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Output Feedback Control of distributed parameter systems Using Adaptive Proper Orthogonal Decomposition

INDUSTRIAL & ENGINEERING CHEMISTRY RESEARCH 2010年第21期49卷 10496-10509页

作者： Pitchaiah, Sivakumar Armaou, Antonios Penn State Univ Dept Chem Engn University Pk PA 16802 USA

We address the problem of tracking and stabilization of dissipative distributed parameter systems, by designing static output feedback controllers using adaptive proper orthogonal decomposition methodology (APOD). Initially, an ensemble of eigenfunctions is constructed based on a relatively small data ensemble which is then recursively updated as additional process data becomes available periodically. The proposed APOD methodology relaxes the need for a representative ensemble of snapshots (in the sense that it contains the global dynamics of the process). An accurate reduced-order model (ROM) is constructed and periodically refined based on these updated eigenfunctions. Using the ROM and continuous measurements available from the restricted number of sensors, a static output feedback controller is subsequently designed. This controller is successfully used to achieve the desired control objective of stabilization and tracking in the Kuramoto-Sivashinksy and FitzHugh-Nagumo equations.

关键词： FEEDBACK control systems distributed parameter systems PROPER orthogonal decomposition EIGENFUNCTIONS PHOTOGRAPHS CHEMICAL engineering DECOMPOSITION (Chemistry) REDUCED-order models

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distributed parameter Modeling of Flexible Ball Screw Drives Using Ritz Series Discretization

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IEEE-ASME TRANSACTIONS ON MECHATRONICS 2015年第3期20卷 1226-1235页

作者： Henke, Benjamin Sawodny, Oliver Neumann, Ruediger Univ Stuttgart Inst Syst Dynam D-70569 Stuttgart Germany Festo AG& Co KG D-737340 Esslingen Germany

Ball screw drives are used in automation applications and machine tools to translate rotational motion of an electric motor into translational motion of a slide. Their frequency responses show characteristic torsional and translational resonances. The resonance frequencies vary with the slide position, which is due to the distributed stiffness and inertia of the flexible ball screw. The proposed model treats the ball screw as a flexible element, using Ritz series expansions to obtain a finite approximation of the continuous deformations. The use of problem-specific basis functions allows for a low-order approximation, making the model especially well suited for control design. The model shows excellent validation results and reproduces the variation of the resonance frequencies with high accuracy.

关键词： Automation distributed parameter systems modeling

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Domain decomposition methods in the distributed estimation of spatially distributed processes with mobile sensors

Domain decomposition methods in the distributed estimation o...

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American Control Conference (ACC)

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

ISBN: (纸本)9781467386821

This paper considers the state estimation of spatially distributed processes via the employment of mobile sensors. In order to reduce the computational demands, a domain decomposition method is utilized and which decomposes the spatial domain into two subdomains. The estimator in the inner domain implements a hybrid Kalman filter with a mobile sensor, whereas the outer subdomain implements a naive observer. Coupling conditions at the inner/outer boundary serve as a means to exchange information between the two estimators and which constitute a consensus protocol. The motion of the mobile sensor is based on a spatial gradient scheme and serves as a further means of reducing the computational load associated with the solution to large scale differential Riccati equations. The proposed scheme is further extended to collaborative distributed estimation in which multiple mobile sensors are enforcing another level of consensus protocol in order to penalize the differences between their state estimates. Extensive numerical simulations of a one-dimensional parabolic partial differential equation are presented to further demonstrate the multi-level computational savings associated with the use of domain decomposition in state estimation of spatially distributed processes with mobile sensors.

关键词： distributed parameter systems scientific computing mobile sensors distributed state estimation

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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 (ACC)

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

ISBN: (纸本)9781467386821

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： distributed parameter systems adaptive observers on-line estimation positive real systems

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An adaptive modeling method for time-varying distributed parameter processes with curing process applications

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NONLINEAR DYNAMICS 2015年第1-2期82卷 865-876页

作者： Lu, XinJiang Zou, Wei Huang, MingHui Cent South Univ Sch Mech & Elect Engn State Key Lab High Performance Complex Mfg Changsha 410083 Hunan Peoples R China

Curing processes are nonlinear distributed parameter systems (DPS) with time-varying spatiotemporal dynamics. However, existing data-driven modeling methods have only considered time-varying dynamics in the time direction and paid less attention to those in the spatial direction. This has led to poor modeling accuracy for nonlinear DPS with time-varying spatiotemporal dynamics. In this paper, we propose an adaptive modeling method to estimate the distribution model for this kind of DPS. An adaptive time/space separation is first developed to decompose the time/space coupling dynamics. Time-varying spatial basis functions are then constructed, which can represent time-varying dynamics in the spatial direction. An adaptive T-S fuzzy modeling method is further developed for online learning of unknown dynamics derived from the data. This modeling can adapt to real-time spatiotemporal variation after the time/space synthesis since it utilizes time-varying spatiotemporal dynamics. Finally, curing experiments successfully test and demonstrate the effectiveness of the proposed method.

关键词： distributed parameter systems Curing process Karhunen-Loeve (KL) method Fuzzy Modeling

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Experimental Study: Neural Network based Model Predictive Control of a distributed parameter System

Experimental Study: Neural Network based Model Predictive Co...

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IEEE International Conference on Control and Automation

作者： Jay N. Sompura Jaivik K. Mankad Nitin U. Padhiyar Electrical Engineering Department Indian Institute of Technology Chemical Engineering Department Indian Institute of Technology

ISBN: (纸本)9781509017393

An experimental set up has been designed for the purpose of spatial property control of a distributed parameter system. The setup consists of a thin metal chip with four temperature sensors along the length of the chip and four electric heaters to regulate the spatial temperature profile of the metal chip. A sequence of random pulse input signals with varying sampling times for the four manipulated inputs were used for live data generation of the transient temperature values at four locations along the metal chip length. Two data-driven models, namely linear state space model and neural network based model are identified and applied for online control. Model predictive control was used to control the spatial temperature profile for set-point tracking and disturbance rejection.

关键词： temperature profiles distributed parameter systems Model predictive control Predictive control Neural network Computer chips DNA Microarrays Temperature Sensor Device Component data generation State space models Disturbance rejection distributed model predictive control nonlinear model predictive control Metals Set of points

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Gain adaptation and sensor guidance of diffusion PDEs using on-line approximation of optimal feedback kernels

Gain adaptation and sensor guidance of diffusion PDEs using ...

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American Control Conference (ACC)

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

ISBN: (纸本)9781467386821

This paper considers the multi-level approximation of controllers for partial differential equations. First, assuming that the full state is available, an optimal controller based on a finite horizon Linear Quadratic Regulator (LQR) design is computed. Assuming that the feedback operator admits a time varying feedback kernel, the first level approximation provides a means to replace the requirement of full state knowledge by the knowledge of the state at the single spatial location that best approximates the kernel by a delta function. This then replaces the full state feedback by a static output feedback that is simultaneously approximating the full state controller and is providing the optimal sensor location. The second level approximation produces the static gain that is needed to multiply the state evaluated at the approximating spatial sensor location. Since the feedback gain is time varying, this two-level approximation is applied at each time instant thus rendering the sensor mobile and the static gain adaptive. Algorithms for PDEs in one and two spatial dimensions are provided along with numerical studies that compare the full-state optimal controllers with the suboptimal static output feedback controllers with mobile sensor.

关键词： distributed parameter systems computational control distributed local controllers mobile sensors kernel approximation

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Decentralized Scheduling of Sensor Networks for parameter Estimation of Spatio-Temporal Processes 12th

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12th International Conference on Diagnostics of Processes and systems (DPS)

作者： Romanek, Adam Patan, Maciej Kowalow, Damian Univ Zielona Gora Zielona Gora Poland

ISBN: (纸本)9783319231808;9783319231792

The activation scheduling problem for a scanning sensor network monitoring a spatio-temporal process is considered. The configuration of an activation schedule for network nodes measuring the system state is formulated in a sense of a suitable criterion quantifying an estimation accuracy for system parameters. Then, a decomposition of the scheduling problem is provided and a proper distribution of total computational effort and consensus between the network nodes is achieved via information flooding based on a pairwise communication scheme. As a result, a simple exchange algorithm is outlined to solve the design problem in a decentralized fashion. The proposed approach is illustrated on an example of sensor network configuration for monitoring an atmospheric pollution transport process.

关键词： Sensor networks distributed parameter systems parameter estimation Optimum experimental design

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Robust Adaptive Model Tracking for distributed parameter Control of Linear Infinite-dimensional systems in Hilbert Space

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IEEE/CAA Journal of Automatica Sinica 2014年第3期1卷 294-301页

作者： Mark J.Balas Susan A.Frost the Embry-Riddle Aeronautical University the NASA Ames Research Center

This paper is focused on adaptively controlling a linear infinite-dimensional system to track a finite-dimensional reference *** a linear continuous-time infinite-dimensional plant on a Hilbert space with disturbances of known waveform but unknown amplitude and phase,we show that there exists a stabilizing direct model reference adaptive control law with the properties of certain disturbance rejection and *** plant is described by a closed,densely defined linear operator that generates a continuous semigroup of bounded operators on the Hilbert space of *** central result will show that all errors will converge to a prescribed neighborhood of zero in an infinitedimensional Hilbert *** result will not require the use of the standard Barbalat’s lemma which requires certain signals to be uniformly *** result is used to determine conditions under which a linear infinite-dimensional system can be directly adaptively controlled to follow a reference *** particular,we examine conditions for a set of ideal trajectories to exist for the tracking *** results are applied to adaptive control of general linear diffusion systems described by self-adjoint operators with compact resolvent.

关键词： Adaptation models Adaptive control Hilbert space Learning (artificial intelligence) Robustness Trajectory adaptive control algorithm adaptive theory distributed parameter system distributed parameter systems Hilbert space trajectory Adaptation models reference model adaptive control Robustness Computer algorithms

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Multi-nodal PWR reactor model - methodology proposition for power distribution coefficients calculation 21

Multi-nodal PWR reactor model - methodology proposition for ...

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21st International Conference on Methods and Models in Automation and Robotics (MMAR)

作者： Puchalski, Bartosz Rutkowski, Tomasz A. Duzinkiewicz, Kazimierz Gdansk Univ Technol Fac Elect & Control Engn G Narutowicza St 11-12 PL-80233 Gdansk Poland

ISBN: (纸本)9781509018666

In the paper the multi-nodal Pressurized Water Reactor (PWR) heat transfer model based on Mann's model is presented. This model is used for heat transfer from fuel to coolant modelling purposes in a reactor core. The authors expand the approach widely used in literature by defining additional coefficients for heat transfer model. These parameters approximate the power generation distribution in the PWR reactor core according to the reactor control rod bank movement. Authors describe in details the proposed methodology for calculation of introduced power distribution coefficients. In the simplest case, those coefficients may be equal and constant over time and space of a reactor. On the other hand, they can be treated as variables that are time and reactor region dependent. By introducing these specific coefficients, the nodal model of heat transfer gains advanced capabilities that can be efficiently used in design and synthesis of more advanced and complex power control system in nuclear reactor with respect to temperature distribution within the reactor core.

关键词： Nuclear power generation Nuclear thermodynamics Mathematical model distributed parameter systems

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