"How to shape robustly the control loop: look into stability margins and uncertainties"
Prof. Michael Ruderman,
University of Agder, Norway
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"Abstract
The design of feedback control today benefits simultaneously from different paradigms when considering dynamic systems (plants and controllers) in terms of the mathematical structure, parameters and states, and (perhaps most important for the applications) in formulating stability and performance criteria for an appropriate operation. Apart from the well-established and widely used state-space methodologies, e.g. [1], energy shaping and power-port system concepts, e.g. [2,3], Lyapunov based analysis and design, e.g. [4,5], the signal-processing viewpoint with the corresponding norms and transfer functions, e.g. [6], remains still one of the most common control design techniques. Having the roots and origins in electrical circuits, this signal processing perspective enjoys a wide acceptance in engineering practice, cf. e.g. [7], and is often interpreted as analysis and design in frequency domain, with use of Fourier transformation and frequency response functions. Control loop shaping and the so-called sensitivity functions play here one of the most important roles for robustness and performance when designing feedback controllers for a given (nominal) input-output system representation. This seminar talk is dedicated to the loop shaping with aspects of robustness in view of system uncertainties, and even varying structures in the interaction of a system plant with its environment. First, some basic loop shaping criteria and formalisms will be recalled. Then, an illustrative case study of a reshaped motion- and impedance-control will be shown along with experimental results for a robust and stable contact transition in unforeseen and contact-critical environmental conditions.
Literature
[1] Kailath, Thomas. Linear systems. Prentice-hall, 1980
[2] Willems, Jan. Paradigms and puzzles in the theory of dynamical systems. IEEE Transactions on automatic control, 1991
[3] Ortega, Romeo, et al. Putting energy back in control. IEEE Control systems magazine, 2001
[4] Hahn, Wolfgang. Stability of Motion. Springer, 1967
[5] Freeman, Randy and Kokotovic, Petar. Robust nonlinear control design: state-space and Lyapunov techniques. Birkhäuser Boston, 1996
[6] Doyle, John, et al. Feedback control theory. Dover publications, 1992
[7] Åström, Karl and Murray, Richard. Feedback systems: an introduction for scientists and engineers. Princeton university press, 2021
Dec 5, 2024, 1.30pm, Seminar Room, Building 3, 1st Floor,
Via Claudio, DIETI Department, Università di Napoli Federico II