Bifurcation theory provides a powerful tool for analyzing the nonlinear dynamic behavior of process systems. However, although the theory in principle applies to lumped as well as distributedparameter processes, it i...
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Bifurcation theory provides a powerful tool for analyzing the nonlinear dynamic behavior of process systems. However, although the theory in principle applies to lumped as well as distributedparameter processes, it is in practice necessary to reduce the order of distributed (partial differential equations, PDE) models prior to application of the theory. As shown in this paper, simply applying some ad hoc discretization method such as finite differences or finite elements, can result in spurious bifurcations and erroneous predictions of stability. To enable detection of such anomalities, and to aid in the selection of a proper model order, we propose a method for estimating the error introduced by the model reduction. Apart from simply providing a label of confidence in the results of the bifurcation analysis, the estimated error can be used to improve the quality of the reduced order model. For this purpose we propose a method based on dynamically moving the discretization mesh such as to minimize the discretization error. The proposed method is based on principles from feedback control, and is both very simple and highly robust compared with existing so-called moving mesh methods. As an application we consider bifurcation analysis of a heat-integrated fixed-bed reactor. (C) 2003 Elsevier Ltd. All rights reserved.
Control of the distributed parameter systems (DPS) usually involves dynamical description of infinite-dimensional Hilbert or Banach spaces of functions. Generally, it is not possible to implement an infinite dimension...
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In the paper, the robust control of temperature fields in the secondary cooling zone of the continuous casting process is presented. Temperature fields are represented by dynamic models in the form of a finite-dimensi...
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ISBN:
(纸本)9781467366274
In the paper, the robust control of temperature fields in the secondary cooling zone of the continuous casting process is presented. Temperature fields are represented by dynamic models in the form of a finite-dimensional approximation of distributed parameter systems. Models are created by means of validated finite element method modelling. The control synthesis is decomposed to the time and space domain. For the control synthesis with internal model control structure in the time domain, an uncertainty of the controlled system is considered and robust controllers are designed.
The optimization and adaptation of the synchronization gains for a class of networked systems is presented in which the state of each of the networked nodes is governed by a distributedparameter system. The design ob...
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ISBN:
(纸本)9781479932740
The optimization and adaptation of the synchronization gains for a class of networked systems is presented in which the state of each of the networked nodes is governed by a distributedparameter system. The design objectives aim at ensuring that all pairwise state differences of the networked systems converge to zero in an appropriate norm and that the states of these systems satisfy the control objective. The proposed static output feedback controllers thus contain a term that addresses the control objective and a consensus term that ensures synchronization. The synchronization gains of the resulting aggregate systems can be viewed as the strengths of the interconnections among the network nodes. Two different optimization schemes for the non-zero entries of the associated graph Laplacian are proposed. An alternate design proposes the on-line adjustment of the entries of the graph Laplacian matrix via an adaptation involving available output signals of the networked systems. The proposed results are demonstrated by a numerical example for a 1D partial differential equation.
In this paper we present an error feedback controller for approximate tracking and disturbance rejection for linear distributed parameter systems. The controller is approximate because it is only guaranteed to produce...
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ISBN:
(数字)9781665451963
ISBN:
(纸本)9781665451963
In this paper we present an error feedback controller for approximate tracking and disturbance rejection for linear distributed parameter systems. The controller is approximate because it is only guaranteed to produce a small tracking error rather than an asymptotic zero tracking error. However, the asymptotic tracking error can be reduced by solving a sequence of controllers, similar in spirit to cascade controllers, where the error at one level becomes the target to track at the next level. At each step the error is reduced geometrically so that achieving a desired tracking level seldom requires more than one or two iterations. An example is given in which the plant is governed by a convection-diffusion equation with non-constant coefficients. In order to compare the effectiveness of our controller with the classical internal model controller the reference signal and disturbance are generated by a six dimensional exosystem. We note that while our approximate controller achieves a small error almost immediately the internal model controller requires much longer transient to achieve a similar level. Furthermore, our controller can handle much more general reference and disturbance signals as demonstrated in a second numerical simulation.
An algorithm for linear quadratic optimal control synthesis for parabolic distributed parameter systems is presented. The distributedparameter system is reduced to lumped parameter system by applying the generalized ...
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ISBN:
(纸本)078037729X
An algorithm for linear quadratic optimal control synthesis for parabolic distributed parameter systems is presented. The distributedparameter system is reduced to lumped parameter system by applying the generalized finite integral transform technique. The control law is related to obtaining solutions of algebraic Riccati equation, which is realized by using neural networks in real time. Numerical examples are, presented.
In this paper, we studied the identification issue of one class of distributed parameter systems based on the Chebyshev polynomials. The proposed method translates distributed parameter systems into lumped parameter s...
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ISBN:
(纸本)9787900719706
In this paper, we studied the identification issue of one class of distributed parameter systems based on the Chebyshev polynomials. The proposed method translates distributed parameter systems into lumped parametersystems by casting state functions into the space spanned by Chebyshev polynomials, and identification can be made with the algorithm of lest square parameter estimation. There is no approximation in dealing with boundary conditions, and high accuracy can be achieved by few polynomials. Numerical example is conducted to demonstrate the validity and accuracy of the proposed method.
In this paper, the input-output finite-time stability and stabilization for distributed parameter systems was studied. The concept of input-output finite-time stability for distributed parameter systems was defined. B...
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ISBN:
(纸本)9781538604854
In this paper, the input-output finite-time stability and stabilization for distributed parameter systems was studied. The concept of input-output finite-time stability for distributed parameter systems was defined. By employing Lyapunov functional theory, sufficient conditions of input-output finitetime stability for distributed parameter systems were given. Sufficient conditions for the existence of distributed state feedback controllers which ensure the closed-loop distributed parameter systems be input-output finite-time stable were also proposed. Finally, a numerical example was given to illustrate our results.
This paper presents a new model-based fault detection and estimation framework for a class of multi-input and multi-output (MIMO) nonlinear distributed parameter systems (DPS) described by partial differential equatio...
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ISBN:
(纸本)9781538683576
This paper presents a new model-based fault detection and estimation framework for a class of multi-input and multi-output (MIMO) nonlinear distributed parameter systems (DPS) described by partial differential equations (PDE) with actuator and sensor faults. The fault functions cover both abrupt and incipient faults. A Luenberger type observer is used to monitor the health of the DPS as a detection observer on the basis of the nonlinear PDE representation of the system with measured output vector. By taking the difference between measured and estimated outputs from this observer, a residual signal is generated for fault detection. If the detection residual exceeds a predefined threshold, a fault will be claimed to be active. Once an actuator or a sensor fault is detected and the fault type is identified, an appropriate fault parameter update law is developed to learn the fault dynamics online with the help of an additional output measurement. Eventually, the proposed detection and estimation framework is demonstrated on a nonlinear process.
In this paper, we consider the filtering of distributed parameter systems (DPS), i.e., systems governed by partial differential equations (PDE). We adopt a reduced order model (ROM) based strategy to solve the problem...
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ISBN:
(纸本)9781457710964
In this paper, we consider the filtering of distributed parameter systems (DPS), i.e., systems governed by partial differential equations (PDE). We adopt a reduced order model (ROM) based strategy to solve the problem. We propose a randomly perturbed iterative version of the snapshot proper orthogonal decomposition (POD) technique, termed RI-POD, to construct ROMs for DPS that is capable of capturing their global behaviour. Further, the technique is entirely data based, and is applicable to forced as well as unforced systems. We apply the ROM generated using the RI-POD technique to construct reduced order Kalman filters to solve the DPS filtering problem. The methodology is tested on the 1-dimensional heat equation.
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