Hold elements

Thankfully, the container holding element l was not destroyed in the accident because this element can be quite poisonous when inhaled. 

Residual. This fraction mainly contains primary and secondary minerals, which hold elements within their crystal structure. This fraction also contains trace elements remained from the extraction of all previous fractions (e.g., humin bound). These metals/trace elements are not expected to be released into soil solutions over a reasonable time span under conditions normally encountered in nature. 

Theoretically there is no output from a sampler between sampling times (Fig. 7.88c). In practice the sampler output is controlled between samples by a filter or hold element. The most common type of filter is the zero-order hold element (ZOH) in which the value of the previous sample is retained until the next sample is taken (Fig. 7.92a). 

Fig. 7.92. Control loop containing a sampler and a zero-order hold element (a) block diagram (b) output of hold element (filter)...

As f (s) is the Laplace transform of the output of the sampler without the ZOH, the remaining term must represent the Laplace transform for the zero-order hold element, i.e. ... 

Gzoh Transfer function of zero order hold element — —... 

Supervisory control and data acquisition Solid-state relay Self-tuning regulator Temperature recorder controller Transistor-transistor logic Zero order hold element... 

Gold, like all metals, is shiny, malleable, ductile, and a good conductor of electricity and heat. Unlike most metals and other elements, however, gold is found in nature in its pure form, as an element. Most elements are chemically combined in the form of compounds. Why is this so Why do atoms of some elements join together as compounds, while others do not In this chapter, you will use the periodic trends you examined in Chapter 2 to help you answer these questions. You will learn about the bonds that hold elements together in compounds. At the same time, you will learn how to write chemical formulas and how to name compounds. 

Figure 10 Some models are made by gluing pieces together. The glue that holds elements together in a chemical compound is the chemical bond. 

The control commands produced by the control program are digital and discrete-time signals. They are first converted to analog by a D/A converter and then to continuous-time signals by simple hold elements before they actuate the final control elements. 

Equation (27.4) yields the first-order hold, and the continuous signal it produces is shown in Figure 27.5c. Notice that the first-order hold element needs at least two values to start construction of the continuous signal, whereas the zero-order hold needs only one. 

It is possible to develop second-, third-, or higher-order hold elements. They need three, four, or more initial discrete-time values before they can start the construction of a continuous signal. As the order of a hold element increases, the computational load increases and becomes more complex, with marginal improvements in the quality of the reconstructed signal. Therefore, for most process control applications the zero-order hold element provides satisfactory results with low computational load and is normally used. To improve the quality of a reconstructed signal, it is better to decrease the period between two successive discrete-time values rather than increase the order of the hold element. 

Example 27.4 Comparing the Results of Zero- and First-Order Hold Elements... 

The mathematical basis behind the construction of a hold element, independently of its order, is the following Consider the continuous signal m(t), which must be constructed from discretetime values m(T), m(2T), m(3T), and so on. The Taylor series of m(t) around a sampled value m(nT) is given by... 

If we retain only the zero-order term (i.e., the constant) we take the zero-order hold element [eq. (27.3)],... 

Thus we take the first-order hold element [eq. (27.4)]... 

Similarly, by retaining additional terms—second order, third order, and so on—we can develop higher-order hold elements. All necessary derivatives will be numerically approximated as above, but they will require an increasing number of discrete-time values. 

The output of a zero-order hold element is like a pulse, having a constant height equal to m(nT) and duration T. After recalling that the Laplace transform of a unit pulse is given by eq. (7.12),... 

Process with the hold element (Figure 29.1b) These are the continuous elements of the DDC loop. The relatonship between the continuous manipulated variable m(t) and continuous output y(t) can be expressed in terms of conventional transfer functions in the Laplace domain. But how can we describe the sampled-... 

The output of the hold element to the impulse c (0) depends on the order of the hold element. For a zero-order hold element its output is a pulse of height c(0) and duration T (Figure 29.5a). This pulse is the input to the process and produces the output MO shown in Figure 29.5b. How can we compute this output ... 

Invert the last equation and find the response of the process output in the time domain, for an impulse input of strength c(0) in the hold element ... 

It is interesting to find out what the process output would have been if a sequence of impulses entered a continuous process directly without passing through a hold element. Consider the case of a first-order lag but without the hold element (Figure 29.8a). Then the pulse transfer function is given by... 

Figure 29.8 (a) First-order lag without hold element (b) its discrete-time response to unit step input. 

VII.25 Compute the discrete-time, closed-loop response to unit step changes in the load for each of the systems described in Problem VII.24. Assume zero-order hold element and sampling period T = 1 sec. 

High selector switch, 403, 404, 405 Hold elements, 558, 576-81 Hot spot, 405... 

How should we reconstruct a continuous signal from its discretetime equivalent so that we can actuate the final control elements How does the type of reconstruction (i.e., type of hold element) affect the quality of control ... 

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