scholarly journals An Accelerated Error Convergence Design Criterion and Implementation of Lebesgue-p Norm ILC Control Topology for Linear Position Control Systems

2021 ◽  
Vol 2021 ◽  
pp. 1-12
Author(s):  
Saleem Riaz ◽  
Hui Lin ◽  
Muhammad Waqas ◽  
Farkhanda Afzal ◽  
Kai Wang ◽  
...  
Keyword(s):  
Iterative Learning Control ◽  
Control Algorithm ◽  
Position Control ◽  
Tracking Error ◽  
Learning Control ◽  
Convergence Condition ◽  
Design Criterion ◽  
Iterative Learning ◽  
Current Error ◽  
P Type

Traditional and typical iterative learning control algorithm shows that the convergence rate of error is very low for a class of regular linear systems. A fast iterative learning control algorithm is designed to deal with this problem in this paper. The algorithm is based on the traditional P-type iterative learning control law, which increases the composition of adjacent two overlapping quantities, the tracking error of previous cycle difference signals, and the current error difference. Using convolution to promote Young inequalities proved strictly that, in terms of Lebesgue-p norm, when the number of iterations tends to infinity, the tracking error converges to zero in the system and presents the convergence condition of the algorithm. Compared with the traditional P-type iterative learning control algorithm, the proposed algorithm improves convergence speed and evades the defect using the norm metric’s tracking error. Finally, the validation of the effectiveness of the proposed algorithm is further proved by simulation results.

Iterative learning control algorithm for sensor fault nonlinear systems

2020 ◽  
pp. 1-8
Author(s):  
Zimian Lan
Keyword(s):  
Nonlinear Systems ◽  
Iterative Learning Control ◽  
Control Algorithm ◽  
Tracking Error ◽  
Learning Control ◽  
Open Loop ◽  
Iterative Learning ◽  
Sensor Fault ◽  
Initial State ◽  
Control Gain

In this paper, we propose a new iterative learning control algorithm for sensor faults in nonlinear systems. The algorithm does not depend on the initial value of the system and is combined with the open-loop D-type iterative learning law. We design a period that shortens as the number of iterations increases. During this period, the controller corrects the state deviation, so that the system tracking error converges to the boundary unrelated to the initial state error, which is determined only by the system’s uncertainty and interference. Furthermore, based on the λ norm theory, the appropriate control gain is selected to suppress the tracking error caused by the sensor fault, and the uniform convergence of the control algorithm and the boundedness of the error are proved. The simulation results of the speed control of the injection molding machine system verify the effectiveness of the algorithm.

Accurate Task-Space Tracking for Humanoids with Modeling Errors Using Iterative Learning Control

2017 ◽  
Vol 14 (03) ◽  
pp. 1750015 ◽  
Author(s):  
Pranav A. Bhounsule ◽  
Katsu Yamane
Keyword(s):  
Iterative Learning Control ◽  
Control Algorithm ◽  
Complex Structure ◽  
Tracking Error ◽  
Kinematic Model ◽  
Type Systems ◽  
Learning Control ◽  
Iterative Learning ◽  
Task Space ◽  
Modeling Errors

Precise task-space tracking with manipulator-type systems requires an accurate kinematic model. In contrast to traditional manipulators, sometimes it is difficult to obtain an accurate kinematic model of humanoid robots due to complex structure and link flexibility. Also, prolonged use of the robot will lead to some parts wearing out or being replaced with a slightly different alignment, thus throwing off the initial calibration. Therefore, there is a need to develop a control algorithm that can compensate for the modeling errors and quickly retune itself, if needed, taking into account the controller bandwidth limitations and high dimensionality of the system. In this paper, we develop an iterative learning control algorithm that can work with existing inverse kinematics solvers to refine the joint-level control commands to enable precise tracking in the task space. We demonstrate the efficacy of the algorithm on a theme-park-type humanoid doing a drawing task, serving drink in a glass, and serving a drink placed on a tray without spilling. The iterative learning control algorithm is able to reduce the tracking error by at least two orders of magnitude in less than 20 trials.

A Task-Level Iterative Learning Control Algorithm for Accurate Tracking in Manipulators With Modeling Errors and Stringent Joint Position Limits

2016 ◽  
Author(s):  
Pranav A. Bhounsule ◽  
Abhishek A. Bapat ◽  
Katsu Yamane
Keyword(s):  
Iterative Learning Control ◽  
Control Algorithm ◽  
Tracking Error ◽  
Learning Control ◽  
Iterative Learning ◽  
Joint Position ◽  
Task Space ◽  
Learning Gain ◽  
End Effector ◽  
Modeling Errors

We present an iterative learning control algorithm for accurate task space tracking of kinematically redundant robots with stringent joint position limits and kinematic modeling errors. The iterative learning control update rule is in the task space and consists of adding a correction to the desired end-effector pose based on the tracking error. The new desired end-effector pose is then fed to an inverse kinematics solver that uses the redundancy of the robot to compute feasible joint positions. We discuss the stability, the rate of convergence and the sensitivity to learning gain for our algorithm using quasi-static motion examples. The efficacy of the algorithm is demonstrated on a simulated four link manipulator with joint position limits that learns the modeling error to draw the figure eight in 4 trials.

Consensus Tracking by Iterative Learning Control for Linear Heterogeneous Multiagent Systems Based on Fractional-Power Error Signals

Algorithms ◽  
2019 ◽  
Vol 12 (9) ◽  
pp. 185 ◽  
Author(s):  
Yu-Juan Luo ◽  
Cheng-Lin Liu ◽  
Guang-Ye Liu
Keyword(s):  
Multiagent Systems ◽  
Iterative Learning Control ◽  
Tracking Error ◽  
Fractional Power ◽  
Learning Control ◽  
Convergence Condition ◽  
Iterative Learning ◽  
Reference Trajectory ◽  
Order Tracking ◽  
Consensus Tracking

This paper deals with the consensus tracking problem of heterogeneous linear multiagent systems under the repeatable operation environment, and adopts a proportional differential (PD)-type iterative learning control (ILC) algorithm based on the fractional-power tracking error. According to graph theory and operator theory, convergence condition is obtained for the systems under the interconnection topology that contains a spanning tree rooted at the reference trajectory named as the leader. Our algorithm based on fractional-power tracking error achieves a faster convergence rate than the usual PD-type ILC algorithm based on the integer-order tracking error. Simulation examples illustrate the correctness of our proposed algorithm.

An Algorithm of Iterative Learning Control Based on Vector Plots Analysis and its Robustness

2012 ◽  
Vol 557-559 ◽  
pp. 2065-2069
Author(s):  
Chang Liang Liu ◽  
Wan Gen Jia
Keyword(s):  
Iterative Learning Control ◽  
Control Algorithm ◽  
Learning Control ◽  
Iterative Learning ◽  
Slow Convergence ◽  
Angle Correction ◽  
Convergence Process ◽  
P Type ◽  
Relationship Of ◽  
The Relationship

Abstract: In order to solve the problem of slow convergence, an iterative learning control algorithm based on vector plots analysis is proposed. By introducing the geometric principle, that angle and side length of corresponding relationship in the same triangle, and transforming output’s error relationship into the relationship of the angel, the P-type is rewarded or penalized. The new algorithm with angle-correction speeds up significantly the convergence process. For illustration, a numerical simulation is utilized to show its efficiency and superiority. Empirical results show that the new algorithm is faster than P-type to make the system convergence .The method modifying P-type by angle is entirely feasible. The system’s output converges to the desired trajectory. The new algorithm can effectively solve the slow convergence problem. Introduction

Data Loss for Power Line Communication of Nonlinear Systems Iterative Learning Control

2014 ◽  
Vol 1048 ◽  
pp. 537-540
Author(s):  
Yin Jun Zhang
Keyword(s):  
Nonlinear Systems ◽  
Packet Loss ◽  
Iterative Learning Control ◽  
Control Algorithm ◽  
Learning Control ◽  
Power Line ◽  
Iterative Learning ◽  
Data Packet ◽  
Convergence Conditions ◽  
P Type

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.

Iterative Learning Control for a Class of Time-Delay Systems with Time-Varying Uncertainties

2013 ◽  
Vol 310 ◽  
pp. 428-434
Author(s):  
Ye Lei Zhao
Keyword(s):  
Time Delay ◽  
Iterative Learning Control ◽  
Control Algorithm ◽  
Tracking Error ◽  
Learning Control ◽  
Iterative Learning ◽  
Delay Systems ◽  
Time Varying ◽  
Adaptive Iterative Learning Control ◽  
Control Approach

An adaptive iterative learning control algorithm is proposed for a class of known time-delay nonlinear system with unknown time-varying parameter. A parameter separation technique is used to deal with time-delay problem. The control approach presented in this paper can guarantee that the tracking error converges to zero uniformly on the iteration interval as the iteration number approaches to infinity. A simulation example is provided to illustrate the efficiency of the proposed control algorithm.

scholarly journals A New Fuzzy Iterative Learning Control Algorithm for Single Joint Manipulator

2016 ◽  
Vol 26 (3) ◽  
pp. 297-310 ◽  
Author(s):  
Meng Wang ◽  
Guangrong Bian ◽  
Hongsheng Li
Keyword(s):  
Fuzzy Control ◽  
Iterative Learning Control ◽  
Control Algorithm ◽  
Tracking Error ◽  
Learning Control ◽  
Iterative Learning ◽  
Repetitive Tasks ◽  
Initial Control ◽  
Self Tuning ◽  
Tracking Trajectory

Abstract This paper present a new fuzzy iterative learning control design to solve the trajectory tracking problem and performing repetitive tasks for rigid robot manipulators. Several times’ iterations are needed to make the system tracking error converge, especially in the first iteration without experience. In order to solve that problem, fuzzy control and iterative learning control are combined, where fuzzy control is used to tracking trajectory at the first learning period, and the output of fuzzy control is recorded as the initial control inputs of ILC. The new algorithm also adopts gain self-tuning by fuzzy control, in order to improve the convergence rate. Simulations illustrate the effectiveness and convergence of the new algorithm and advantages compared to traditional method.

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