State Observer-Based Iterative Learning Control of an Uncertain Continuous-Time System
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BUST, ADAPTIVE, AND NETWORK CONTROL
State Observer-Based Iterative Learning Control of an Uncertain Continuous-Time System J. P. Emelianova Arzamas Polytechnic Institute of R.E. Alekseev Nizhny Novgorod State Technical University, Arzamas, Russia e-mail: [email protected] Received November 27, 2019 Revised February 11, 2020 Accepted March 4, 2020
Abstract—Linear systems with the affine model of parametric uncertainty that operate in a repetitive mode are considered. For such systems, a new iterative learning control design method is proposed. This method is based on the use of a full-order state observer and an auxiliary 2D model in the form of a differential repetitive process whose stability guarantees the convergence of the learning process. For obtaining stability conditions, the divergent method of vector Lyapunov functions is used. An example illustrating the features and advantages of the new iterative learning control design method is presented. Keywords: iterative learning control, observer, 2D systems, stability, vector Lyapunov function, differential repetitive processes DOI: 10.1134/S000511792007005X
1. INTRODUCTION Feedback control is the most effective way to achieve important system properties such as stability, robustness, optimality in the sense of a given criterion, etc. In practice, there are many systems operating in a repetitive mode with the same length of each repetition (also called iteration, trial or pass), during which systems must track a reference signal with a required accuracy. When using feedback control, the tracking error will be the same regardless of the number of passes. Due to this fact, new solutions are needed for reducing the tracking error as the number of passes increases. Iterative learning control is one possible solution for this class of systems, which is organized in such a way as to successively reduce the tracking (learning) error in repeated operations. The iterative learning control problem is to find an appropriate control signal enabling the output variable to track a desired trajectory (pass profile) on a finite time interval by the iterative refinement of this signal. This type of control uses information about the error, information from the previous passes, and some preliminary information about the system to construct an input signal that will guarantee the convergence of the learning error to zero as the number of passes increases. Unlike adaptive control, the system parameters here remain unchanged. The surveys [1, 2] can be one starting point for the literature. Iterative learning control has been successfully used in numerous applications, from medical robots for stroke rehabilitation [3, 4] and ventricular assist devices [5] to laser metal deposition processes [6], marine vibrators [7], and manufacturing systems [8]. 1230
STATE OBSERVER-BASED ITERATIVE LEARNING CONTROL
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Since the pioneering publication [9], it has been noted that iterative learning control is adequately modeled by a two-dimensional (2D) system. Really, on the one hand, iterativ
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