This monograph studies the design of robust, monotonically-convergent it- ative learning controllers for discrete-time systems. Iterative learning control (ILC) is well-recognized as an e?cient method that o?ers signi?cant p- formance improvement for systems that operate in an iterative or repetitive fashion (e. g. , robot arms in manufacturing or batch processes in an industrial setting). Though the fundamentals of ILC design have been well-addressed in the literature, two key problems have been the subject of continuing - search activity. First, many ILC design strategies assume nominal knowledge of the system to be controlled. Only recently has a comprehensive approach to robust ILC analysis and design been established to handle the situation where the plant model is uncertain. Second, it is well-known that many ILC algorithms do not produce monotonic convergence, though in applications monotonic convergencecan be essential. This monograph addresses these two keyproblems by providingauni?ed analysisanddesignframeworkforrobust, monotonically-convergent ILC. The particular approach used throughout is to consider ILC design in the iteration domain, rather than in the time domain. Using a lifting technique, the two-dimensionalILC system, whichhas dynamics in both the time and - erationdomains,istransformedintoaone-dimensionalsystem,withdynamics only in the iteration domain. The so-called super-vector framework resulting from this transformation is used to analyze both robustness and monotonic convergence for typical uncertainty models, including parametric interval - certainties, frequency-like uncertainty in the iteration domain, and iterati- domain stochastic uncertainty.
Shows the reader how to use robust iterative learning control in the face of model uncertainty
Helps to improve the performance of repetitive electromechanical tasks, widespread in industry
Provides a rounded and self-contained approach to the subject of iterative learning control not available elsewhere
This monograph studies the design of robust, monotonically-convergent iterative learning controllers for discrete-time systems. Two key problems with the fundamentals of iterative learning control (ILC) design as treated by existing work are: first, many ILC design strategies assume nominal knowledge of the system to be controlled and; second, it is well-known that many ILC algorithms do not produce monotonic convergence, though in applications monotonic convergence is often essential.
Iterative Learning Control takes account of the recently-developed comprehensive approach to robust ILC analysis and design established to handle the situation where the plant model is uncertain. Considering ILC in the iteration domain, it presents a unified analysis and design framework that enables designers to consider both robustness and monotonic convergence for typical uncertainty models, including parametric interval uncertainties, iteration-domain frequency uncertainty, and iteration-domain stochastic uncertainty. Topics include:
• Use of a lifting technique to convert the two-dimensional ILC system, which has dynamics in both the time and iteration domains, into the supervector framework, which yields a one-dimensional system, with dynamics only in the iteration domain.
• Development of iteration-domain uncertainty models in the supervector framework.
• ILC design for monotonic convergence when the plant is subject to parametric interval uncertainty in its Markov matrix.
• An algebraic H-infinity design methodology for ILC design when the plant is subject to iteration-domain frequency uncertainty.
• Development of Kalman-filter-based ILC algorithms when the plant is subject to iteration-domain stochastic uncertainties.
• Analytical determination of the base-line error of ILC algorithms.
• Solutions to three fundamental robust interval computational problems (used as basic tools for designing robust ILC controllers): finding the maximum singular value of an interval matrix, determining the robust stability of interval polynomial matrix, and obtaining the power of an interval matrix.
Iterative Learning Control will be of great interest to academic researchers in control theory and to industrial control engineers working in robotics-oriented manufacturing and batch-processing-based industries. Graduate students of intelligent control will also find this volume instructive.
Iterative Learning Control Overview.- An Overview of the ILC Literature.- The Super-vector Approach.- Robust Interval Iterative Learning Control.- Robust Interval Iterative Learning Control: Analysis.- Schur Stability Radius of Interval Iterative Learning Control.- Iterative Learning Control Design Based on Interval Model Conversion.- Iteration-domain Robustness.- Robust Iterative Learning Control: H? Approach.- Robust Iterative Learning Control: Stochastic Approaches.- Conclusions.