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CHAPTER
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hat makes control loops behave the way they do Some are fast, some slow; some oscillate, others loll in stability. What determines how well a given variable can be controlled How are the optimum controller settings related to the process These questions must be answered before the reader can feel he really comprehends the essence of the control problem. They will be answered in the pages that follow. Negative feedback is the basic regulating mechanism of automatic systems-but it is not the only mechanism. Feedback has certain limitations which sometimes go unnoticed in the pursuit of better feedback controllers. Yet before progress can be made to more effective systems, the properties of simple feedback loops must be well defined. Fortunately, a process need not be very complicated before the properties of the typical feedback loop make their appearance. A rapid introduction to loop behavior may be presented using the simplest dynamic element found in the process-dead time. This chapter is devoted exclusively to discussion of the control of simple dynamic ele3
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1 Ud erstanding Feedback Control n
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ments which may never exist. in the pure form. But these elements do exist in various proportions in every real process. Therefore a thorough familiarity with the parts is essential for estimating the behavior of the whole.
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NEGATIVE FEEDBACK
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There are two kinds of feedback possible in a closed loop: positive and negative. Positive feedback is an operation which augments an imbalcontroller with ance, thereby precluding &ability. If a temperature positive feedback were used to heat a room, it would increase the heat when the temperature was above the set point and turn it off when it was below. Loops with positive feedback lock at one extreme or the other. Obviously this property is not conducive to regulation and therefore will be of no further concern at this time. Negative feedback, on the other hand, works toward restoring balance. If the temperature is too high, the heat is reduced. The action takenheating-is manipulated negatively, in effect, to the direction of the controlled variable-temperature. Figure 1.1 shows the flow of information in a feedback loop. Throughout the text, c will refer to the controlled variable, r to the reference or set point, e to the error or deviation, and m to the variable manipulated by the controller. Note again that the effect of e, the controller input, is opposite to that of c. This can be looked on as a reversal of phase taking place at the summing junction. All negative feedback controllers exhibit this characteristic-a phase shift of 180 gives the feedback its negative sense.
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Oscillation in the Closed Loop
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Rather than prove that, a feedback loop can oscillate sinusoidally, we shall assume that it does (a common observation) and shall attempt, to find out why. Oscillations are characterized by periodic applications of force in phase with the effect of the last application. In order to bounce a ball, a person must strike it repeatedly at the correct time, otherwise
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Controller
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FIG 1.1. The flow of information is backward from process output through the controller to process input.
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Dynamic Elements in the Control Loop
it will cease to bounce. The correct time turns out to be the correct phase. If the ball is struck at any phase angle other than 360 (of motion) from where it was last struck, the oscillation will be changed. It is apparent, then, that if oscillations are to persist, the shift in phase of a signal after proceeding through the entire loop must be exactly 360 . It has already been pointed out that negative feedback, being negative, introduces 180 of phase shift. This means that if a closed loop is to oscillate, the dynamic elements in the controller and the process must contribute an additional 180 .
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