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On inherent limitations in robustness and performance for a class of prescribed-time algorithms

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arXiv 2022年

作者： Aldana-López, Rodrigo Seeber, Richard Haimovich, Hernan Gómez-Gutiérrez, David Zaragoza Spain Graz University of Technology Institute of Automation and Control Christian Doppler Laboratory for Model Based Control of Complex Test Bed Systems Graz Austria CONICET-UNR Rosario2000 Argentina Intel Tecnología de México Intel Labs Intelligent Systems Research Lab Jalisco Mexico Tecnológico Nacional de México Instituto Tecnológico José Mario Molina Pasquel y Henríquez Unidad Académica Zapopan Jalisco Mexico

Prescribed-time algorithms based on time-varying gains may have remarkable properties, such as regulation in a user-prescribed finite time that is the same for every nonzero initial condition and that holds even under matched disturbances. However, at the same time, such algorithms are known to lack robustness to measurement noise. This note shows that the lack of robustness of a class of prescribed-time algorithms is of an extreme form. Specifically, we show the existence of arbitrarily small measurement noises causing considerable deviations, divergence, and other detrimental consequences. We also discuss some drawbacks and trade-offs of existing workarounds as motivation for further analysis. © 2022, CC BY-NC-ND.

关键词： Economic and social effects

Lyapunov-based observer design for steam boilers

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IFAC-PapersOnLine 2020年第2期53卷 5915-5921页

作者： Stefan L. Hölzl Richard Seeber Markus Tranninger Robert Bauer Martin Horn Christian Doppler Laboratory for Model Based Control of Complex Test Bed Systems Institute of Automation and Control GrazUniversity of Technology Graz Austria. Institute of Automation and Control Graz University of TechnologyGraz Austria. Kristl Seibt & Co GmbH Graz Austria

Steam boilers are widely used in industrial applications ranging from air conditioning to power plants. Advanced control schemes for such boilers require the knowledge of internal state variables, which are not always measurable. This paper proposes a new observer for steam boilers whose construction builds on a special state variable choice and a Lyapunov-based design of the observer gains. Tuning insight is gained from an oscillator-like structure of the (linearised) observer error dynamics. Comparisons to an extended Kalman filter in simulations and on experimental data from a small-scale automotive application demonstrate the performance of the proposed approach.

关键词： Non-linear observer design Lyapunov methods time-varying systems water level estimation air conditioning automotive test beds fuel cell test beds

Finite-horizon linear quadratic control for networked control systems with non-distributed plants

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arXiv 2020年

作者： Palmisano, Marijan Steinberger, Martin Horn, Martin The Institute of Automation and Control Graz University of Technology Graz Austria The Christian Doppler Laboratory for Model Based Control of Complex Test Bed Systems Institute of Automation and Control Graz University of Technology Graz Austria

An optimal control law for networked control systems with a discrete-time linear time-invariant (LTI) system as plant and networks between sensor and controller as well as between controller and actuator is proposed. This controller is designed by solving an optimization problem that is a generalization of the optimization problem used to obtain the Linear Quadratic Regulator (LQR) for deterministic discrete-time LTI systems. The networks are represented by random delays and drop outs of transmitted data packets. Copyright © 2020, The Authors. All rights reserved.

关键词： Networked control systems

Uniform detectability of linear time varying systems with exponential dichotomy

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arXiv 2020年

作者： Tranninger, Markus Seeber, Richard Steinberger, Martin Horn, Martin Institute of Automation and Control Graz University of Technology Graz8010 Austria Christian Doppler Laboratory for Model Based Control of Complex Test Bed Systems Institute of Automation and Control Graz University of Technology Graz Austria

Exponential dichotomies play a central role in stability theory for dynamical systems. They allow to split the state space into two subspaces, where all trajectories in one subspace decay whereas all trajectories in the other subspace grow, uniformly and exponentially. This paper studies uniform detectability and observability notions for linear time varying systems, which admit an exponential dichotomy. The main contributions are necessary and sufficient detectability conditions for this class of systems. Copyright © 2020, The Authors. All rights reserved.

关键词： Dynamical systems

Designing controllers with predefined convergence-time bound using bounded time-varying gains

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arXiv 2023年

作者： Aldana-López, Rodrigo Seeber, Richard Haimovich, Hernan Gómez-Gutiérrez, David María de Luna s/n Zaragoza50018 Spain Graz University of Technology Christian Doppler Laboratory for Model Based Control of Complex Test Bed Systems Institute of Automation and Control Graz Austria CONICET-UNR Rosario2000 Argentina Intel Corporation Intel Labs Av. del Bosque 1001 Jalisco Zapopan45019 Mexico Tecnológico Nacional de México Instituto Tecnológico José Mario Molina Pasquel y Henríquez Unidad Académica Zapopan Cam. Arenero 1101 Jalisco Zapopan45019 Mexico

Recently, there has been a great deal of attention in a class of controllers based on time-varying gains, called prescribed-time controllers, that steer the system's state to the origin in the desired time, a priori set by the user, regardless of the initial condition. Furthermore, such a class of controllers has been shown to maintain a prescribed-time convergence in the presence of disturbances even if the disturbance bound is unknown. However, such properties require a time-varying gain that becomes singular at the terminal time, which limits its application to scenarios under quantization or measurement noise. This chapter presents a methodology to design a broader class of controllers, called predefined-time controllers, with a prescribed convergence-time bound. Our approach allows designing robust predefined-time controllers based on time-varying gains while maintaining uniformly bounded time-varying gains. We analyze the condition for uniform Lyapunov stability under the proposed time-varying controllers. © 2023, CC BY-NC-ND.

关键词： controllers

Performance Preserving Integral Extension of Linear and Homogeneous State-Feedback controllers

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IFAC-PapersOnLine 2020年第2期53卷 5129-5134页

作者： Richard Seeber Jaime A. Moreno Christian Doppler Laboratory for Model Based Control of Complex Test Bed Systems Institute of Automation and Control Graz University of Technology Graz Austria Instituto de Ingeneria Universidad Nacional Autónoma de MéxicoMexico City Mexico

The problem of extending an existing state-feedback controller by an integrator is considered. A structural insight into the design of such controllers is presented for the linear case, which allows to preserve the performance of the given controller in a certain sense. Using this insight, a second order homogeneous state feedback controller with discontinuous integral action is proposed, which can reject arbitrary slope bounded, i.e., Lipschitz continuous, perturbations. By means of Lyapunov methods, stability conditions for the closed loop system and a bound for its finite convergence time are derived. Numerical simulations illustrate the results and provide further insight into the tuning of the proposed approach.

关键词： state-feedback weighted homogeneity integral control finite-time convergence

Model-based Temperature control of a Continuous Flow Heater for Efficient Processing of Silicon Wafers

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Model-based Temperature Control of a Continuous Flow Heater ...

control Technology and Applications (CCTA),

作者： Martin Kleindienst Stefan Koch Markus Reichhartinger Lam Research AG Villach Austria The Christian Doppler Laboratory for Model Based Control of Complex Test Bed Systems Institute of Automation and Control Graz University of Technology Graz Austria The Institute of Automation and Control Graz University of Technology Graz Austria

ISBN: (数字)9781728171401

ISBN: (纸本)9781728171418

This paper proposes a model-based control approach for a liquid flow heater operated within silicon wafer processing tools used in the semiconductor industry. A distributed-parameter model is presented to describe the thermal dynamic behavior of the heater. Adopting the early-lumping approach, an observer-based controller is designed. This controller ensures a vanishing steady-state error in the case of constant input signals and disturbances. The implemented feedback loop relies on an observer-based anti-windup technique. Real-world tests demonstrate the effectiveness and feasibility of the proposed approach.

关键词： Heating systems Liquids Mathematical model Temperature measurement Metals Heat transfer

Strong detectability and observers for linear time varying systems

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arXiv 2021年

作者： Tranninger, Markus Seeber, Richard Rueda-Escobedo, Juan G. Horn, Martin Institute of Automation and Control Graz University of Technology Inffeldgasse 21B/II Graz8010 Austria Christian Doppler Laboratory for Model Based Control of Complex Test Bed Systems Institute of Automation and Control Graz University of Technology Inffeldgasse 21B/II Graz8010 Austria Fachgebiet Regelungssysteme und Netzleittechnik Brandenburgische Technische Universität Cottbus - Senftenberg Siemens-Halske-Ring 14 Cottbus03046 Germany

This work presents a notion of strong detectability for linear time varying systems affected by unknown inputs. It is shown that this notion is equivalent to detectability of an auxiliary system without unknown inputs. This allows a straightforward observer design for dependable state estimation in the presence of unknown inputs. The design reduces to a deterministic Kalman filter design problem, where the observer gains can be obtained from the solution of a differential Riccati equation. The efficacy of the proposed approach is demonstrated by means of a numerical example. Copyright © 2021, The Authors. All rights reserved.

关键词： Riccati equations

Discrete-Time Super Twisting controller for Networked control systems

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IFAC-PapersOnLine 2019年第16期52卷 789-794页

作者： Jakob Ludwiger Markus Reichhartinger Martin Steinberger Martin Horn Institute of Automation and Control Graz University of Technology Graz Austria Christian Doppler Laboratory for Model Based Control of Complex Test Bed Systems Institute of Automation and Control Graz University of Technology Graz Austria

In this paper, a sliding mode based control concept for networked control systems in the presence of variable time delays and external perturbations is proposed. The control concept consists of a buffering mechanism and a discrete time integral sliding mode based control law. This setting offers the possibility to use discrete-time sliding mode control techniques designed for relative degree one systems. As a consequence, networked control algorithms can be developed based on recent results from this active field of research. Using a discretized version of the super twisting algorithm, which is obtained by the so-called matching approach, increases the accuracy due to the absence of discretization chattering. The effectiveness of the proposed control strategy is demonstrated by means of laboratory experiments.

关键词： Time-varying delay Sliding-mode control Discretization Closed-loop control