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On Discretization Methods for Indirect Adaptive Sliding Mode control

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On Discretization Methods for Indirect Adaptive Sliding Mode...

IEEE Conference on Decision and control

作者： Christina Hettiger Lars Watermann Kiran Kumari Lukas Eisenzopf Florian Weissenberger Martin Horn Stefan Koch Johann Reger Markus Reichhartinger Control Engineering Group Technische Universität Ilmenau Ilmenau Germany 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

ISBN: (数字)9781665467612

ISBN: (纸本)9781665467629

In this paper, discrete-time versions of the first-order indirect adaptive sliding mode control (SMC) algorithm are developed and analyzed. In particular, a scalar linear system with parametric uncertainty linear in the state and with bounded input disturbance is considered. The discretization of continuous-time first-order indirect adaptive SMC algorithm may not preserve continuous-time properties like asymptotic stability of the origin. In order to ensure boundedness, knowledge about where the actual parameter may be located is used in this work. Then, for each proposed discretization scheme, conditions on the sampling time are derived that guarantee convergence into a bounded set. The theoretical results are illustrated with simulation examples and the proposed discretization schemes are compared with regard to the condition on sampling time and precision.

关键词： Linear systems Asymptotic stability Adaptation models Uncertainty Adaptive systems Complex systems Sliding mode control

Efficient temperature profile estimation for silicon wafers based on subspace observers 21st

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Efficient temperature profile estimation for silicon wafers ...

21st IFAC World Congress 2020

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

This work proposes a computationally efficient observation algorithm for the surface temperature profile of heated silicon wafers. The observer exploits the fact that only a few modes of the original large-order model are unstable or slowly converging. In this case, it suffices to modify only these modes by the observer's output feedback gain. Compared to classical observation techniques, the proposed method allows to compute the feedback gain for a state space of lower dimension, which reduces computational complexity. A comparison of the approach with the extended Kalman-Bucy filter using experimental data shows its appealing performance. Copyright © 2020 The Authors. This is an open access article under the CC BY-NC-ND license

关键词： Riccati equations

Optimal robust exact first-order differentiators with Lipschitz continuous output

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arXiv 2024年

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

The signal differentiation problem involves the development of algorithms that allow to recover a signal's derivatives from noisy measurements. This paper develops a first-order differentiator with the following combination of properties: robustness to measurement noise, exactness in the absence of noise, optimal worst-case differentiation error, and Lipschitz continuous output where the output's Lipschitz constant is a tunable parameter. This combination of advantageous properties is not shared by any existing differentiator. Both continuous-time and sample-based versions of the differentiator are developed and theoretical guarantees are established for both. The continuous-time version of the differentiator consists in a regularized and sliding-mode-filtered linear adaptive differentiator. The sample-based, implementable version is then obtained through appropriate discretization. An illustrative example is provided to highlight the features of the developed differentiator. © 2024, CC BY.

关键词： Continuous time systems

Sliding Surface Selection for Saturated Sliding-Mode control of Linear Time-Invariant Plants

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Sliding Surface Selection for Saturated Sliding-Mode Control...

IEEE Conference on Decision and control

作者： Richard Seeber Markus Reichhartinger Christian Doppler Laboratory for Model Based Control of Complex Test Bed Systems Institute of Automation and Control Graz University of Technology Graz Austria Institute of Automation and Control Graz University of Technology Graz Austria

ISBN: (纸本)9781665436601

The design of sliding-mode controllers with continuous control signals in the presence of saturated actuators is a challenging task. This paper analyzes existing formal assumptions required by such designs, and proposes a new controller design that is applicable for a large class of linear time-invariant plants. The proposed design is based on the suitable selection of a sliding surface, to which the conditioned super-twisting algorithm is then applied. Stability conditions for the closed loop in presence of perturbations with bounded amplitude and slope are given. Simulation results obtained with the model of a continuous flow heater for silicon wafer processing illustrate the presented approach.

关键词： Semiconductor device modeling Heating systems Simulation Perturbation methods Conferences Stability analysis Silicon

Integral State-Feedback control of Linear Time-Varying systems: A Performance Preserving Approach

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arXiv 2021年

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

An integral extension of state-feedback controllers for linear time-varying plants is proposed, which preserves performance of the nominal controller in the unperturbed case. Similar to time-invariant state feedback with integral action, the controller achieves complete rejection of disturbances whose effective action on the plant is constant with respect to the control input. Moreover, bounded-input bounded-state stability with respect to arbitrary disturbances is shown. A modification for preventing controller windup as well as tuning guidelines are discussed. The efficacy of the proposed technique is demonstrated in simulation for a two-tank system that is linearized along a time-varying reference trajectory. © 2021, CC BY-NC-ND.

关键词： Disturbance rejection

A non-conservative stability criterion for networked control systems with time-varying packet delays

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arXiv 2021年

作者： 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 Graz8010 Austria

A networked output feedback loop subject to packetized transmissions of the output signal is considered. Based on the small gain theorem, an easy-to-use stability criterion covering two important cases is presented. In the first case a packet numbering mechanism is employed whereas in the second case neither packet numbering nor synchronization between sender and receiver is assumed. The analysis makes use of acausal subsystems and deduces the optimal constant time delay that should be used in a nominal controller design such that additional packet delay variations introduced by the network are maximized. A simulation example of a networked control system with a filtered Smith predictor illustrates the application of the proposed criterion and compares the results to different approaches from literature. Copyright © 2021, The Authors. All rights reserved.

关键词： Networked control systems

Optimal Robust Exact Differentiation via Linear Adaptive Techniques

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arXiv 2021年

作者： Seeber, Richard Haimovich, Hernan 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

The problem of differentiating a function with bounded second derivative in the presence of bounded measurement noise is considered in both continuous-time and sampled-data settings. Fundamental performance limitations of causal differentiators, in terms of the smallest achievable worst-case differentiation error, are shown. A robust exact differentiator is then constructed via the adaptation of a single parameter of a linear differentiator. It is demonstrated that the resulting differentiator exhibits a combination of properties that outperforms existing continuous-time differentiators: it is robust with respect to noise, it instantaneously converges to the exact derivative in the absence of noise, and it attains the smallest possible—hence optimal—upper bound on its differentiation error under noisy measurements. For sample-based differentiators, the concept of quasi-exactness is introduced to classify differentiators that achieve the lowest possible worst-case error based on sampled measurements in the absence of noise. A straightforward sample-based implementation of the proposed linear adaptive continuous-time differentiator is shown to achieve quasi-exactness after a single sampling step as well as a theoretically optimal differentiation error bound that, in addition, converges to the continuous-time optimal one as the sampling period becomes arbitrarily small. A numerical simulation illustrates the presented formal results. © 2021, CC BY.

关键词： Errors

Adaptive Gain Super-Twisting-Algorithm: Design and Discretization

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Adaptive Gain Super-Twisting-Algorithm: Design and Discretiz...

IEEE Conference on Decision and control

作者： Lukas Eisenzopf Lars Watermann Stefan Koch Markus Reichhartinger Johann Reger Martin Horn Institute of Automation and Control Graz University of Technology Graz Austria Control Engineering Group Technische Universität Ilmenau Germany Christian Doppler Laboratory for Model-Based Control of Complex Test Bed Systems Institute of Automation and Control Graz University of Technology Graz Austria

ISBN: (纸本)9781665436601

In this paper, an eigenvalue-based discretization scheme is applied to a novel adaptive super-twisting-algorithm. Following the proposed procedure the discretization chattering effect is avoided entirely. An attractive property of the adaptation law is the insensitivity of the closed-loop system to overly large gains which in existing laws potentially leads to instability. Using Lyapunov’s direct method the stability of the feedback loop is shown. Numerical examples underline the beneficial properties of the proposed methodology.

关键词： Feedback loop Conferences Hardware Numerical stability

Unknown input observer design for linear time-invariant systems - A unifying framework

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arXiv 2021年

作者： Tranninger, Markus Niederwieser, Helmut Seeber, Richard Horn, Martin Institute of Automation and Control Graz University of Technology Graz Austria BEST - Bioenergy and Sustainable Technologies GmbH 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

This paper presents a new observer design approach for linear time invariant multivariable systems subject to unknown inputs. The design is based on a transformation to the so-called special coordinate basis. This form reveals important system properties like invertability or the finite and infinite zero structure. Depending on the system's strong observability properties, the special coordinate basis allows for a straightforward unknown input observer design utilizing linear or nonlinear observers design techniques. The chosen observer design technique does not only depend on the system properties, but also on the desired convergence behavior of the observer. Hence, the proposed design procedure can be seen as a unifying framework for unknown input observer design. © 2021, CC BY-NC-ND.

关键词： Time varying control systems