A simple method for simulating gasdynamic systems

A simple method for performing digital simulation of gasdynamic systems is presented. The approach is somewhat intuitive, and requires some knowledge of the physics of the problem as well as an understanding of the finite difference theory. The method is explicitly shown in appendix A which is taken from the book by P.J. Roache, 'Computational Fluid Dynamics,' Hermosa Publishers, 1982. The resulting method is relatively fast while it sacrifices some accuracy

Temperature control in continuous furnace by structural diagram method

The fundamentals of the structural diagram method for distributed parameter systems (DPSs) are presented and reviewed. An example is given to illustrate the application of this method for control design

A hierarchy for modeling high speed propulsion systems

General research efforts on reduced order propulsion models for control systems design are overviewed. Methods for modeling high speed propulsion systems are discussed including internal flow propulsion systems that do not contain rotating machinery, such as inlets, ramjets, and scramjets. The discussion is separated into four areas: (1) computational fluid dynamics models for the entire nonlinear system or high order nonlinear models; (2) high order linearized models derived from fundamental physics; (3) low order linear models obtained from the other high order models; and (4) low order nonlinear models (order here refers to the number of dynamic states). Included in the discussion are any special considerations based on the relevant control system designs. The methods discussed are for the quasi-one-dimensional Euler equations of gasdynamic flow. The essential nonlinear features represented are large amplitude nonlinear waves, including moving normal shocks, hammershocks, simple subsonic combustion via heat addition, temperature dependent gases, detonations, and thermal choking. The report also contains a comprehensive list of papers and theses generated by this grant

Approximate truncated balanced realizations for infinite dimensional systems

This paper presents an approximate method for obtaining truncated balance realizations of systems represented by non-rational transfer functions, that is infinite dimensional systems. It is based on the approximation to the Hankel operator

Anterior Hippocampus and Goal-Directed Spatial Decision Making

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Physical lumping methods for developing linear reduced models for high speed propulsion systems

In gasdynamic systems, information travels in one direction for supersonic flow and in both directions for subsonic flow. A shock occurs at the transition from supersonic to subsonic flow. Thus, to simulate these systems, any simulation method implemented for the quasi-one-dimensional Euler equations must have the ability to capture the shock. In this paper, a technique combining both backward and central differencing is presented. The equations are subsequently linearized about an operating point and formulated into a linear state space model. After proper implementation of the boundary conditions, the model order is reduced from 123 to less than 10 using the Schur method of balancing. Simulations comparing frequency and step response of the reduced order model and the original system models are presented

A Method for Generating Reduced Order Linear Models of Supersonic Inlets

For the modeling of high speed propulsion systems, there are at least two major categories of models. One is based on computational fluid dynamics (CFD), and the other is based on design and analysis of control systems. CFD is accurate and gives a complete view of the internal flow field, but it typically has many states and runs much slower dm real-time. Models based on control design typically run near real-time but do not always capture the fundamental dynamics. To provide improved control models, methods are needed that are based on CFD techniques but yield models that are small enough for control analysis and design

The role of syllable structure in verbal short-term memory

Remembering the sound of a new word when it is first encountered is an important skill which plays a critical role in the development of vocabulary (Gathercole & Baddeley, 1989), yet the mechanisms underlying this form of verbal short-term memory are not well understood. Errors in the repetition and serial recall of nonwords indicate that structural properties of the syllable are represented in short-term memory, but existing accounts of serial learning and recall do not incorporate any representation of linguistic structure. Models of speech production implicate syllable structure in the representation of phonological form, but do not explain how such representations are acquired. This thesis draws together theories of speech production and serial memory to develop a computational model of nonword repetition based on the novel idea that short-term memory for the serial order of a sequence of speech sounds is constrained by a syllabic template. The results of simulations using the model are presented and compared with experimental findings concerning short-term memory for nonwords. The interaction of short- and long-term phonological memory systems and the aquisition of vocabulary are discussed in terms of the model. The model is evaluated in comparison with other contemporary theories

Intitialization, Conceptualization, and Application in the Generalized Fractional Calculus

This paper provides a formalized basis for initialization in the fractional calculus. The intent is to make the fractional calculus readily accessible to engineering and the sciences. A modified set of definitions for the fractional calculus is provided which formally include the effects of initialization. Conceptualizations of fractional derivatives and integrals are shown. Physical examples of the basic elements from electronics are presented along with examples from dynamics, material science, viscoelasticity, filtering, instrumentation, and electrochemistry to indicate the broad application of the theory and to demonstrate the use of the mathematics. The fundamental criteria for a generalized calculus established by Ross (1974) are shown to hold for the generalized fractional calculus under appropriate conditions. A new generalized form for the Laplace transform of the generalized differintegral is derived. The concept of a variable structure (order) differintegral is presented along with initial efforts toward meaningful definitions

A Solution to the Fundamental Linear Fractional Order Differential Equation

This paper provides a solution to the fundamental linear fractional order differential equation, namely, (sub c)d(sup q, sub t) + ax(t) = bu(t). The impulse response solution is shown to be a series, named the F-function, which generalizes the normal exponential function. The F-function provides the basis for a qth order "fractional pole". Complex plane behavior is elucidated and a simple example, the inductor terminated semi- infinite lossy line, is used to demonstrate the theory