An Iterative Learning Control for Uncertain Systems Using Structured Singular Value

1999 ◽  
Vol 121 (4) ◽  
pp. 660-667 ◽  
Author(s):  
Tae-Yong Doh ◽  
Jung-Ho Moon ◽  
Myung Jin Chung
Keyword(s):  
Robust Stability ◽  
Iterative Learning Control ◽  
Design Method ◽  
Learning Control ◽  
Convergence Condition ◽  
Singular Value ◽  
Iterative Learning ◽  
Structured Singular Value ◽  
Plant Uncertainty ◽  
Uncertain Linear Systems

To deal with an iterative learning control (ILC) system with plant uncertainty, a set of new terms related with robust convergence is first defined. This paper proposes a sufficient condition for not only robust convergence but also robust stability of ILC for uncertain linear systems, including plant uncertainty. Thus, to find a new condition unrelated to the uncertainty, we first separate it into a known part and uncertainty one using linear fractional transformations (LFTs). Then, robust convergence and robust stability of an ILC system is determined by structured singular value (μ) of only the known part. Based on the novel condition, a learning controller and a feedback controller are developed at the same time to ensure robust convergence and robust stability of the ILC system under plant uncertainty. Lastly, the feasibility of the proposed convergence condition and design method are confirmed through computer simulation on an one-link flexible arm.

scholarly journals An Iterative Learning Control Design Method for Nonlinear Discrete-Time Systems with Unknown Iteration-Varying Parameters and Control Direction

2016 ◽  
Vol 2016 ◽  
pp. 1-7 ◽  
Author(s):  
Duo Zhao ◽  
Yong Yang
Keyword(s):  
Discrete Time ◽  
Iterative Learning Control ◽  
Design Method ◽  
Learning Control ◽  
Convergence Condition ◽  
Iterative Learning ◽  
Unknown Parameters ◽  
Varying Parameters ◽  
Control Direction ◽  
And Control

An iterative learning control (ILC) scheme is designed for a class of nonlinear discrete-time dynamical systems with unknown iteration-varying parameters and control direction. The iteration-varying parameters are described by a high-order internal model (HOIM) such that the unknown parameters in the current iteration are a linear combination of the counterparts in the previous certain iterations. Under the framework of ILC, the learning convergence condition is derived through rigorous analysis. It is shown that the adaptive ILC law can achieve perfect tracking of system state in presence of iteration-varying parameters and unknown control direction. The effectiveness of the proposed control scheme is verified by simulations.

A Two-Step Optimization-Based Iterative Learning Control for Quadrotor Unmanned Aerial Vehicles

2021 ◽  
Vol 143 (7) ◽  
Author(s):  
Revant Adlakha ◽  
Minghui Zheng
Keyword(s):  
Unmanned Aerial Vehicles ◽  
Design Problem ◽  
Iterative Learning Control ◽  
Design Method ◽  
Learning Control ◽  
Iterative Learning ◽  
Learning Performance ◽  
Aerial Vehicles ◽  
Quadrotor Unmanned Aerial Vehicles ◽  
Optimization Based Design

Abstract This paper presents a two-step optimization-based design method for iterative learning control and applies it onto the quadrotor unmanned aerial vehicles (UAVs) trajectory tracking problem. Iterative learning control aims to improve the tracking performance through learning from errors over iterations in repetitively operated systems. The tracking errors from previous iterations are injected into a learning filter and a robust filter to generate the learning signal. The design of the two filters usually involves nontrivial tuning work. This paper presents a new two-optimization design method for the iterative learning control, which is easy to obtain and implement. In particular, the learning filter design problem is transferred into a feedback controller design problem for a purposely constructed system, which is solved based on H-infinity optimal control theory thereafter. The robust filter is then obtained by solving an additional optimization to guarantee the learning convergence. Through the proposed design method, the learning performance is optimized and the system's stability is guaranteed. The proposed two-step optimization-based design method and the regarding iterative learning control algorithm are validated by both numerical and experimental studies.

scholarly journals Iterative learning control with applications in energy generation, lasers and health care

2016 ◽  
Vol 472 (2193) ◽  
pp. 20150569 ◽  
Author(s):  
E. Rogers ◽  
O. R. Tutty
Keyword(s):  
Health Care ◽  
Iterative Learning Control ◽  
Design Method ◽  
Learning Control ◽  
Iterative Learning ◽  
Free Electron Lasers ◽  
Time Duration ◽  
Physical Systems ◽  
Mode Of Operation ◽  
Duration Task

Many physical systems make repeated executions of the same finite time duration task. One example is a robot in a factory or warehouse whose task is to collect an object in sequence from a location, transfer it over a finite duration, place it at a specified location or on a moving conveyor and then return for the next one and so on. Iterative learning control was especially developed for systems with this mode of operation and this paper gives an overview of this control design method using relatively recent relevant applications in wind turbines, free-electron lasers and health care, as exemplars to demonstrate its applicability.

Pseudo-Inverse Based Iterative Learning Control for Linear Nonminimum Phase Plants with Unmodeled Dynamics*

2004 ◽  
Vol 126 (3) ◽  
pp. 661-665 ◽  
Author(s):  
Jayati Ghosh ◽  
Brad Paden
Keyword(s):  
Iterative Learning Control ◽  
Low Frequency ◽  
Learning Control ◽  
Iterative Learning ◽  
Nonminimum Phase ◽  
Low Pass ◽  
Frequency Components ◽  
Iteration Loop ◽  
Plant Uncertainty ◽  
Pseudo Inverse

Learning control is a very effective approach for tracking repetitive processes. In this paper, the stable-inversion based learning controller as presented in (Ghosh, J. and Paden, B., 1999, “Iterative Learning Control for Nonlinear Nonminimum Phase Plants with Input Disturbances,” in Proc. of American Control Conference; Ghosh, J. and Paden, B., 1999, “A pseudo-inverse based Iterative Learning Control for Nonlinear Plants with Disturbances,” in Proc. of 38th Conference on Decision and Control.) is modified to accommodate linear nonminimum phase plants with uncertainties. The design of the learning controller is based on the computation of an approximate inverse of the nominal model of the linear plant, rather than its exact inverse. The advantages of this approach are that the output of the plant need not be differentiated and also the plant model need not be exact. A low pass zero-phase filter is used in the iteration loop to achieve robustness to plant uncertainty. The structure of the controller is such that the low frequency components of the trajectory converge faster than the high frequency components.

Iterative Learning Control for Hybrid Systems

2020 ◽  
Author(s):  
Kirti D. Mishra ◽  
K. Srinivasan
Keyword(s):  
Hybrid Systems ◽  
Iterative Learning Control ◽  
Design Method ◽  
Tracking Error ◽  
Control Design ◽  
Learning Control ◽  
Iterative Learning ◽  
Linear Matrix ◽  
Triangular Structure ◽  
Form Representation

Abstract Iterative learning control (ILC) has been growing in applicability, along with growth in theory for classes of linear and nonlinear systems, and this study extends the theory of ILC to hybrid systems. A lifted form representation of hybrid systems with input-output dependent switching rules is developed, and the proposed lifted form representation is modeled as a switched system with arbitrary/unconstrained switching rules in the trial domain for control design. The causality of hybrid systems in the time domain results in the (lower) triangular structure of switched systems in the trial domain, the triangular structure enabling systematic and efficient control design. A unique aspect of the control design method developed for ILC of hybrid systems in this study is that a solution to the required set of linear matrix inequalities (LMIs) is guaranteed to exist under mild assumptions, which is in contrast to many other studies proposing LMI based solutions in controls literature. The proposed method is validated numerically for a motion control application, and robust and monotonic convergence of the tracking error to zero is demonstrated.

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