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Flatness-based algebraic fault diagnosis for distributed-parameter systems

AUTOMATICA 2020年 117卷 108987-108987页

作者： Fischer, Ferdinand Deutscher, Joachim Univ Erlangen Nurnberg Lehrstuhl Regelungstech Cauerstr 7 D-91058 Erlangen Germany Univ Ulm Inst Mess Regel & Mikrotech Albert Einstein Allee 41 D-89081 Ulm Germany

This paper presents a flatness-based approach to the fault diagnosis for a large class of parabolic and biharmonic distributed-parameter systems (DPS). The inputs. outputs and disturbances of the faulty DPS can be defined in-domain or at a boundary. Time-varying additive actuator and sensor faults of polynomial form are considered. In the presence of disturbances with polynomial form, fault identification is achieved in finite-time by evaluating an algebraic expression depending on the known inputs and measurements. This expression results from applying integral transformations to the faulty DPS. It is shown that the corresponding integral kernels follow from the flatness-based realization of a set-point change for a DPS. The solvability of the latter results in fault identifiability conditions. For bounded disturbances of unknown form acting on the DPS, a threshold for secured finite-time fault detection is introduced. The results of the paper are demonstrated for a cantilever beam subject to in-domain actuator and boundary sensor faults. For polynomial type and bounded stochastic disturbances fault detection is verified for the faulty beam in simulations. (C) 2020 Elsevier Ltd. All rights reserved.

关键词： distributed-parameter systems Fault diagnosis Flatness Motion planning Modulating functions

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Fault detection for linear distributed-parameter systems using finite-dimensional functional observers

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INTERNATIONAL JOURNAL OF CONTROL 2016年第3期89卷 550-563页

作者： Deutscher, Joachim Univ Erlangen Nurnberg Lehrstuhl Regelungstech Cauerstr 7 D-91058 Erlangen Germany

In this article, finite-dimensional residual generators are directly designed for Riesz-spectral systems with bounded input and output operators to detect faults. This is achieved by using finite-dimensional observers, that can estimate linear functionals of the state without spillover. These observers allow for a decoupling of the unknown disturbances from the estimation error dynamics under mild assumptions. Then, a finite-dimensional residual generator is obtained by approximately decoupling the state from the residual, that is generated by the observer states and the outputs. It is shown that the resulting approximation error can be made small by increasing the observer order. Then, fault detection with the finite-dimensional residual generator can be assured by introducing a time-varying threshold. A faulty Euler-Bernoulli beam with structural damping illustrates the proposed finite-dimensional fault detection approach.

关键词： distributed-parameter systems Riesz-spectral systems fault detection functional observer actor faults

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Algebraic fault detection and isolation for parabolic distributed-parameter systems using modulation functions

Algebraic fault detection and isolation for parabolic distri...

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2nd IFAC Workshop on the Control of systems Modeled by Partial Differential Equations (CPDE)

作者： Fischer, F. Deutscher, J. Univ Erlangen Nurnberg Lehrstuhl Regelungstech Cauerstr 7 D-91058 Erlangen Germany

In this article an algebraic approach to the fault detection for parabolic distributed-parameter systems is described. The modulation functions approach is used to obtain an algebraic fault detection equation, that only depends on known signals and the fault. Assuming piecewise constant faults, this allows the detection of the absolute fault value without any system approximation. Furthermore, different additional requirements, such as fault isolation or decoupling of disturbances can be met. The corresponding modulation functions are obtained by the realization of a set-point change for their signal models. Hence, the modulation functions can be determined using existing results to the motion planning and open-loop control for distributed-parameter systems. The proposed fault detection and isolation method is illustrated for a faulty heat conductor. (C) 2016, IFAC (International Federation of Automatic Control) Hosting by Elsevier Ltd. All rights reserved.

关键词： distributed-parameter systems fault detection fault isolation modulation function set-point change trajectory planning

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A Discrete-Time Formulation of Nonlinear distributed-parameter Port-Hamiltonian systems

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IEEE CONTROL systems LETTERS 2024年 8卷 802-807页

作者： Macchelli, Alessandro Univ Bologna Dept Elect Elect & Informat Engn I-40136 Bologna Italy

This letter introduces a new framework of nonlinear, discrete-time, boundary control systems (BCSs) in the port-Hamiltonian form. The contribution is twofold. We start with a discrete-time approximation of a nonlinear port-Hamiltonian BCS, i.e., a dynamical system modelled by a nonlinear partial differential equation with boundary actuation and sensing. The most important feature is that the discretisation is performed in time only so that the "distributed nature" of the state is preserved. By approximating the gradient of the Hamiltonian density with its discrete gradient, the obtained sampled dynamics inherit the passivity of the original one. Besides, we prove that, under mild conditions, it is well-posed, i.e., the "next" state always exists. The second contribution deals with control design. More precisely, we have determined sufficient conditions for the plant dynamics and a static output feedback gain to make the closed-loop system asymptotically stable.

关键词： Sensors Mathematical models Output feedback Sufficient conditions Discrete-time systems Control design Partial differential equations port-Hamiltonian systems distributed-parameter systems passivity-based control sampled-data control

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Flatness-Based Output Feedback Tracking Control of a Hyperbolic distributed-parameter System

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IEEE CONTROL systems LETTERS 2022年 6卷 992-997页

作者： Gehring, Nicole Woittennek, Frank Johannes Kepler Univ Linz Inst Automat Control & Control Syst Technol A-4040 Linz Austria Tyrolean Private Univ Inst Automat & Control Engn A-6060 Hall In Tirol Austria

The hyperbolic distributed-parameter system under consideration comprises a second-order partial differential equation that is bidirectionally coupled with a first-order ordinary differential equation. The system models the transmission at a pneumatic test bench with boundary control and collocated measurement, yet stands in place for several other lossy or loss-free transmission problems. In the paper, an observer-based output feedback tracking controller is designed using the concept of flatness. It is a design based on normal forms, as both the state feedback tracking controller and the state observer are derived using canonical coordinates, which in turn rely on special parametrizations of the system's solutions. Additionally, a new transformation between the coordinates of the so-called hyperbolic controller and observer canonical form is presented that allows for the implementation of the observer-based controller. Overall, the closed-loop system is exponentially stable. Simulation results illustrate the tracking behavior.

关键词： Mathematical model Observers Backstepping State feedback Feedforward systems Power transmission lines Output feedback Boundary control distributed-parameter systems flatness hyperbolic systems pneumatic systems

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Adaptive sliding mode boundary control of a perturbed diffusion process

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INTERNATIONAL JOURNAL OF ROBUST AND NONLINEAR CONTROL 2024年第15期34卷 10055-10067页

作者： Mayr, Paul Orlov, Yury Pisano, Alessandro Koch, Stefan Reichhartinger, Markus Graz Univ Technol Inst Automat & Control Graz Austria CICESE Res Ctr Elect & Telecommun Dept Ensenada Mexico Univ Cagliari Dept Elect & Elect Engn Cagliari Italy Graz Univ Technol Inst Automat & Control Christian Doppler Lab Model Based Control Complex Graz Austria

This paper proposes a sliding-mode-based adaptive boundary control law for stabilizing a class of uncertain diffusion processes affected by a matched disturbance. The matched disturbance is assumed to be uniformly bounded along with its time derivative, whereas the corresponding upper bounding constants are not known. This motivates the use of adaptive control strategies. In addition, the spatially-varying diffusion coefficient is also uncertain. To achieve asymptotic stability of the plant origin in the L2$$ {L}_2 $$-sense in the presence of the disturbance, a discontinuous boundary feedback law is proposed where the gain of the discontinuous control term is adjusted according to a gradient-based adaptation law. A constructive Lyapunov analysis supports the stability properties of the considered closed-loop system, yielding sufficient convergence conditions in terms of suitable inequalities involving the controllers' tuning parameters. Simulation results are presented to corroborate the theoretical findings.

关键词： adaptive control boundary control diffusion process distributed-parameter systems disturbance rejection disturbances with unknown upper bound sliding mode control

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Event-Triggered Boundary Control of 2 x 2 Semilinear Hyperbolic systems

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IEEE TRANSACTIONS ON AUTOMATIC CONTROL 2024年第1期69卷 418-425页

作者： Strecker, Timm Cantoni, Michael Aamo, Ole Morten Univ Melbourne Dept Elect & Elect Engn Parkville Vic 3010 Australia Norwegian Univ Sci & Technol Dept Engn Cybernet Trondheim Norway

In this article, we present an event-triggered boundary control scheme for hyperbolic systems. The trigger condition is based on predictions of the state on determinate sets, and the control input is updated only when the predictions deviate from the reference by a given margin. Nominal closed-loop stability, the absence of Zeno behavior, and robustness to uncertainty and disturbances, are all established analytically. For the special case of linear systems, the trigger condition can be expressed in closed-form as an L-2-scalar product of kernels with the distributed state. The presented controller can also be combined with existing observers to solve the event-triggered output-feedback control problem. A numerical simulation demonstrates the effectiveness of the proposed approach.

关键词： Heuristic algorithms Convergence Linear systems Data models Stability criteria Robustness Prediction algorithms Boundary control distributed-parameter systems event-triggered control semilinear hyperbolic systems

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Robust Cooperative Output Regulation for Networks of Hyperbolic PIDE-ODE systems

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IEEE TRANSACTIONS ON AUTOMATIC CONTROL 2024年第2期69卷 888-903页

作者： Gabriel, Jakob Deutscher, Joachim Ulm Univ Inst Measurement Control & Microtechnol Ulm Germany

In this article, the robust cooperative output regulation problem for multiagent systems (MASs) with general heterodirectional hyperbolic PIDE-ODE agents is considered. This setup also covers networks of ODEs with arbitrarily long input and output delays. The output of the agents can be defined at all boundaries and in-domain and may depend on the ODE state while disturbances act on the agents in-domain, at the boundaries, the output, and the ODE. The communication network is described by a constant digraph and if its Laplacian is reducible, then heterogeneous agents are permitted also in the nominal case. The solution is based on the cooperative internal model principle, which requires to include a diffusively driven internal model in the controller. The corresponding state feedback regulator design starts with a local backstepping stabilization of the coupled hyperbolic PIDE-ODE systems. It is shown that the remaining simultaneous stabilization of the MAS can be traced back to the simultaneous stabilization of the finite-dimensional cooperative internal model. Solvability conditions in terms of the network topology and the agents' transfer behavior are presented. The new design method is applied to the formation control of a platoon of uncertain heavy ropes carrying loads to verify its applicability. Simulations confirm the synchronization performance achieved by the resulting networked controller.

关键词： distributed-parameter systems PIDE-ODE systems backstepping cooperative output regulation hyperbolic systems multiagent systems

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Using dynamic extensions for the backstepping control of hyperbolic systems

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AUTOMATICA 2025年 173卷

作者： Gehring, Nicole Deutscher, Joachim Irscheid, Abdurrahman Johannes Kepler Univ Linz Inst Automat Control & Control Syst Technol Linz Austria Ulm Univ Inst Measurement Control & Microtechnol Ulm Germany Saarland Univ Chair Syst Theory & Control Engn Saarbrucken Germany

This paper systematically introduces dynamic extensions for the boundary control of general heterodirectional hyperbolic PDE systems. These extensions, which are well known in the finite-dimensional setting, constitute the dynamics of state feedback controllers. They make it possible to achieve design goals beyond what can be accomplished by a static state feedback. The design of dynamic state feedback controllers is divided into first introducing an appropriate dynamic extension and then determining a static feedback of the extended state, which includes the system and controller state, to meet some design objective. In the paper, the dynamic extensions are chosen such that all transport velocities are homogenized on the unit spatial interval. Based on the dynamically extended system, a backstepping transformation allows to easily find a static state feedback that assigns a general dynamics to the closed-loop system, with arbitrary in-domain couplings. This new design flexibility is also used to determine a feedback that achieves complete input-output decoupling in the closed loop with ensured internal stability. It is shown that the modularity of this dynamic feedback design allows for a straightforward transfer of all results to hyperbolic PDE-ODE systems. An example demonstrates the new input-output decoupling approach by dynamic extension. (c) 2024 Elsevier Ltd. All rights are reserved, including those for text and data mining, AI training, and similar technologies.

关键词： distributed-parameter systems Hyperbolic systems Backstepping Boundary control Dynamic state feedback Dynamic extension Decoupling control

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P-Δ Effect Analysis of Tall Slender Structures Subjected to Arbitrary Time-Variant Axial Forces: A Differential Quadrature-Based Approach

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INTERNATIONAL JOURNAL OF STRUCTURAL STABILITY AND DYNAMICS 2025年第0期

作者： Lu, Yan Zhai, Yinquan Li, Hongjing Yang, Xiaopeng Sun, Guangjun Nanjing Tech Univ Engn Mech Inst Nanjing 211816 Peoples R China

Traditional methods for analyzing the P-Delta effect in tall structures often fail to fully account for time-varying axial forces, potentially underestimating the impact of the P-Delta effect on structural safety. To address this limitation, this paper introduces a high-precision method based on the Differential Quadrature Method (DQM) for advanced analysis of the P-Delta effect, applicable to both distributed mass, and concentrated mass structural systems. This method discretizes the partial differential equations governing the motion of structures subjected to arbitrary lateral and axial dynamic loads using Differential Quadrature (DQ) principles, applying DQ weighting matrix corrections method to handle boundary conditions. Additionally, it incorporates the unconditionally stable Newmark average acceleration method to solve for dynamic responses inclusive of the P-Delta effect. The method is validated through case studies of high-rise buildings and tall bridge piers, demonstrating strong agreement with results from general finite element software. Results indicate that the proposed method not only effectively captures the influence of time-invariant and time-varying axial forces on lateral vibration characteristics but also provides high-precision dynamic response analysis, offering a highly efficient, and practical tool for analyzing dynamic responses in tall structures.

关键词： P-Delta effect differential quadrature method time-varying axial force tall pier distributed-parameter systems

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