Iterative Learning Control Algorithms and Experimental Benchmarking (eBook)

Eric Rogers, Bing Chu, Christopher Freeman, Paul Lewin (Autoren)

eBook Download: EPUB

2023
John Wiley & Sons (Verlag)
978-1-118-53537-0 (ISBN)

Infos

Iterative Learning CONTROL ALGORITHMS AND EXPERIMENTAL BENCHMARKING

Iterative Learning Control Algorithms and Experimental Benchmarking

Presents key cutting edge research into the use of iterative learning control

The book discusses the main methods of iterative learning control (ILC) and its interactions, as well as comparator performance that is so crucial to the end user. The book provides integrated coverage of the major approaches to-date in terms of basic systems, theoretic properties, design algorithms, and experimentally measured performance, as well as the links with repetitive control and other related areas.

Key features:

• Provides comprehensive coverage of the main approaches to ILC and their relative advantages and disadvantages.
• Presents the leading research in the field along with experimental benchmarking results.
• Demonstrates how this approach can extend out from engineering to other areas and, in particular, new research into its use in healthcare systems/rehabilitation robotics.

The book is essential reading for researchers and graduate students in iterative learning control, repetitive control and, more generally, control systems theory and its applications.

Professor Eric Rogers, Dr. Bing Chu, Professor Christopher Freeman, and Professor Paul Lewin, University of Southampton, UK

Textauszug

1
Iterative Learning Control: Origins and General Overview

A commonly encountered requirement in some industries is for a machine to repeat the same finite duration operation over and over again. The exact sequence is that the procedure is completed and then the system or process involved resets to the starting location and the next one begins. A typical scenario is a gantry robot, such as the one shown in Figure 1.1, undertaking a “pick and place” operation encountered in many industries where the following steps must be conducted in synchronization with a conveyor system: (i) collect an object from a fixed location, (ii) transfer it over a finite duration, (iii) place it on the moving conveyor, (iv) return to the original location for the next object and then, (v) repeat the previous four steps for as many objects as required or can be transferred before it is necessary to stop for maintenance or other reasons. Stopping these robots for such reasons in high-throughput applications means down time and lost production.

Figure 1.2 shows a 3D reference trajectory for the gantry robot and Figure 1.3 its -axis component. On each execution a variable, say is defined over the finite duration taken to move from the pick to place locations, e.g. , but it is also required to distinguish variables according to which execution is under consideration. One option, used except where stated otherwise in this book, is to write where is a nonnegative integer termed the trial number with denoting the trial duration or length.

Let be a prespecified 3D path or trajectory that the robot is required to follow between the “pick” and “place” locations (and back to the “pick” location), such as Figure 1.2 or, to focus on one axis, Figure 1.3. Then on trial , the error is and if the question is: how should the control input signal be adjusted to reduce or remove this error?

In applications such as the one considered, the system is performing the same operation repeatedly under the same operating conditions. One approach to control design is to copy human behavior and aim to learn from experience, i.e. the errors generated on previous trials are rich in information. This information is not exploited by a standard controller that would produce the same error on each trial. Iterative learning control (ILC) aims to improve performance by using information from previous trials to update the control law to be applied on the next one. As the above example illustrates, a significant application area for ILC is robotics.

As with other areas within control systems, there has been a debate, see the next section, on the origins of ILC. Since the 1980s, when concentrated research began, applications for ILC have spread beyond robotics in the industrial domain and outside engineering into healthcare. An example from the latter area, in the form of robotic-assisted upper-limb stroke rehabilitation, is introduced in Section 2.4 and considered in depth in Sections 4.2, 10.2, 10.3, and 11.4 of this book.

Figure 1.1 A gantry robot for a pick-and-place operation with the axes marked.

Figure 1.2 D reference trajectory for the gantry robot.

1.1 The Origins of ILC

According to [2, 33] and others, the basic idea of ILC was first proposed in a 1971 patent [89] and the journal article [256] published in Japanese. The first concerted volume of work that initiated widespread interest was, in particular, the journal paper [12], which considers a simple first-order linear servomechanism system for speed control of a voltage-controlled DC-servomotor. In this section, this system is used to highlight the essence of ILC, and it is appropriate to start by quoting parts of the opening two paragraphs in this paper.

Figure 1.3 -axis component of the gantry robot reference trajectory.

“It is human to make mistakes, but it also human to learn from such experience. Athletes have improved their form of body motion by learning through repeated training and skilled hands have mastered the operation of machines or plants by acquiring skill in practice and gaining knowledge. Is it possible to think of a way to implement such a learning ability in the automatic operation of dynamic systems?”

Motivated by this consideration, Arimoto et al. [12] proposed “a practical approach to the problem of bettering the present operation of mechanical robots by using the data of previous operations.” This work constructed an “iterative betterment process for the dynamics of robots so that the trajectory of their motion approaches asymptotically a given desired trajectory as the number of operation trials increases.” The example in [12] is next used to illustrate the construction of ILC laws and the behavior that can arise. A critical feature is “the direct use of the underlying dynamics of the objective systems.”

The form of the control law developed in [12] applies to systems that are required to track a desired reference trajectory of a fixed length and specified a priori. After each trial, resetting of the system states occurs, during which time the measured output is used in the construction of the control input for application on the next trial. In [12], the system dynamics were assumed trial-invariant and invertible. These six distinguishing features of ILC highlighted in bold provided the basis for a major area of research in the control systems community internationally, both in terms of theory and an ever-broadening list of applications, many with supporting experimental verification or actual implementation.

As a motivating example, Arimoto et al. [12] considered speed control of a voltage-controlled DC servomotor where if the armature inductance is sufficiently small and mechanical friction is ignored, the resulting controlled dynamics are described by

(1.1)

where denotes the angular velocity of the motor, is the input voltage, and and are constants.

Suppose that a reference signal, or trajectory, , for the angular velocity is given over the fixed finite duration and also that the system dynamics are unknown in the sense that the exact values of and in (1.1) may not be available. Also, it is assumed that is continuously differentiable, which is a commonly used assumption in differential ILC design.

The design problem is to construct an input voltage that coincides with over If an arbitrary input is applied, the error between the desired output and the first response is

(1.2)

where

(1.3)

Also, construct the voltage

(1.4)

and apply this as the input on the next trial. Storing the resulting error constructing , and continuing this sequence of operations give on trial

(1.5)

Suppose that for all Then since is continuously differentiable and using (1.5) gives

(1.6)

Hence,

(1.7)

where

Supporting simulation studies are in [12]. Since this first work, various definitions of ILC have been given in the literature, including the following quoted in [2]:

1. The learning control concept stands for the repeatability of operating a given objective system and the possibility of improving the control input on the basis of previous actual operation data [12].
2. It is a recursive online control method that relies on less calculation and less a priori knowledge about the system dynamics. The idea is to apply a simple algorithm repetitively to an unknown system, until perfect tracking is achieved [26].
3. ILC is an approach to improve the transient response of the system that operates repetitively over a fixed time interval [166].
4. ILC considers systems that repetitively perform the same task with a view to sequentially improving accuracy [4].
5. ILC is to utilize the system repetitions as an experience to improve the system control performance even under incomplete knowledge of the system to be controlled [50].
6. The controller learns to produce zero-tracking error during repetitions of a command or learns to eliminate the effects of a repeating disturbance on a control system [210].
7. The main idea behind ILC is to iteratively find an input sequence such that the output of the system is as close as possible to a desired output. Although ILC is directly associated with control, it is important to note that the end result is that the system has been inverted.
8. We learned that ILC is about enhancing a system's performance by means of repetition, but we did not learn how it is done. This brings us to the core activity in ILC research, which is the construction and subsequent analysis of algorithms [266].

Each of these definitions has their focus, but the underlying question is the same: how to improve performance using information from previous trials to update the control law applied on the current one? In some applications, ILC will form only one possible way of designing the controller...

Produkt-Details

• Erscheint lt. Verlag: 12.1.2023
• Sprache: englisch
• Themenwelt: Technik ► Maschinenbau
• Schlagworte: biomedical engineering • Biomedizintechnik • Control Process & Measurements • Control Systems Technology • Electrical & Electronics Engineering • Elektrotechnik u. Elektronik • Iteration • Maschinenbau • mechanical engineering • Mess- u. Regeltechnik • Regelungstechnik • Rehabilitation Engineering & Prosthetics • Reha-Technik u. Prothesen
• ISBN-10: 1-118-53537-5 / 1118535375
• ISBN-13: 978-1-118-53537-0 / 9781118535370