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Disturbance Rejection in the Interior Domain of Linear 2 x 2 Hyperbolic systems

IEEE TRANSACTIONS ON AUTOMATIC CONTROL 2015年第1期60卷 186-191页

作者： Anfinsen, Henrik Aamo, Ole Morten Norwegian Univ Sci & Technol Dept Engn Cybernet N-7491 Trondheim Norway

In this technical note, we develop a full state feedback law for disturbance rejection in systems described by linear 2 x 2 partial differential equations of the hyperbolic type, with the disturbance modelled as an autonomous, finite dimensional linear system affecting the PDE's left boundary, and actuation limited to the right boundary. The effect of the disturbance is rejected at an arbitrary point in the domain within a finite time. The performance is demonstrated through simulation.

关键词： distributed parameter systems disturbance rejection fluid flow systems

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Stabilizability and Controllability of Spatially Invariant PDE systems

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IEEE TRANSACTIONS ON AUTOMATIC CONTROL 2015年第2期60卷 383-392页

作者： Curtain, Ruth F. Univ Groningen Bernoulli Inst Math & Comp Sci NL-9700 AK Groningen Netherlands

In this paper, we derive new readily testable criteria for exponential stabilizability, approximate controllability, and exact controllability for multiplicative systems arising from linear partial differential equations on an infinite domain. These multiplicative systems have an unbounded semigroup generator, but bounded input and output operators. The theoretical results are illustrated by several examples. In particular, explicit, easily verifiable conditions for exponential stabilizability, approximate and exact controllability are given for second-order P.D.E. systems. Dual results for exponential detectability, approximate and exact observability are also included.

关键词： Controllability distributed parameter systems spatially invariant systems stabilizability

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Dynamic shaping of transport-reaction processes with a combined sliding mode controller and Luenberger-type dynamic observer design

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CHEMICAL ENGINEERING SCIENCE 2015年 138卷 673-684页

作者： Pourkargar, Davood Babaei Armaou, Antonios Penn State Univ Dept Chem Engn University Pk PA 16802 USA

We focus on shaping the long-term spatiotemporal dynamics of transport-reaction processes which can be described by semi-linear partial differential equations (PDEs). The dynamic shaping problem is addressed via error dynamics regulation between the governing PDE and a target PDE which describes the desired spatiotemporal behavior. A model order reduction methodology is utilized to construct the required reduced order models (ROMs) for governing and target dynamics via Galerkin's method. We subtract the governing from the target ROMs to obtain reduced offset dynamics error. Then an output feedback sliding mode control structure is synthesized to stabilize the reduced error dynamics and correspondingly synchronize the system and the target spatiotemporal behaviors. A Luenberger-type dynamic observer is applied to estimate the states of the governing ROM required by the sliding mode controller. The proposed approach is applied to address the thermal spatiotemporal dynamic shaping problem in a tubular chemical reactor. (C) 2015 Elsevier Ltd. All rights reserved.

关键词： Dynamic shaping distributed parameter systems Model order reduction Sliding mode control Dynamic observer Process control

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Uniform exponential stability of the time varying singular distributed parameter systems in Hilbert space

Uniform exponential stability of the time varying singular d...

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Chinese Control Conference (CCC)

作者： Feng Liu Guodong Shi Jiangsu Teachers University of Technology Changzhou 213001 China Changzhou University 213164 China

Uniform exponential stability of the time varying singular distributed parameter system is discussed in the light of GE 0 - semigroup theory and GE mild evolution operators in Hilbert space. The necessary and suffici... 详细信息

关键词： Asymptotic stability distributed parameter systems Hilbert space Thermal stability Circuit stability Stability analysis

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Adaptive observers for non-square positive real infinite dimensional systems

Adaptive observers for non-square positive real infinite dim...

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American Control Conference

作者： Michael A. Demetriou Worcester Polytechnic Institute Dept of Mechanical Engineering MA 01609 USA

ISBN: (纸本)9781467386838

This paper considers the adaptive estimation of parabolic partial differential equations with boundary control and observation. Structured perturbations enter at the boundary and are collocated either with the control or the measurement. Various combinations of boundary control, observation and structured perturbations are considered and viewed as evolution equations in a Hilbert space via the use of Dirichlet maps. When certain conditions are met, the systems can utilize results on the adaptive estimation of positive real infinite dimensional systems. Extensive simulation studies of 1D parabolic partial differential equation with the structured perturbation collocated either with the input or the output operator are presented to demonstrate the utilization of results on adaptive estimation of positive real infinite dimensional systems for diffusion PDEs.

关键词： positive real systems distributed parameter systems adaptive observers on-line estimation adaptive estimation distributed parameter systems Multidimensional systems Partial differential equations Differential equations Hilbert space boundary layer perturbation Real number

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Optimal experimental design for identification of transport coefficient models in convection-diffusion equations

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COMPUTERS & CHEMICAL ENGINEERING 2015年 80卷 101-113页

作者： Karalashvili, Maka Marquardt, Wolfgang Mhamdi, Adel Rhein Westfal TH Aachen AVT Proc Syst Engn D-52064 Aachen Germany

Methods for the careful design of optimal experiments for the identification of the structure and parameters of transport models often strongly depend on a-priori knowledge about the unknown model. However, this kind of knowledge is usually poor for complex systems. We propose a novel procedure that is less sensitive with respect to poor a-priori knowledge;it relies on an optimization problem to maximize the information content of the measurement data for the purpose of model identification. Specifically, based on existing model-based methods, optimal design of experiments is addressed in the context of three-dimensional, time-dependent transport problems by introducing experiment design variables and the transport coefficient as degrees of freedom of the optimization. The problem is solved by means of an iterative strategy that - by sequentially designing a series of experiments - strives to adjust the settings of the experimental conditions by exploiting the results from previous experiments. The key methodical ingredient of the novel procedure is the use of incremental model identification introduced previously. The suggested procedure is illustrated by means of an extensive numerical case study for a convection-diffusion equation originating from the modeling and simulation of energy transport in laminar wavy film flow. (C) 2015 Elsevier Ltd. All rights reserved.

关键词： distributed parameter systems Modeling and identification Inverse problem parameter estimation Model selection Optimal experimental design (OED)

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PDE Backstepping Boundary Observer Design for Microfluidic systems

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IEEE TRANSACTIONS ON CONTROL systems TECHNOLOGY 2015年第1期23卷 380-388页

作者： Khosroushahi, Reza Banaei Marquez, Horacio J. Univ Alberta Dept Elect & Comp Engn Edmonton AB T6G 2V4 Canada

In this brief, we explore the use of conformal mapping theory to reduce the complexity in PDE backstepping boundary observer design. The technique is applied to a genetic analysis microchip that features a collocated sensor-actuator architecture in which the temperature of the reaction chamber is the spatially distributed control variable. The size and structure of the microchip do not allow for sensor placement within the reaction chamber, making temperature estimation mandatory. The PDE backstepping boundary observer design is chosen to provide real-time data from the temperature inside the microchip. The standard PDE backstepping boundary observer design results in a partial differential equation for the kernel function with double the spatial dimension of the original problem, which makes the design intractable for the problems with dimensions higher than one. We show that the spatial domain of the original problem can be reduced with the use of the conformal mapping. The resulting observer is tested and experimentally validated, shown excellent performance with respect to the spacial L2 norm of the estimation error.

关键词： Conformal mapping distributed parameter systems lab-on-a-chip (LOC) partial differential equation (PDE) backstepping PDE boundary observer

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Reduced-order model for the analysis of mass transfer enhancement in membrane channel using electro-osmosis

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CHEMICAL ENGINEERING SCIENCE 2015年 122卷 86-96页

作者： Setiawan, Ridwan Ratnayake, Pesila Bao, Jie Weihs, Gustavo A. Fimbres Wiley, Dianne E. Univ New S Wales Sch Chem Engn Sydney NSW 2052 Australia

Flow control has the potential to mitigate concentration polarization and fouling in membrane systems by enhancing mixing near the membrane surface. Although Computational Fluid Dynamics (CM) modeling has been used to study the effect of externally induced unsteady flow on mass transfer enhancement, the analysis based on CM results is computationally expensive and cannot be performed systematically. Existing systematic approaches to quantify mixing enhancement only consider hydrodynamics but not the direct effect on mass transfer improvement, due to the difficulties caused by the non spatially invariant nature of the mass transfer phenomenon. This paper presents a reduced order model that combines the discretized mass transfer and linearized Navier-Stokes partial differential equations. The proposed model can be used to simulate and systematically analyze mass transfer enhancement caused by the flow induced by a pair of electrodes. When the Reynolds number and temporal frequency of the external field are low (Re < 2000), the effect of a forced wall slip velocity on the overall flow profile in a 2D channel can be approximated by its instantaneous component. This allows mass transfer enhancement to be analyzed explicitly using a discretized mass transfer equation. The results predicted by the reduced order model are in good agreement with CFD simulations. The benefit of the proposed reduced order model is demonstrated by the frequency response analysis to identify the temporal frequency that has the maximum effect on mass transfer enhancement. (C) 2014 Elsevier Ltd. All rights reserved.

关键词： distributed parameter systems Multidimensional frequency analysis Reduced-order modeling Electro-osmosis Membrane separation

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Nonlinear control under wave actuator dynamics with time- and state-dependent moving boundary

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INTERNATIONAL JOURNAL OF ROBUST AND NONLINEAR CONTROL 2015年第2期25卷 222-251页

作者： Cai, Xiushan Krstic, Miroslav Zhejiang Normal Univ Coll Math Phys & Informat Engn Jinhua 321004 Peoples R China Univ Calif San Diego Dept Mech Aerosp Engn La Jolla CA 92093 USA

We consider the stabilization of nonlinear ODE systems with actuator dynamics modeled by a wave PDE whose boundary is moving and is a function of time and of the ODE's state. Such a problem is inspired by applications in oil drilling where the position of the drill bit is a state variable in the ODE modeling the friction-dominated drill bit dynamics while at the same time being the position of the moving boundary of the wave PDE that models the distributed torsional dynamics of the drillstring. For moving boundaries that depend only on time, we extend the global result recently developed by Bekiaris-Liberis and Krstic for constant boundaries. For moving boundaries that also depend on the ODE's state, we develop a local result where the initial condition is restricted in such a way that it is ensured that the rate of movement of the boundary (both leftward' and rightward') is bounded by unity in closed-loop. For strict-feedforward systems under wave actuator dynamics with moving boundaries, the predictor-based feedback laws are obtained explicitly. The feedback design is illustrated through an example. Copyright (c) 2013 John Wiley & Sons, Ltd.

关键词： nonlinear control distributed parameter systems delay systems partial differential equations stabilization

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Boundary control design for a flexible string system with input backlash

Boundary control design for a flexible string system with in...

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American Control Conference

作者： Shuang Zhang Wei He Gun Li School of Aeronautics and Astronautic University of Electronic Science and Technology of China Chengdu 611731 China School of Automation and Electrical Engineering University of Science and Technology Beijing 100083 China

ISBN: (纸本)9781467386838

In this paper, we design a boundary control law and an observer for a flexible string system with external disturbance and input backlash. A novel `disturbance-like' term is put forward to cancel the effect of input backlash nonlinearity. Under the proposed control, we show that the transverse deflection is regulated effectively despite of the existence of external disturbance. The control parameters are chosen to ensure the control performance of the system. Simulations are provided to verify the effectiveness of the proposed control scheme.

关键词： Observers distributed parameter systems Payloads Vibrations Cranes Boundary conditions

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