barcode reader project in c#.net PROPORTIONAL-INTEGRAL-DERIVATIVE (PID) CONTROL. This mode of in Software

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PROPORTIONAL-INTEGRAL-DERIVATIVE (PID) CONTROL. This mode of
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control is combination of the previous modes and is given by the expression p = K,e+KcrDdt+l dt +ps
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In this case, the controller contains three knobs for adjusting K,, Q, and 71. The transfer function for this controller can be obtained from the Laplace transform of Eq. (10.9); thus
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P(s) = K, l+q,.s+~ E(S)
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(10.10)
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Motivation for Addition of Integral and Derivative Control Modes
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Having introduced ideal transfer functions for integral and derivative modes of control, we now wish to indicate the practical motivation for use of these modes. The curves of Fig. 10.7 show the behavior of a typical, feedback control system using different kinds of control when it is subjected to a permanent disturbance. This may be visualized in terms of the tank-temperature control system of Chap. 1 after a step change in Ti. The value of the controlled variable is seen to rise
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Control action None Proportional Proportional-integral Proportional-integral-derivative
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Response of a typical control system showing the effects of various modes of control.
CONTROLLERS AND FINAL CONTROL ELEMENTS
at time zero owing to the disturbance. With no control, this variable continues to rise to a new steady-state value. With control, after some time the control system begins to take action to try to maintain the controlled variable close to the value that existed before the disturbance occurred. With proportional action only, the control system is able to arrest the rise of the controlled variable and ultimately bring it to rest at a new steady-state value. The difference between this new steady-state value and the original value is called o& . For the particular system shown, the offset is seen to be only 22 percent of the ultimate change that would have been realized for this disturbance in the absence of control. As shown by the PI curve, the addition of integral action eliminates the offset; the controlled variable ultimately returns to the original value. This advantage of integral action is balanced by the disadvantage of a more oscillatory behavior. The addition of derivative action to the PI action gives a definite improvement in the response. The rise of the controlled variable is arrested more quickly, and it is returned rapidly to the original value with little- or no oscillation. Discussion of the PD mode is deferred to a later chapter. The selection among the control systems whose responses are shown in Fig. 10.7 depends on the particular application. If an offset of 22 percent is tolerable, proportional action would likely be selected. If no offset were tolerable, integral action would be added. If excessive oscillations had to be eliminated, derivative action might be added. The addition of each mode means, as we shall see in later chapters, more difficult controller adjustment. Our goal in forthcoming chapters will be to present the material that will enable the reader to develop curves such as those of Fig. 10.7 and thereby to design efficient, economic control systems. SUMMARY In this chapter we have presented a brief discussion of control valves and controllers. In addition, we have presented ideal transfer functions to represent their dynamic behavior and some typical results of using these controllers. The ideal transfer functions actually describe the action of many types of controllers, including pneumatic, electronic, computer-based, hydraulic, mechanical, and electrical systems. Hence, the mathematical analyses of control systems to be presented in later chapters, which are based upon first- and second-order
systems, transportation lags, and ideal controllers, generalize to many branches of the control field. After studying this text on process control, the reader should he able to apply the knowledge to, for example, problems in mechanical control systems. All that is required is a preliminary study of the physical nature of the systems involved. PROBLEMS
10.1. A pneumatic PI controller has an output pressure of 10 psi when the set point and
pen point are together. The set point and pen point are suddenly displaced by 0.5 in. (i.e., a step change in error is introduced) and the following data are obtained:
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