Dynamic Behavior of Processes

Friedly, John C.; Foss, Alan S.

doi:10.1115/1.3426731

Cited by 32 publications

(33 citation statements)

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“…As the frequency increases, this effect repeats itself, which can be observed as oscillations on the Bode plot or as characteristic ''loops'' on the Nyquist plot. These oscillations are closely associated with the wave phenomena taking place inside the exchanger pipes [14].…”

Section: Frequency Responsesmentioning

confidence: 99%

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Transfer function-based analysis of the frequency-domain properties of a double pipe heat exchanger

Bartecki

2014

Heat Mass Transfer

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This paper discusses irrational transfer function representation for a typical thick-walled double pipe heat exchanger. Closed-form analytical expressions for the individual elements of 2 9 2 transfer function matrix are derived both for the parallel-and the counter-flow configurations using the Laplace transform method. Based on the transfer function representation, its frequency responses are demonstrated both in the form of three-dimensional graphs as well as classical, two-dimensional Bode and Nyquist plots. Finally, steady-state temperature profiles are presented and compared for both flow arrangements considered.

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Section: Frequency Responsesmentioning

confidence: 99%

“…Considering as an example the Bode plot, the expressions for the logarithmic gain and phase take the following wellknown form [14]:…”

Section: Frequency Responsesmentioning

confidence: 99%

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Transfer function-based analysis of the frequency-domain properties of a double pipe heat exchanger

Bartecki

2014

Heat Mass Transfer

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“…Finding the inverse Laplace transform of (68) and (69) with respect to q by taking advantage of the following property (Friedly, 1972): where S(q) and T (q) represent polynomials in q of degree M and N > M, respectively, and λ j is a single root of T (q), yields the following form of the equations:…”

Section: Analytical Expressions For the Transfer Functions Propositimentioning

confidence: 99%

“…In practice, almost all industrial processes fall into this category, while the existence of the so-called Lumped Parameter Systems (LPSs) results mainly from the adoption of a simplified model of the reality, in which spatial effects are neglected or averaged. Typical examples of a DPS include heat transfer and fluid flow phenomena, as well as processes occurring in chemical reactors, semiconductor manufacturing, polymer processing, air pollution monitoring and many others (Friedly, 1972;Wu and Liou, 2001;Bounit, 2003;Bartecki, 2007;Zavala-Rio et al, 2009;Li and Qi 2010;Ucinski, 2012;Patan, 2012).…”

Section: Introductionmentioning

confidence: 99%

A general transfer function representation for a class of hyperbolic distributed parameter systems

Bartecki

2013

International Journal of Applied Mathematics and Computer Science

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Results of transfer function analysis for a class of distributed parameter systems described by dissipative hyperbolic partial differential equations defined on a one-dimensional spatial domain are presented. For the case of two boundary inputs, the closed-form expressions for the individual elements of the 2×2 transfer function matrix are derived both in the exponential and in the hyperbolic form, based on the decoupled canonical representation of the system. Some important properties of the transfer functions considered are pointed out based on the existing results of semigroup theory. The influence of the location of the boundary inputs on the transfer function representation is demonstrated. The pole-zero as well as frequency response analyses are also performed. The discussion is illustrated with a practical example of a shell and tube heat exchanger operating in parallel-and countercurrent-flow modes.

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Model reduction and the design of reduced‐order control laws

1974

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This paper is concerned with the problem of designing satisfactory loworder (incomplete state feedback) controllers starting with a high-order, state-space model. Two design approaches are considered: the control law reduction technique, recently developed by the authors (Wilson et al., 19731, and the well-known model reduction approach. These two design techniques are used to develop a variety of low-order controllers for a double-effect evaporator starting with a 10th-order model. Experimental and simulated response data from the computer-controlled evaporator demonstrate the superiority of the control law reduction approach in this application. It is also shown that several of the previously published modal approaches to model reduction are basically equivalent since they yield identical reduced-order models. ROBERT SCOPEIn many practical applications of modern control theory the most difficult problem is to obtain a suitable process model. An analytical approach using basic chemical engineering principles often results in a dynamic model which consists of a large number of nonlinear differential equations. The model is usually too complicated for use in controller design or for implementation as part of the actual control system. Consequently, for purposes of control system design it is common practice to linearize the model and assume time-invariant behavior. Fortunately, the resulting linear "state-space model" (that is, a set of firstorder differential equations) will usually adequately describe the process transients in the region of normal operation and provide a suitable basis for control system design. However, many of the multivariable control design techniques (Gould, 1969) result in a control law that requires the availability of all elements of the state vector. Such control laws are frequently impractical because of their complexity and because in many applications it is not practical to measure or estimate all of the state variables. Hence there has been widespread interest in developing control laws that require only a subset of the state vector to be available. The resulting controllers are usually referred to as incomplete state feedback or low-order controllers.This investigation is concerned with the problem of designing a satisfactory low-order, multivariable controller starting with a high-order, state-space model of a process. To be judged satisfactory, the low-order controller should perform almost as well as more complicated high-order (state-feedback) controllers. Emphasis is placed on discrete process models and discrete controllers since they are more convenient than their continuous counterparts for on-line implementation via digital process computers. Two basic approaches were used to design loworder controllers:1. Model Reduction Approach. The original high-order model is simplified using a modal analysis to eliminate selected state variables, that is, to reduce the order of the model. The resulting low-order model then serves as a basis for designing a low-order controller usin...

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Dynamic Behavior of Processes

Cited by 32 publications

References 0 publications

Transfer function-based analysis of the frequency-domain properties of a double pipe heat exchanger

Transfer function-based analysis of the frequency-domain properties of a double pipe heat exchanger

A general transfer function representation for a class of hyperbolic distributed parameter systems

Model reduction and the design of reduced‐order control laws

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