scholarly journals New Iterative Learning Control Algorithm Using Learning Gain Based on σ Inversion for Nonsquare Multi-Input Multi-Output Systems

2018 ◽  
Vol 2018 ◽  
pp. 1-9 ◽  
Author(s):  
Leila Noueili ◽  
Wassila Chagra ◽  
Moufida Ksouri
Keyword(s):  
Iterative Learning Control ◽  
Mimo Systems ◽  
Linear Time ◽  
Tracking Error ◽  
Learning Control ◽  
Convergence Condition ◽  
Iterative Learning ◽  
Learning Gain ◽  
Model Inversion ◽  
Direct Model

Model inversion Iterative Learning Control (ILC) for a class of nonsquare linear time variant/invariant multi-input multi-output (MIMO) systems is considered in this paper. A new ILC algorithm is developed based on σ-right inversion of nonsquare learning gain matrices to resolve the matrix inversion problems appeared in the direct model inversion of nonsquare MIMO systems. Furthermore, a sufficient and necessary monotonic convergence condition is established. With rigorous analysis, the proposed ILC scheme guarantees the convergence of the tracking error. To prove the effectiveness and to illustrate the performance of the proposed approach for linear time-invariant (LTI) and time-varying nonsquare systems, two illustrative examples are simulated.

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.

scholarly journals A Design of Parameter Optimal Iterative Learning Control for Linear Discrete-Time Systems

2014 ◽  
Vol 2014 ◽  
pp. 1-6 ◽  
Author(s):  
Wataru Kase
Keyword(s):  
Iterative Learning Control ◽  
Tracking Error ◽  
Learning Control ◽  
Iterative Learning ◽  
Learning Gain ◽  
Quadratic Cost ◽  
Discrete Time Systems ◽  
Monotonic Convergence ◽  
Time Systems ◽  
Quadratic Cost Function

The iterative learning control algorithm proposed by Owens and Feng, which guarantees the monotonic convergence of the tracking error norms along with the trial, will be modified. The learning gain of the proposed method will be determined through a quadratic cost function. MIMO plant case will be also discussed. Numerical simulations will be presented to confirm the validity of the proposed design.

Iterative Learning Identification/Iterative Learning Control for Linear Time-Varying Systems

2016 ◽  
Vol 138 (10) ◽  
Author(s):  
Nanjun Liu ◽  
Andrew Alleyne
Keyword(s):  
Iterative Learning Control ◽  
Linear Time ◽  
Tracking Error ◽  
Learning Control ◽  
Iterative Learning ◽  
Parameter Estimates ◽  
Time Varying ◽  
Fixed Parameter ◽  
Time Varying Systems ◽  
And Control

This paper integrates a previously developed iterative learning identification (ILI) (Liu, N., and Alleyne, A. G., 2016, “Iterative Learning Identification for Linear Time-Varying Systems,” IEEE Trans. Control Syst. Technol., 24(1), pp. 310–317) and iterative learning control (ILC) algorithms (Bristow, D. A., Tharayil, M., and Alleyne, A. G., 2006, “A Survey of Iterative Learning Control,” IEEE Control Syst. Mag., 26(3), pp. 96–114), into a single norm-optimal framework. Similar to the classical separation principle in linear systems, this work provides conditions under which the identification and control can be combined and guaranteed to converge. The algorithm is applicable to a class of linear time-varying (LTV) systems with parameters that vary rapidly and analysis provides a sufficient condition for algorithm convergence. The benefit of the integrated ILI/ILC algorithm is a faster tracking error convergence in the iteration domain when compared with an ILC using fixed parameter estimates. A simple example is introduced to illustrate the primary benefits. Simulations and experiments are consistent and demonstrate the convergence speed benefit.

scholarly journals Data-Driven Networked Optimal Iterative Learning Control for Discrete Linear Time-Varying Systems with One-Operation Bernoulli-Type Communication Delays

2017 ◽  
Vol 2017 ◽  
pp. 1-12 ◽  
Author(s):  
Yan Geng ◽  
Xiaoe Ruan ◽  
Hyo-Sung Ahn
Keyword(s):  
Iterative Learning Control ◽  
Linear Time ◽  
Tracking Error ◽  
Learning Control ◽  
Iterative Learning ◽  
Data Driven ◽  
Time Varying ◽  
Communication Delays ◽  
System Matrix ◽  
Time Varying Systems

This paper develops a type of data-driven networked optimal iterative learning control strategy for a class of discrete linear time-varying systems with one-operation Bernoulli-type communication delays. In terms of the stochastic Bernoulli-type one-operation communication delayed inputs and outputs, the previous-iteration synchronous compensations are adopted. By means of deriving gradients of two types of objective functions that express the optimal approximation of the system matrix and the minimal tracking error, the strategy approximates the system matrix and upgrades the control inputs in an interact mode as the iteration evolves. By taking advantage of matrix theory and statistical technique, it is derived that the approximation discrepancy of the system matrix is bounded and the mathematical expectation of the tracking error vanishes as the iteration goes on. Numerical simulations manifest the validity and effectiveness.

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.

Design and Convergence of a Time-Varying Iterative Learning Control Law

2004 ◽  
Author(s):  
Marina Tharayil ◽  
Andrew Alleyne
Keyword(s):  
Frequency Domain ◽  
Iterative Learning Control ◽  
Linear Time ◽  
Learning Control ◽  
Convergence Condition ◽  
Iterative Learning ◽  
Control Law ◽  
Equivalent Condition ◽  
Time Varying ◽  
Linear Time Invariant

This paper presents a novel linear time-varying (LTV) iterative learning control law that can provide additional performance while maintaining the robustness and convergence properties comparable to those obtained using traditional frequency domain design techniques. Design aspects of causal and non-causal linear time-invariant (LTI), along with the proposed LTV, ILC update laws are discussed and demonstrated using a simplified example. Asymptotic as well as monotonic convergence, robustness and performance characteristics of such systems are considered, and an equivalent condition to the frequency domain convergence condition is presented for the time-varying ILC. Lastly the ILC algorithm developed here is implemented on a Microscale Robotic Deposition system to provide experimental verification.

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.

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