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Unformatted text preview: General Form of Dynamic Models Srinivas Palanki University of South Alabama Srinivas Palanki (USA) General Form of Dynamic Models 1 / 20 General Form of Dynamic Process Models Mathematical Representation A general representation of the dynamic process models derived in the previous lecture is: x 1 = f 1 ( x 1 , x 2 , ..., x n , u 1 , u 2 , ..., u m , p 1 , p 2 , ..., p r ) x 2 = f 2 ( x 1 , x 2 , ..., x n , u 1 , u 2 , ..., u m , p 1 , p 2 , ..., p r ) . . . x n = f n ( x 1 , x 2 , ..., x n , u 1 , u 2 , ..., u m , p 1 , p 2 , ..., p r ) (1) where x i state variable u i input variable p i parameter and the initial conditions of x i are known. Srinivas Palanki (USA) General Form of Dynamic Models 2 / 20 General Form of Dynamic Process Models The above equations are first order nonlinear ordinary differential equations These set of equations are typically solved numerically . Srinivas Palanki (USA) General Form of Dynamic Models 3 / 20 General Form of Dynamic Process Models Definitions State Variable: A state variable is a variable that arises naturally in the accumulation term of a dynamic material or energy balance. A state variable is a measurable (at least conceptually) quantity that indicates the state of system. Examples of state variables include concentrations (from mass balance) and temperature (from energy balance) . Input Variable: An input variable is a variable that normally must be specified before a problem can be solved or a process can be operated. Inputs are normally specified by the engineer based on knowledge of the system. Input variables typically include flowrates of streams entering or leaving the system. Input variables are manipulated to achieve desired performance . Srinivas Palanki (USA) General Form of Dynamic Models 4 / 20 General Form of Dynamic Process Models Parameter: A parameter is typically a physical or chemical property value that must be specified or known to mathematically solve a problem....
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This note was uploaded on 01/07/2011 for the course CHE 452 taught by Professor Dr.srinivaspalanki during the Spring '10 term at S. Alabama.
 Spring '10
 Dr.SrinivasPalanki

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