Iterative Learning Control Algorithm Research Articles

A gradient-descent iterative learning control algorithm for a non-linear system

Original iterative learning control (OILC) has been proved a powerful tool in dealing with the model-free control problems by repetitively corrections based on the control error. However, the steady-state error under widely-used proportional-type original iterative learning control (P-type OILC) is highly corresponded to the proportional learning gain, making the algorithm parameter-determined. Therefore, a new gradient-descent iterative learning control (GDILC) algorithm is proposed to achieve a parameter-free approach by simulating the gradient-descent process. First, GDILC problem is formulated mathematically. Next, the idea of the algorithm is proposed, the analyses of the convergence and the steady-state error are conducted and the algorithm is implemented. GDILC will generate a random correction with a gradient-descent upper bound, rather than a correction proportional to the error in P-type OILC. Finally, illustrative and application simulations are conducted to validate the algorithm. Results show that the algorithm will be convergent after adequate iterations under proper corrections. The steady-state error will be less affected by the algorithm parameters under GDILC than that under OILC.

Adaptive iterative learning control of soft robot for beating heart tracking

Purpose Soft robots are known for their excellent safe interaction ability and promising in surgical applications for their lower risks of damaging the surrounding organs when operating than their rigid counterparts. To explore the potential of soft robots in cardiac surgery, this paper aims to propose an adaptive iterative learning controller for tracking the irregular motion of the beating heart. Design/methodology/approach In continuous beating heart surgery, providing a relatively stable operating environment for the operator is crucial. It is highly necessary to use position-tracking technology to keep the target and the surgical manipulator as static as possible. To address the position tracking and control challenges associated with dynamic targets, with a focus on tracking the motion of the heart, control design work has been carried out. Considering the lag error introduced by the material properties of the soft surgical robotic arm and system delays, a controller design incorporating iterative learning control with parameter estimation was used for position control. The stability of the controller was analyzed and proven through the construction of a Lyapunov function, taking into account the unique characteristics of the soft robotic system. Findings The tracking performance of both the proportional-derivative (PD) position controller and the adaptive iterative learning controller are conducted on the simulated heart platform. The results of these two methods are compared and analyzed. The designed adaptive iterative learning control algorithm for position control at the end effector of the soft robotic system has demonstrated improved control precision and stability compared with traditional PD controllers. It exhibits effective compensation for periodic lag caused by system delays and material characteristics. Originality/value Tracking the beating heart, which undergoes quasi-periodic and complex motion with varying accelerations, poses a significant challenge even for rigid mechanical arms that can be precisely controlled and makes tracking targets located at the surface of the heart with the soft robot fraught with considerable difficulties. This paper originally proposes an adaptive interactive learning control algorithm to cope with the dynamic object tracking problem. The algorithm has theoretically proved its convergence and experimentally validated its performance at the cable-driven soft robot test bed.

Event-triggered iterative learning control for discrete parabolic distributed parameter systems

Iterative learning control (ILC) is an intelligent control strategy which can achieve the desired trajectory tracking by continuously renewing the control signal based on the previous experience. In this article, an event-triggered condition that can save system resources by reducing the number of iterative updates is proposed. Moreover, an event-triggered ILC algorithm is designed for linear discrete parabolic distributed parameter systems, the system input is updated with the learning law only when the derived triggered condition is met. Through rigorous mathematical analysis, the tracking error can converge to zero when the iterative batch approaches infinity under the given sufficient condition. Then, we also extended the above ideas to nonlinear case. By simulation, the effectiveness of the designed algorithm are illustrated.

Robust model-free adaptive iterative learning control for an autonomous bus trajectory tracking system.

A robust model-free adaptive iterative learning control (R-MFAILC) algorithm is proposed in this work to address the issue of laterally controlling an autonomous bus. First, according to the periodic repetitive working characteristics of autonomous buses, a novel dynamic linearized method used in the iterative domain is utilized, and a time-varying data model with a pseudo gradient (PG) is given. Then, the R-MFAILC controller is designed with a proposed adaptive attenuation factor. The proposed algorithm's advantage lies in the R-MFAILC controller, which solely utilizes the input and output data of the regulated entity. Moreover, the R-MFAILC controller has strong robustness and can handle the nonlinear measurement disturbances of the system. In simulations based on the Truck-Sim simulation platform, the effectiveness of the proposed algorithm is verified. A rigorous mathematical analysis is employed to demonstrate the stability and convergence of the proposed algorithm.

Data-driven robust iterative learning control of linear systems

We propose a data-driven robust iterative learning control (ILC) technique to multi-input-multi-output (MIMO) linear systems. Control of MIMO linear systems, particularly with strong cross-axis coupling, is challenging as modeling of a MIMO system can be complicated, time-consuming, and often requires a trade-off between robustness and performance. As such, limitations exist in current ILC techniques. The aim of this paper is to develop an efficient and easy-to-use data-driven ILC technique to output tracking of MIMO linear systems under random disturbance. Through the proposed technique, the complicated modeling process and the robustness-accuracy trade-off are avoided, and the up-to-now system dynamics is captured by constructing and updating the iteration gain using the input and output data in the last iteration. It is shown that monotonic convergence of the ILC algorithm is guaranteed, and an optimal gain can be obtained to maximize the convergence rate and minimize the residual tracking error. The proposed technique is illustrated through experiments on a three-input three-output piezoelectric actuator system, with comparison to the adaptive multi-axis inversion-based iterative control (A-MAIIC) technique. The experimental results show rapid convergence and improved formance of the proposed technique when the cross-axis coupling is strong.

Iterative learning control for non-normal and biased measured targets

In the original iterative learning control (ILC) algorithm, it is commonly assumed that the target signal remains constant throughout iterations. However, this assumption may not be satisfied in practical industrial applications. Therefore, this paper proposes a novel ILC approach for non-normal and biased measured targets, in which the target is not predetermined by a fixed curve or formula but generated from the generation system. The iterative learning control problem is first formulated, followed by algorithm implementation through mechanism analysis, process determination, and assessments for feasibility and convergence. The proposed algorithm is simulated subsequently. Results demonstrate that application of this algorithm can effectively minimize expected error between non-normal and biased measured targets and output. After a sufficient number of iterations, the tracking error will originate solely from the trajectory itself.

Multi-Parameter Fuzzy-Based Neural Network Sensorless PMSM Iterative Learning Control Algorithm for Vibration Suppression of Ship Rim-Driven Thruster

Aiming to reduce motor speed estimation and torque vibration present in the permanent magnet synchronous motors (PMSMs) of rim-driven thrusters (RDTs), a position-sensorless control algorithm using an adaptive second-order sliding mode observer (SMO) based on the super-twisting algorithm (STA) is proposed. In which the sliding mode coefficients can be adaptively tuned. Similarly, an iterative learning control (ILC) algorithm is presented to enhance the robustness of the velocity adjustment loop. By continuously learning and adjusting the difference between the actual speed and given speed of RDT motor through ILC algorithm, online compensation for the q-axis given current of RDT motor is achieved, thereby suppressing periodic speed fluctuations during motor running. Fuzzy neural network (FNN) training can be used to optimize the STA-SMO and ILC parameters of RDT control system, while improving speed tracking accuracy. Finally, simulation and experimental verifications have been conducted on the vector control system based on the conventional PI-STA and modified ILC-STA. The results show that the modified algorithm can effectively suppress the estimated speed and torque ripple of RDT motor, which greatly improves the speed tracking accuracy.

Sampling-based event-triggered iterative learning control in nonlinear hyperbolic distributed parameter systems

This article explores a sampling-based event-triggered iterative learning control (SETILC) method for achieving precise control in nonlinear hyperbolic distributed parameter systems. Firstly, by designing a Lyapunov function regarding the system output error, reasonable triggering conditions are derived to selectively update the system control input. Subsequently, a sampling-based event-triggered iterative learning control algorithm is proposed to further enhance the control performance of the system while avoiding the occurrence of Zeno phenomena. A condition sufficient for ensuring the convergence of the system’s tracking error to zero is presented, and its convergence is proven. Finally, the proposed method’s effectiveness is verified through numerical simulations.

Iterative learning control with parameter estimation for non-repetitive time-varying systems

This paper presents an extension method of iterative learning control (ILC) to address the applications associated with non-repetitive time-varying systems (NTVSs). Conventional ILC approaches employ fixed nominal system models, but non-repetitive time-varying models may lead to accumulated model uncertainties, which fails to satisfy the robust convergence conditions. To tackle this issue, a novel ILC algorithm with parameter estimation is proposed using back propagation neural network. This algorithm incorporates an approach that utilizes Bayesian regularization training mechanism to accurately estimate non-repetitive time-varying parameters. Through comprehensive experiment on Monolithic XY Stage, the performance of proposed algorithm is validated to demonstrate its feasibility and effectiveness while handling tasks on NTVSs.

Performance-Based Iterative Learning Control for Task-Oriented Rehabilitation: A Pilot Study in Robot-Assisted Bilateral Training

Active participation from human subjects can enhance the effectiveness of robot-assisted rehabilitation. Developing interactive control strategies for customized assistance is therefore essential for encouraging human-robot engagement. However, existing human-robot interactive control strategies lack precise evaluation indicators with effective convergence method to steadily and rapidly customize appropriate assistance during task-oriented training. This study proposes a performance-based iterative learning control algorithm for robot-assisted training, which aims at providing subject-specific robotic assistance to encourage active participation. Three performance indicators based on a Fugl-Meyer Assessment (FMA) regression model are introduced to associate clinical scales with robot-based measures, and a fuzzy logic is employed for comprehensive performance evaluation. To increase efficient training time, a piecewise learning rate based iterative law is applied to quickly converge to a subject-specific control parameter session by session. The proposed strategy is preliminarily estimated for a case of bilateral upper limb training with an end-effector based robotic system. Experimental results with human subjects indicate that the proposed strategy can obtain appropriate parameters after only several iterations and adapt to random perturbations (like muscle fatigue).

Robust model-based predictive iterative learning control for systems with non-repetitive disturbances

Iterative Learning Control (ILC) is commonly used for batch processes. However, it may face difficulties when dealing with non-repetitive disturbances and inconsistent initial states. In situations with non-repetitive disturbances, the output may disobey constraints and negatively impact tracking performance when using existing predictive ILC algorithms. This paper introduces a new model-predictive ILC incorporating feed-forward and feedback mechanisms. This new approach evaluates and attenuates the impact of non-repetitive disturbances on the output. As a result, constraints are guaranteed, and tracking performance is preserved and improved, even in the presence of non-repetitive disturbances. Furthermore, if the desired trajectory is unattainable, the proposed ILC can robustly track an optimal trajectory while still guaranteeing constraints. The convergence is proven rigorously. Finally, two examples are provided to demonstrate the effectiveness of this new approach.

Parameter-Optimal-Gain-Arguable Iterative Learning Control for Linear Time-Invariant Systems with Quantized Error

In this paper, a parameter optimal gain-arguable iterative learning control algorithm is proposed for a class of linear discrete-time systems with quantized error. Based on the lifting model description for ILC systems, the iteration time-variable derivative learning gain in the algorithm is optimized by resolving a minimization problem regarding the tracking error energy and the learning effort amplified by a weighting factor. Further, the tracking error can be monotonically convergent to zero when the condition is guaranteed and the rate of convergence can be adjusted by scaling the weighting factor of an optimization problem. This algorithm is more innovative when compared with the existing iterative learning control algorithm for quantization systems. The innovations of this algorithm are as follows: (i) this optimization-based strategy for selecting learning gains can improve the active learning ability of the control mechanism and avoid the passivity of existing selective learning gains; (ii) the algorithm of POGAILC with data quantization can improve the convergence performance of tracking errors and reduce the negative effects of data quantization on the control performance of the logarithmic quantizer; and (iii) we provide a rigorous algorithm convergence analysis by deriving the existence of the unique solution for the optimal learning-gain vector under a singular and nonsingular tracking-error diagonalized matrix. Finally, numerical simulations are used to demonstrate the effectiveness of the algorithm.

P-Accelerated normal S-iterative learning control algorithm for linear discrete singular time-delay systems

This article addresses the issue of iterative learning control for a specific category of discrete linear singular time-delay systems. A new iterative learning control algorithm based on the p-accelerated normal S-iteration method is proposed, and convergence analysis of the corresponding learning control algorithm is studied. With certain assumptions, the proposed algorithm guarantees that the output of the system converges to the desired output trajectory within a finite time interval. The theoretical analysis is supported by numerical examples. The results indicate that the p-accelerated normal S-iterative learning control algorithm outperforms both the first-order PD-type iterative learning control and second-order PD-type iterative learning control algorithms for discrete linear singular systems theoretically and numerically.

Two-Dimensional Fractional Order Iterative Learning Control for Repetitive Processes

The convergence and robustness rejecting parameters variations and external disturbance of the system are crucial for repetitive processes. In this paper, a two-dimensional robust fractional-order iterative learning control (FOILC) is proposed for the repetitive motion process to enhance the convergence and robustness. A fractional-order proportional derivative function (FOPDF) is designed as the control variable to replace the tracking error of the integer-order iterative learning control (IOILC) algorithm. The required dynamic output fractional-order iterative learning controller is constructed by solving a set of linear matrix inequalities (LMI), and the control parameters are adjusted according to the given specifications. Simulation and experimental results in robot torque control are given to prove the effectiveness and feasibility of the proposed design method.

Layered and subregional control strategy based on model-free adaptive iterative learning for laser additive manufacturing process

Improving stability in process and the quality of manufactured parts is critical to laser additive manufacturing (LAM). Developing appropriate control methods is essential for this purpose. Layered control approaches are commonly utilized in current research on LAM process control, with a primary focus on the pattern of layer-by-layer deposition. However, these strategies might neglect the dynamic and evolving characteristics of the process along the scanning direction. Due to the complex nature of the LAM process, such layered control approaches could be inadequate in addressing intra-layer instability, potentially resulting in metallurgical defects. To overcome these limitations, we propose a layered-and-subregional model-free adaptive iterative learning control (LS-MFAILC) method. Considering the cyclic and the layer-by-layer processing principle of LAM, we develop a subregional control strategy and integrate it with a layered control framework. In addition, the model-free adaptive iterative learning control (MFAILC) algorithm is utilized as the controller due to its ability to control complex and time-varying systems with repetitive running characteristics. In the proposed method, each target layer to be printed in process is divided into multiple non-overlapping regions along the scanning direction, and the process parameters for each region are adaptively controlled based on historical information acquired from previous layers during the process. The temperature information of the melt pool is captured and extracted using a thermal imager integrated with the printing system. Experimental results and comparison with the layered control approach demonstrate the effectiveness and superiority of our method.

Neural network-based iterative learning control for trajectory tracking of unknown SISO nonlinear systems

This paper proposes a neural network-based (NN-based) data-driven iterative learning control (ILC) algorithm for the tracking problem of nonlinear single-input single-output (SISO) discrete-time systems with unknown models and repetitive tasks. The control objective is to make the output of the system track the reference trajectory in each iteration process. Therefore, at each relative time during every iteration process, a generalized regression neural network (GRNN) is used as the estimator to solve the key parameters of the system, and a radial basis function neural network (RBFNN) is used as the controller to solve the control input. Compared with the traditional ILC algorithm, the two complex solving processes, i.e., dynamic linearization and criterion function minimization, are replaced and simplified into the iterative training of GRNNs and RBFNNs. The proposed algorithm is out-of-the-box and uses a point-to-point method to calculate the control input for each relative time of the system iteration, driving the tracking error of the system to approach zero. In addition, it is proved that the tracking error of the system under the proposed control algorithm is uniformly ultimately bounded. Finally, a numerical example shows the effectiveness and superiority of the control algorithm, and a path tracking experiment of an unmanned vehicle further verifies its practicability.

Multi-link mechanism-inspired palletizing manipulator: Design, optimization and experimental results

The precision of trajectory tracking and stable operation with sorting merchandise are the main challenges for palletizing manipulators in different working conditions, especially in sorting glass-substrate. To ensure the adaptability of the manipulator under different working conditions, including operational efficiency, motion space, and control accuracy, the structural optimization and the motion control methods of the manipulator should be considered. In this paper, the structure optimization and tracking control of the manipulator for sorting glass substrates are studied. Firstly, considering the optimization factors including stroke speed ratio k, transmission angle [Formula: see text] and the sum of link-rod lengths l of the crank rocker mechanism, a structural optimization method based on genetic algorithm is applied to enhance the flexible maneuverability. Furthermore, a feedforward-feedback iterative learning control (ILC) algorithm is adopted to the high accuracy of position tracking. Finally, experimental results verify the feasibility of structural optimization and tracking control, which can be effective applied in practical engineering.

Hybrid-based model-free iterative learning control with optimal performance

In this paper, a hybrid-based model-free iterative learning control algorithm is proposed to improve the robustness and convergence speed of model-free iterative learning control in noisy environments. The proposed algorithm divides the iterative process into a rapidly decreasing error phase and an error convergence phase, and uses different control algorithms in different phases, thus combining different advantages of the original algorithms. In addition to this, this work proves the convergence and robustness of the proposed algorithm and summarises the design idea of this controller. Finally, the convergence performance of the algorithm in noisy environments and in variable reference trajectory environment is simulated to demonstrate the effectiveness of the algorithm proposed in this work.

Iterative Learning Control for Compliant Underactuated Arms

Operations involving safe interactions in unstructured environments require robots with adapting behaviors. Compliant manipulators are a promising technology to achieve this goal. Despite that, some classical control problems such as following a trajectory are still open. A typical solution is to compensate the system dynamics with feedback loops. However, this solution increases the effective robot stiffness and jeopardizes the safety property provided by the compliant design. On the other hand, purely feedforward approaches can achieve good tracking performance while preserving the robot intrinsic compliance. However, a feedforward control framework for robots with passive elastic joints is still missing. This article presents an iterative learning control algorithm for purely feedforward trajectory tracking for compliant underactuated arms. Each arm is composed of active elastic joints and a generic number of passive ones connected through rigid links. We prove the convergence of the iterative method, also in the presence of uncertainties and bounded disturbances. Different output functions are analyzed providing conditions, based on the system inertial properties that ensure the algorithm applicability. Additionally, an automatic selection of the learning gain is proposed. Finally, we extensively validate the theoretical results with simulations and experiments.

An Optimal Iterative Learning Control Approach for Linear Systems With Nonuniform Trial Lengths Under Input Constraints

In practical applications of iterative learning control (ILC), the repetitive process may end up early by accident during the performance improvement along the trial axis, which yields the nonuniform trial length problem. For such practical systems, input signals are usually constrained because of some certain physical limitations. This article proposes an optimal ILC algorithm for linear time-invariant multiple-input–multiple-output (MIMO) systems with nonuniform trial lengths under input constraints. The optimal ILC framework is specifically modified for the nonuniform trial length problem, where the primal–dual interior point method is introduced to deal with the input constraints. Hence, the constraint handling capability are improved compared with the conventional counterparts for nonuniform trial lengths. Also, the monotonic convergence property of the proposed optimal ILC algorithm is obtained in the sense of mathematical expectation. Finally, the effectiveness of the proposed algorithm is verified on the numerical simulation of a mobile robot.