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Iterative Learning Control for Discrete Parabolic distributed parameter systems

International Journal of Automation and computing 2015年第3期12卷 316-322页

作者： Xi-Sheng Dai Sen-Ping Tian Ya-Jun Guo College of Electrical Engineering and Automation Shandong University of Science and Technology School of Electrical and Information Engineering Guangxi University of Science and Technology School of Automation Science and Engineering South China University of Technology

In this paper, iterative learning control(ILC) technique is applied to a class of discrete parabolic distributed parameter systems described by partial difference equations. A P-type learning control law is established for the system. The ILC of discrete parabolic distributed parameter systems is more complex as 3D dynamics in the time, spatial and iterative domains are *** overcome this difficulty, discrete Green formula and analogues discrete Gronwall inequality as well as some other basic analytic techniques are utilized. With rigorous analysis, the proposed intelligent control scheme guarantees the convergence of the tracking error. A numerical example is given to illustrate the effectiveness of the proposed method.

关键词： Intelligent control iterative learning control discrete systems distributed parameter systems convergence analysis.

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Design of APOD-based switching dynamic observers and output feedback control for a class of nonlinear distributed parameter systems

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CHEMICAL ENGINEERING SCIENCE 2015年 136卷 62-75页

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

The output feedback control problem for a class of nonlinear distributed parameter systems with limited number of continuous measurement sensors that describes a wide range of physico-chemical systems is investigated using adaptive proper orthogonal decomposition (APOD) method. Specifically, APOD is used to initiate and recursively revise locally valid reduced order models (ROMs) that approximate the dominant dynamic behavior of such physico-chemical systems. The controller is designed based on ROMs by combining a robust state controller with an APOD-based nonlinear Luenberger-type switching dynamic observer of the system states to reduce measurement sensor requirements. The important static observer requirements on the number of measurement sensors (that they must be supernumerary to the ROM dimension) and their location are circumvented by synthesizing dynamic observers. Three different approaches are introduced to recursively compute the dynamic observer gains at the ROM revisions. The stability of the closed-loop system is proven via Lyapunov and hybrid system stability arguments without invoking the separation principle between control and observation. The proposed method is successfully used to regulate a physico-chemical system that can be described in the form of the Kuramoto-Sivashinsky equation when the process exhibits significant nonlinear behavior. (C) 2015 Elsevier Ltd. All rights reserved.

关键词： distributed parameter systems Output feedback control Adaptive model reduction Nonlinear systems Dynamic observer Process control

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Using H₂-Control Performance Metrics for the Optimal Actuator Location of distributed parameter systems

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IEEE TRANSACTIONS ON AUTOMATIC CONTROL 2015年第2期60卷 450-462页

作者： Morris, Kirsten Demetriou, Michael A. Yang, Steven D. Univ Waterloo Dept Appl Math Waterloo ON N2L 3G1 Canada Worcester Polytech Inst Dept Mech Engn Worcester MA 01609 USA Univ Waterloo Dept Elect & Comp Engn Waterloo ON N2L 3G1 Canada

This paper is concerned with the use of H-2-control performance metrics in finding optimal actuator locations for a class of infinite-dimensional systems. Conditions that guarantee convergence of the optimal actuator location for the finite-dimensional representation of the infinite-dimensional system to the optimal actuator location of the original infinite-dimensional system are provided. Minimizing an H-2-performance index, parameterized by the possible actuator locations and disturbance functions, leads to optimal locations that in addition to enhanced performance, also provide robustness with respect to the spatial distribution of disturbances. Numerical studies for a cantilever beam and a diffusion problem are used to demonstrate the effects of the spatial distribution of disturbances on the optimal actuator location. The effect of the diffusivity parameter on the best actuator locations is also considered.

关键词： distributed parameter systems H-2-control optimal actuator location spatial disturbances

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APOD-Based Control of Linear distributed parameter systems Under Sensor/Controller Communication Bandwidth Limitations

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AICHE JOURNAL 2015年第2期61卷 434-447页

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

The synthesis of a model-based control structure for general linear dissipative distributed parameter systems (DPSs) is explored in this manuscript. Discrete-time distributed state measurements (called process snapshots) are used by a continuous-time regulator to stabilize the process. The main objective of this article is to identify a criterion to minimize the communication bandwidth between sensors and controller (snapshots acquisition frequency) using linear systems analysis and still achieve closed-loop stability. This objective is addressed by adding a modeling layer to the regulator. Theoretically, DPSs can be well described by low dimensional ordinary differential equation models when represented in functional spaces;practically, the model accuracy hinges on finding basis functions for these spaces. Adaptive proper orthogonal decomposition is used to identify statistically important basis functions and establish locally accurate reduced order models which are then used in controller design. The proposed approach is successfully applied toward thermal regulation in a tubular chemical reactor. (c) 2014 American Institute of Chemical Engineers AIChE J, 61: 434-447, 2015

关键词： distributed parameter systems adaptive model reduction adaptive proper orthogonal decomposition process control hybrid systems

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Data-driven model reduction-based nonlinear MPC for large-scale distributed parameter systems

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JOURNAL OF PROCESS CONTROL 2015年 35卷 50-58页

作者： Xie, Weiguo Bonis, Ioannis Theodoropoulos, Constantinos Univ Manchester Sch Chem Engn & Analyt Sci Manchester M13 9PL Lancs England

Model predictive control (MPC) has been effectively applied in process industries since the 1990s. Models in the form of closed equation sets are normally needed for MPC, but it is often difficult to obtain such formulations for large nonlinear systems. To extend nonlinear MPC (NMPC) application to nonlinear distributed parameter systems (DPS) with unknown dynamics, a data-driven model reduction-based approach is followed. The proper orthogonal decomposition (POD) method is first applied off-line to compute a set of basis functions. Then a series of artificial neural networks (ANNs) are trained to effectively compute POD time coefficients. NMPC, using sequential quadratic programming is then applied. The novelty of our methodology lies in the application of POD's highly efficient linear decomposition for the consequent conversion of any distributed multi-dimensional space-state model to a reduced 1-dimensional model, dependent only on time, which can be handled effectively as a black-box through ANNs. Hence we construct a paradigm, which allows the application of NMPC to complex nonlinear high-dimensional systems, even input/output systems, handled by black-box solvers, with significant computational efficiency. This paradigm combines elements of gain scheduling, NMPC, model reduction and ANN for effective control of nonlinear DPS. The stabilization/destabilization of a tubular reactor with recycle is used as an illustrative example to demonstrate the efficiency of our methodology. Case studies with inequality constraints are also presented. (C) 2015 Elsevier Ltd. All rights reserved.

关键词： Proper orthogonal decomposition Nonlinear model predictive control Sequence of artificial neural networks distributed parameter systems Control of highly nonlinear systems

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

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IFAC-PapersOnLine 2016年第8期49卷 162-167页

作者： Fischer, F. Deutscher, J. Lehrstuhl fur Regelungstechnik Universität Erlangen-Nürnberg Cauerstraße 7 ErlangenD-91058 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. © 2016

关键词： Fault detection Algebra distributed parameter control systems Modulation Motion planning distributed parameter systems Fault isolation Modulation functions Setpoints Trajectory Planning

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Adaptive Control of Chemical distributed parameter systems 9

Adaptive Control of Chemical Distributed Parameter Systems

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9th IFAC Symposium on Advanced Control of Chemical Processes ADCHEM 2015

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

The adaptive output feedback control problem of chemical distributed parameter systems is investigated while the process parameters are unknown. Such systems can be usually modeled by semi linear partial differential equations (PDEs). A combination of Galerkin's method and proper orthogonal decomposition is applied to generate a reduced order model which captures the dominant dynamic behavior of the system and can be used as the basis for Lyapunov-based adaptive controller design. The proposed control method is illustrated on thermal dynamics regulation in a tubular chemical reactor where the temperature spatiotemporal dynamic behavior is modeled in the form of a semi-linear PDE. (C) 2015, IFAC (International Federation of Automatic Control) Hosting by Elsevier Ltd. Ail rights reserved.

关键词： distributed parameter systems adaptive control model reduction output feedback partial differential equations Lyapunov stability process control

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Actuator location optimization in synchronization control of networked distributed parameter systems

Actuator location optimization in synchronization control of...

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American Control Conference

作者： Demetriou, Michael A. Worcester Polytech Inst Dept Mech Engn Worcester MA 01609 USA

ISBN: (纸本)9781479986842

This work examines the effects of actuator location in networked distributed parameter systems. In particular, the effects of the optimal actuator location for one networked system can impact the collective behavior of the networked systems. The actuator optimization cannot be performed on the individual networked systems, but must be considered for the aggregate of the networked systems. To tackle the actuator optimization problem, the networked systems are viewed collectively and with the implementation of a synchronization controller, the resulting closed-loop aggregate system is parameterized by the actuator location. Using different metrics for the success of synchronization, the resulting actuator optimization problem is recast as a minimization of a performance index. The solution to this optimization is expressed as the minimization of the trace of a location-parameterized Lyapunov operator. Simulation studies on seven networked diffusion partial differential equations in one spatial dimension reveal the effects of a correct actuator placement on synchronization.

关键词： distributed parameter systems synchronization controllers networked systems actuator optimization

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A simple observer scheme for a class of 1-D semi-linear parabolic distributed parameter systems

A simple observer scheme for a class of 1-D semi-linear para...

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European Control Conference (ECC)

作者： Schaum, Alexander Moreno, Jaime A. Alvarez, Jesus Meurer, Thomas Christian Albrechts Univ Kiel Chair Automat Control Kiel Germany Univ Nacl Autonoma Mexico Inst Ingn Mexico City DF Mexico Univ Autonoma Metropolitana Iztapalapa Dept Proc & Hidraul Mexico City DF Mexico

ISBN: (纸本)9783952426937

In this paper, a simple observer design scheme is proposed for a class of 1-D semi-linear parabolic distributed parameter systems with in-domain measurement. The main idea of the design resides in imposing the measurement on the observer dynamics in a similar way as it is done in the finite-dimensional reduced order observer design. For the distributed system this is achieved through an additional algebraic constraint in the domain instead of an output injection mechanism. Correspondingly, the observer convergence is not induced by the correction scheme, but by the sensor location and the system parameters, and thus amounts on the underlying detectability property rather than the system observability. Possible applications to the case of unknown inputs are discussed. The proposed estimation approach is illustrated and tested through simulations with two representative examples: an unstable diffusive linear system with Dirichlet boundary conditions, and a stable isothermal single-species nonlinear tubular reactor with non-monotonic kinetics and Robin-Newman (i.e., Danckwerts) boundary conditions.

关键词： algebra control system synthesis distributed parameter systems linear systems multidimensional systems observers 1-D semi-linear parabolic distributed parameter systems Dirichlet boundary conditions Robin-Newman boundary conditions algebraic constraint finite-dimensional reduced order observer design in-domain measurement sensor location simple observer scheme stable isothermal single-species nonlinear tubular reactor system parameters unstable diffusive linear system Boundary conditions Convergence distributed parameter systems Eigenvalues and eigenfunctions Inductors Mathematical model Observers

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Explicit/Multi-Parametric Model Predictive Control of Dissipative distributed parameter systems

Explicit/Multi-Parametric Model Predictive Control of Dissip...

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American Control Conference

作者： Liu, Liu Huang, Biao Dubljevic, Stevan Univ Alberta Dept Chem & Mat Engn Edmonton AB T6G 2V4 Canada

ISBN: (纸本)9781479986842

This work focuses on the development of an explicit/multi-parametric model predictive control algorithm to stabilize the discrete infinite-dimensional system arising from the discrete state space modeling of certain class of dissipative distributed parameter systems, specifically, parabolic partial differential equation (PDE) systems. In particular, the class of parabolic PDEs that captures a large number of transport-reaction systems yields a discrete modal representation which captures the dominant dynamics of the parabolic PDE system. The proposed explicit/multi-parametric model predictive control algorithm is constructed in a way that the objective function is concerned with only the low-order modes, while the state constraints involve both the low-order and higher-order modes. The explicit model predictive control problem is solved offline by dynamic programming and multi-parametric quadratic programming techniques, and the solution is expressed as a piecewise affine function with its corresponding critical regions.

关键词： Predictive control distributed parameter systems Mathematical model Quadratic programming Optimal control Programming

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