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By Robert C. Baker

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Sample text

Another case where discrete models of dead time may be important is when digital equipment is used to control continuous time systems. This is a very common situation because, in practice, on many occasions controllers are implemented using microprocessors. For the analysis and design of these discrete controllers two different approaches can be made: (i) Using a continuous design and then computing a discrete approximation of the continuous controller or (ii) using a direct discrete design based on the discrete representation of the continuous process.

U, Y ) plane of operating points This procedure can be repeated for all the operating points obtaining a function Y = f (U ) that represents the static characteristics of the process. In general f (U ) is a nonlinear function. However, if only the behaviour of the process close to one operating point (Up , Yp ) is considered, f (U ) can be approximated by a linear function that uses the tangent of f (U ) at the desired 1 In this book we consider stability in the bounded-input−bounded-output sense, that is, a system is considered stable if for any bounded input its output is also bounded.

Several ideas will be introduced and will be discussed in the following chapters. 1 Dead-time Systems: Some Case Studies In this first section, some examples of dead-time systems are presented. These examples come from different fields and show that dead times are present almost everywhere. 1 A Heated Tank with a Long Pipe Consider a water heater system such as the one shown in Fig. 1. The water is heated in the tank using an electric resistor and driven by a pump along a thermally insulated pipe to the output of the system.

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