By Robert C. Baker
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Additional resources for Linear Electronics in Control Systems
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.