Nonlinear Iterative Learning Control Research Articles

Nonlinear time-frequency iterative learning control for micro-robotic deposition system using adaptive Fourier decomposition approach

Nonlinear time-frequency iterative learning control for micro-robotic deposition system using adaptive Fourier decomposition approach

Self-Tuning Nonlinear Iterative Learning for a Precision Testing Stage: A Set-Membership Approach

Iterative learning control (ILC) is an appealing method in motion control applications that can achieve the performance limit of feedforward compensation in repeating tasks. Compensating for the repetitive errors rapidly (G1) and at the same time reducing the accumulation of the non-repetitive errors effectively (G2) are two major goals of ILC. However, in the simultaneous presence of model uncertainties and noises, most ILC methods that have been used in application cannot fully achieve these two goals. To tackle this problem, this paper develops a self-tuning nonlinear ILC method (STNILC). Firstly, a new nonlinear ILC method (NILC) is designed in the set-membership framework based on the boundedness noise-uncertainty assumption. Then, a self-tuning algorithm is developed to determine the unknown noise-uncertainty bound that is required by NILC. Theoretical results confirm that desirable transient and steady-state convergence performances can be achieved by the proposed STNILC method.Comparative experimental results on a short-stroke stage for testing the lithographic projection lens verify the superiorities of STNILC in sufficiently achieving G1 and G2.

Fault-tolerant design of non-linear iterative learning control using neural networks

The design of neural-network-based iterative learning control for non-linear systems is addressed in the setting of a fault tolerant control regime. Taking advantage of the repetitive character of the control task, the inherent uncertainty related to a potential faulty system state can be properly accommodated in terms of a data-driven iterative learning scheme with neural networks used for forward/inverse modeling as well as for controller synthesis. The resulting control technique is supposed to be flexible enough to accurately compensate the faults occurring on both the sensors and actuators and, additionally, take into account the disturbances and noise acting on the system. A complete characterization of the novel fault-tolerant iterative learning scheme is provided including system identification, fault detection and accommodation. Also, the painstaking convergence analysis is presented and the resulting sufficient conditions can be constructively used to determine the update of control law in the consecutive process trial. The excellent performance of the developed control scheme is illustrated by a nontrivial example of tracking control for a magnetic brake system on various scenarios involving actuator and/or sensor faults.

Nonlinear Iterative Learning Control: A Frequency-Domain Approach for Fast Convergence and High Accuracy

Iterative learning control (ILC) involves a trade-off between perfect, fast attenuation of iteration-invariant disturbances and amplification of iteration-varying ones. The aim of this paper is to develop a nonlinear ILC framework that achieves fast convergence, robustness, and low converged error values in ILC. To this end, the method includes a deadzone nonlinearity in the learning update, which uses the difference in amplitude characteristics of repeating and varying disturbances to modify the learning gain for each error sample. A criterion for monotonic convergence of the nonlinear ILC algorithm is provided, which is used in combination with system measurements to select suitable design parameters. The proposed algorithm is validated using simulations, in which fast convergence to low error values is demonstrated.

Data-Based Control for Learning Systems With Nonlinear Dynamics: A Case Study

This paper focuses on exploiting a data-based control design framework for a class of iterative learning control (ILC) systems with nonlinear dynamics. A test method is first presented for nonlinear ILC systems to generate some helpful output data under some specific test inputs. Then, a data-based P-type ILC updating law is developed by resorting to these input and output data, for which a simple data-based selection condition on the gain matrix is provided to accomplish the perfect tracking objective of ILC systems having the globally Lipschitz nonlinear dynamics. The proposed data-based P-type ILC updating law is applicable for nonlinear ILC systems without the common full rank requirement, where none of the specific model information is utilized. A simulation example is given to illustrate the validity of the data-based ILC design framework for nonlinear ILC systems.

LMI based nonlinear Iterative Learning Control for uncertain discrete repetitive system

LMI based nonlinear Iterative Learning Control for uncertain discrete repetitive system

Event-Triggered Nonlinear Iterative Learning Control.

An event-triggered nonlinear iterative learning control (ET-NILC) method is presented for repetitive nonaffine and nonlinear systems that have 2-D dynamic behavior along both time and iteration directions. Based on the virtual linear data model, the ET-NILC method is proposed by designing an event triggering condition based on the Lyapunov-like stability analysis conducted along the iteration direction. The learning gain function of ET-NILC is nonlinear and updated by designing an iterative learning parameter estimation law to enhance the robustness. From the perspective of the time dynamics, the proposed ET-NILC is a feedforward control and the event-triggering condition can be verified offline using tracking errors, event triggering errors, and the estimated parameters together. Moreover, the proposed ET-NILC is a data-driven scheme since it merely uses I/O data for the design. The results are also extended to repetitive multiple-input-multiple-output (MIMO) nonaffine nonlinear systems using the property of input-to-state stability as the basic mathematical tool. The convergence of the proposed ET-NILC methods is proved. Several simulations illustrate the effectiveness of the proposed methods.

Data-driven nonlinear ILC with varying trial lengths

This work considers randomly varying trial lengths of a nonlinear and non-affine repetitive system and proposes a data-driven nonlinear iterative learning control (DDNILC) method via dynamic linearization. A nonlinear learning control law and a nonlinear parameter estimation law are developed by introducing a stochastic variable to describe the varying trial lengths. The learning gain is both nonlinear and iteration-time-varying, and is iteratively estimated through the parameter updating law so that the system uncertainties can be addressed more effectively. Moreover, the results are extended to the MIMO case. The proposed methods as well as the introduced dynamic linearization are data-driven without the need of an explicit model. Under the Bernoulli distribution assumption, the convergence analysis is performed rigorously in the probability sense. Illustrative examples are provided to verify the derived theoretical results.

Iterative Learning Control and Gaussian Process Regression for Hydraulic Cushion Control

In this paper, we investigate on extending a feed-forward control scheme for the force control circuit of a hydraulic cushion with Gaussian Process nonlinear regression and Iterative Learning Control. Gaussian Processes allow the possibility of estimating the unknown proportional valve nonlinearities and provide uncertainty measurements of the predictions. However, the system must realize a high precision tracking control which is not achievable if any uncertainty remains in the estimation. Therefore, an extra feed-forward signal based on Iterative Learning Control is used to obtain a precise and fast force reference tracking performance. The design of the Iterative Learning Control is based on an inverted linearized model in which a fourth-order low-pass filter is included to attenuate the unknown valve dynamics. The low-pass filter is split up into two second-order low-pass filters, one of which is applied in the positive, the other in the negative, direction of time, resulting in zero-phase filtering. Simulation results show that Gaussian Process regression allows the possibility of using feed-forward control and that the force tracking performance is improved by introducing Iterative Learning Control.

Contraction analysis of nonlinear noncausal iterative learning control

Iterative learning control (ILC) is a method for learning input signals for repetitive control tasks. In this paper, we provide a new method based on convex optimization for certifying convergence and estimating convergence rate in ILC schemes involving a nonlinear plant and a noncausal update law, which are common in practice. Using sum-of-squares (SOS) optimization, we compute the convergence rate of an example nonlinear, noncausal ILC system and verify its accuracy in experiment.

Iterative learning control for noninstantaneous impulsive fractional‐order systems with varying trial lengths

SummaryIn this paper, we propose five iterative learning control (ILC) schemes for noninstantaneous impulsive fractional‐order systems with randomly varying trial lengths. We introduce a domain alignment operator to establish a rigorous convergence analysis for nonlinear fractional‐order systems. This operator guarantees that the input, state, output, and tracking error are constrained in a function space that is designed in advance. Moreover, with the help of this operator, we extend the conventional ILC scheme from discrete systems to continuous and algebraic systems with incorporating redundant tracking information. In addition, nonlinear ILC schemes are also presented with a geometric analysis concept. All proposed schemes are shown to be convergent to the desired tracking trajectory. Two illustrative examples are provided to verify the theoretical results.

Convergence for SISO ILC Systems with Locally Lipschitz Nonlinear Dynamics

This paper is devoted to iterative learning control (ILC) for single-input single-output (SISO), affine nonlinear systems with locally Lipschitz dynamics and subject to iteration-varying uncertainties arising from external disturbances and initial state shifts. By adopting a P-type update law, a necessary and sufficient condition is proposed to ensure the convergence of nonlinear SISO ILC. It is shown that the ILC process converges robustly with the final error bound depending continuously upon the bounds of iteration-varying uncertainties. Simulations illustrate the validity of the convergence results.

Contraction Analysis of Nonlinear Iterative Learning Control

Iterative learning control (ILC) is widely used as a simple method for precise tracking of systems under repetitive conditions. ILC operates by “learning” from the previous iteration’s errors, correcting them over a number of iterations. However, the question of whether or not a nonlinear ILC system converges is still in general an open one. Assuming a state-space formulation, we use contraction analysis to formulate a convergence condition for ILC system as a linear matrix inequality (LMI). Finally, we compute a convergence certificate for a simple example involving “anticogging” a permanent-magnet synchronous motor driving a pendulum in simulation.

Contour accuracy improvement of a flexure-based micro-motion stage for tracking repetitive trajectory

Flexure-based micro-motion mechanisms have been widely utilized in modern precision industry due to their inherent merits, while model uncertainty, uncertain nonlinearity, and cross-coupling effect will obviously deteriorate their contour accuracy, especially in the high-speed application. This paper aims at improving the contouring performance of a flexure-based micro-motion stage utilized for tracking repetitive trajectories. The dynamic characteristic of the micro-motion stage is first studied and modeled as a second-order system, which is identified through an open-loop sinusoidal sweeping test. Then the iterative learning control (ILC) scheme is utilized to improve the tracking performance of individual axis of the stage. A nonlinear cross-coupled iterative learning control (CCILC) scheme is proposed to reduce the coupling effect among each axis, and thus improves contour accuracy of the stage. The nonlinear gain function incorporated into the CCILC controller can effectively avoid amplifying the non-recurring disturbances and noises in the iterations, which can further improve the stage’s contour accuracy in high-speed motion. Comparative experiments between traditional PID, ILC, ILC & CCILC, and the proposed ILC & nonlinear CCILC are carried out on the micro-motion stage to track circular and square trajectories. The results demonstrate that the proposed control scheme outperforms other control schemes much in improving the stage’s contour accuracy in high-speed motion. The study in this paper provides a practically effective technique for the flexure-based micro-motion stage in high-speed contouring motion.

Data loss for PLC of nonlinear systems Iterative Learning Control Algorithm

When we use power line as data carrier, due to the complexity of the PLC network environment, data packet loss frequently, so the paper deal with the iterative learning control for a class of nonlinear systems with measurement dropouts in the PLC, and studies the P-type iterative learning control algorithm convergence issues, the data packet loss is described as a stochastic Bernoulli process, on this basis we given convergence conditions for the P-type iterative learning control algorithm. The theoretically analysis is supported by the simulation of a numerical example; the convergence of ILC can be guaranteed when some output measurements are missing.

An alternative update formula for non-linear model-based iterative learning control

The conventional iterative learning control (ILC) algorithm for model-based ILC of non-linear systems is presented with the use of a non-linear inverse model as ILC compensator. The non-linear inverse model is solved with stable inversion. In addition, an alternative ILC algorithm for model-based ILC of non-linear systems is developed, also with using a non-linear inverse model as ILC compensator. Some connections between the conventional and alternative ILC algorithms and Picard, Mann and Ishikawa iterations are explored. The conventional and alternative algorithms are compared in a number of theoretical examples.

Nonlinear Iterative Learning Control of Travelling Wave Ultrasonic Motor

The relatively simple control strategy can decrease the complexity of the ultrasonic motor system and increase the cost performance. The nonlinear iterative learning control algorithm is simple, the control parameters can be determined according to little experimental knowledge. According to the control characteristics of ultrasonic motor, the nonlinear iterative learning control algorithm is improved and the nonlinear iterative learning control strategy of motor’s speed is designed. Experiments show that the motor system has good iterative learning capacity, the control effect is improved generally in the repeated learning process and the control strategy is simple and effective.

Iterative learning control with sampled-data feedback for robot manipulators

Abstract This paper deals with the improvement of the stability of sampled-data (SD) feedback control for nonlinear multiple-input multiple-output time varying systems, such as robotic manipulators, by incorporating an off-line model based nonlinear iterative learning controller. The proposed scheme of nonlinear iterative learning control (NILC) with SD feedback is applicable to a large class of robots because the sampled-data feedback is required for model based feedback controllers, especially for robotic manipulators with complicated dynamics (6 or 7 DOF, or more), while the feedforward control from the off-line iterative learning controller should be assumed as a continuous one. The robustness and convergence of the proposed NILC law with SD feedback is proven, and the derived sufficient condition for convergence is the same as the condition for a NILC with a continuous feedback control input. With respect to the presented NILC algorithm applied to a virtual PUMA 560 robot, simulation results are presented in order to verify convergence and applicability of the proposed learning controller with SD feedback controller attached

Iterative learning control for robotic manipulators: A bounded‐error algorithm

SUMMARYThis paper presents a model‐based nonlinear iterative learning control (NILC) for nonlinear multiple‐input and multiple‐output mechanical systems of robotic manipulators. An algorithm of a new strategy for the NILC implementation is proposed. This algorithm ensures that trajectory‐tracking errors of the proposed NILC, when implemented, are bounded by a given error norm bound. Both standard and bounded‐error learning control laws with feedback controllers attached are considered. The NILC synthesis is based on a dynamic model of a six degrees of freedom robotic manipulator. The dynamic model includes viscous and Coulomb friction and input generalized torques are bounded. With respect to the bounded‐error and standard learning processes applied to a virtual PUMA 560 robot (Unimation, Inc. Danburry, CT, USA), simulation results are presented in order to verify maximal tracking errors, convergence and applicability of the proposed learning control. Copyright © 2013 John Wiley & Sons, Ltd.

A New Nonlinear Iterative Learning Controller for Road Simulator

A new model based nonlinear iterative learning controller to replicate multiple reference trajectory is presented. The approach consists of a constrained Gauss-Newton numerical optimization algorithm, which is able to inverse a nonlinear system accurately. It uses the moving horizon idea from MPC to improve the computational efficiency. Combined with a class of nonlinear state-space model and an existing nonlinear iterative learning control scheme, this allows accurate tracking control of a nonlinear system. Numerical results are used to illustrate the algorithm.