since the nice desired traffic densities designed for the coordinated control objective of the AILC for freeway traffic flow systems are generally unknown, the improved bacterial forging optimization (IBFO) algorithm is used to optimize the fitness function, which is constructed by the coordinated control objective including (1) minimum total travel time, (2) minimum on-ramp average waiting time, and (3) minimum changes of desired traffic densities. Finally, a computer simulation example is used to verify the learning performance of the proposed fuzzy-neural AILC for freeway traffic flow systems using IBFO-based desired traffic densities planning.

Discrete PID-Type Iterative Learning Control for Mobile Robot

Through studying tracking problems of the wheeled mobile robot, this paper proposed a discrete iterative learning control approach based on PID with strong adaptability, fast convergence, and small error. This algorithm used discrete PID to filter rejection and restrained the influence of interference and noise on trajectory tracking, which made it more suitable for engineering application. The PID-type iterative learning convergence condition and certification procedure are presented. The results of simulation reveal that the PID-type ILC holds the features of simplicity, strong robustness, and high repeating precision and can well meet the control requirement of nonlinear discrete system.

Iterative learning control for discrete-time switched systems with attenuation factor

In order to decrease the effects of measurement noise on the trajectory tracking control of discrete-time switched systems, this paper proposes a discrete iterative learning control algorithm with an attenuation factor. The proposed algorithm adds a learning gain attenuated along the iteration horizon into measurement errors interfered by measurement noise for modifying the control rules of switched systems, in order to decay measurement noise as iterations increase. The convergence of each subsystem is proven rigidly with λ-norm theory, and the convergent condition of switched systems is provided. Theoretical results indicate that the proposed algorithm can effectively suppress non-repetitive measurement noise, and realize the complete tracking of the desired trajectory for the output of a discrete-time switched system within limited time. The final simulation results verify the validity of the proposed algorithm.

Iterative learning control for discrete time-varying switched systems

Aiming at the problem of trajectory tracking in a class of discrete time-varying switched system with arbitrary sequence, in this paper we propose a discrete iterative learning control algorithm. Under the precondition that the switched sequence does not change along the iterative axis but it does along the time axis, this algorithm divides the whole finite time region into several finite subintervals, and uses -norm to prove the convergence strictly, and provides the sufficient convergent condition of the algorithm in the norm form. This method not only realizes the complete tracking for a discrete time-varying switched system within a limited time, but also has a simple structure easy to be realized in engineering. Simulation results verify the validity of the method.

Model Free Adaptive Iterative Learning Control for Farm Vehicle Path Tracking

Abstract Duo to the periodicity of farm cropping, harvesting, seeding and spraying, a discrete time model free adaptive iterative learning control (MFAILC) algorithm for path tracking of farm vehicle is proposed. Based on the dynamical form linearization model for farm vehicle kinematic model l, the MFAILC algorithm can be designed just depending on the I/O data of the farm vehicle. The proposed method also can compensate the effect of initial shifting to preserve a perfect tracking. Simulations results illustrate the validity of the proposed methods.

Robust H∞ Stabilization of Uncertain T-S Fuzzy Systems via Dynamic Integral Sliding Mode Control

Abstract Duo to the periodicity of farm cropping, harvesting, seeding and spraying, a discrete time model free adaptive iterative learning control (MFAILC) algorithm for path tracking of farm vehicle is proposed. Based on the dynamical form linearization model for farm vehicle kinematic model l, the MFAILC algorithm can be designed just depending on the I/O data of the farm vehicle. The proposed method also can compensate the effect of initial shifting to preserve a perfect tracking. Simulations results illustrate the validity of the proposed methods.

Necessary and sufficient stability condition of LTV iterative learning control systems using a 2‐D approach

AbstractThis paper deals with the stability analysis of discrete iterative learning control (ILC) by developing a two‐dimensional (2‐D) approach under the Roesser systems framework. The system under consideration is a class of multiple‐input multiple‐output (MIMO), linear time‐varying (LTV) systems. Using a type of two‐gain ILC, it is shown that once the theory is established for the discrete‐time‐varying 2‐D Roesser systems, a necessary and sufficient condition for the stability of ILC process can be determined directly. Numerical simulation is included to verify the theoretical results.Copyright © 2010 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society

Design of Iterative Learning Controllers for Linear Discrete Systems with Multiple Time Delays

The problem of iterative learning control is considered for a class of linear discrete systems with multiple time delays. In this paper, it is assumed that the initial condition for discrete time-delay systems is unknown at each iteration. For such a class of discrete time-delay systems, a method is presented whereby a class of discrete iterative learning control schemes can be constructed. It is shown that under some given conditions, the constructed iterative learning controllers can guarantee the asymptotic convergence of the output error between the given desired output and the actual output through the iterative learning process. Finally, a numerical example is given to demonstrate the validity of the results.

A note on causal and CITE iterative learning control algorithms

The convergence properties of causal and current iteration tracking error (CITE) discrete time iterative learning control (ILC) algorithms are studied using time and frequency domain convergence criteria. Of particular interest are conditions for monotone convergence, and these are evaluated using a discrete-time version of Bode's integral theorem.

A discrete iterative learning control for a class of nonlinear time-varying systems

A discrete iterative learning control is presented for a class of discrete-time nonlinear time-varying systems with initial state error, input disturbance, and output measurement noise. A feedforward learning algorithm is designed under a stabilizing controller and is updated by more than one past control data in the previous trials. A systematic approach is developed to analyze the convergence and robustness of the proposed learning scheme. It is shown that the learning algorithm not only solves the convergence and robustness problems but also improves the learning rate for discrete-time nonlinear time-varying systems.

On the realization of an accurate hydraulic servo through an iterative learning control

Many hydraulically-operated process such as machining, injection molding and metal forming process are usually represented by a hydraulic actuator-load system whose dynamic characteristics are complex and highly nonlinear. Due to these characteristics, the conventional approach to the controller design for these systems may not guarantee accurate tracking control performance. Taking into account the repetitive nature of the operations in those processes, a discrete iterative learning control algorithm is proposed to realize an accurate hydraulic servo system. In the algorithm, the control input sequence for next operation is determined by utilizing the tracking error as well as information of the dynamic characteristics obtained from the past operations such that the output trajectory tracks the given desired trajectory as closely as possible. To investigate gradual improvement of tracking performance in consecutive operations, the proposed algorithm is implemented to the hydraulic servo system. A series of experiments was performed for the position tracking control of the system. The experimental results show that regardless of inherent nonlinearities and uncertainties associated with hydraulic system, an accurate tracking control performance is obtained using the proposed learning control algorithm characterized by recursive operations.

An Iterative Learning Controller for Hydraulic Servo-Systems Subjected to Unknown Disturbances

Many processes such as machining, injection-moulding and metal-forming are usually operated by hydraulic servo-systems. The dynamic characteristics of these systems are complex and highly non-linear and are often subjected to the uncertain external disturbances associated with the processes. Consequently, the conventional approach to the controller design for these systems may not guarantee accurate tracking-control performance. Taking into account the repetitive nature of the operations in those processes, a discrete iterative learning control algorithm is proposed to realize an accurate hydraulic servo-system regardless of the uncertainties and the external disturbances. In the algorithm, the control input sequence for the next operation is determined by utilizing the tracking error, as well as information on the dynamic characteristics obtained from the past operations, so that the output trajectory tracks the given the desired trajectory as closely as possible. To investigate a gradual improvement of tracking performance in consecutive operations, the proposed algorithm was implemented on a hydraulic servo-system. A series of experiments was performed for the position-tracking control of the system subjected to external disturbances. The experimental results show that, regardless of inherent non-linearities and disturbances, an accurate tracking-control performance is obtained using the proposed learning control algorithm characterized by recursive operations.