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Barcode Reader In C#.NET Using Barcode scanner for Visual Studio .NET Control to read, scan read, scan image in .NET applications. Painting USS Code 128 In ObjectiveC Using Barcode encoder for iPhone Control to generate, create Code128 image in iPhone applications. forward, the resulting linear model can only be used over a narrow range of variables. The analysis of the gas absorber gave some insight into the dynamic character of a typical multistage process that is widely used in the chemical process industries. A linear analysis of an nplate column leads to IZ ordinary differential equations, which combine to give an overdamped nthorder response. Nonlinearities may be present in this system in such forms as a product of flow and concentration or a nonlinear equilibrium relationship. When changes in inlet flow occur, a set of differential equations describing the dynamics of the liquid flow must be added to those describing mass transfer. When the change of plate efficiency with flow is considered, the model of a gas absorber becomes even more complex. Most of the design techniques developed in the past for multistage operations (gas absorption, distillation, etc.) have applied to steadystate operation. The dynamic analysis of such processes calls for dynamic parameters that are usually unavailable. For example, the liquidflow dynamics of trays used in distillation towers are relatively unknown. The discussion of distributedparameter systems further illustrated the complexities that can arise in physical systems. The distributedparameter systems lead to partial differential equations, which may be very difficult to solve for most of the forcing functions of practical interest. However, we saw that the response of distributedparameter systems to sinusoidal forcing functions can be obtained directly by application of the substitution rule, in which s is replaced by jw. A distributedparameter system features nonminimum phase lag characteristics. This is in sharp contrast to the lumpedparameter systems for which the phase angle approaches a limit at infinite frequency. As systems are analyzed in mom detail and with fewer assumptions, the models that describe them become more complex, although more accurate. To predict the response of the system from the model requires that equations of the model be solved for some specific input disturbance. The only practical way to solve a complex model is to use a computer. This method of solving the mathematical model is often called computer simulation. The computer response will resemble that of the physical system if the model is accurate. In the last section of this text, the computer and its use to simulate control systems will be discussed in considerable detail.

