Temperature Control Theory Essay Research Paper Process — страница 3

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Process systems that are inherent to experience high frequency random fluctuations, such as flow processes, will be adversely affected by derivative action. This arises from the general nature of the derivative action. Any high frequency, random fluctuations will result in a derivative of the controlled variable which acts in an unrestrained fashion. Consequently, derivative action will amplify the noise of a system [4]. A low-pass filtering device, such as a mixing tank can lessen this effect. The combination of proportional, integral, and derivative control results in the three-mode proportional-plus-integral-plus-derivative controller (PID) [4]. Here as stated before the derivative action allows the controller to predict the future behavior of the error signal. Consider the

following situation. The inlet temperature to a process, TI(t) begins to decrease and by consequence the outlet temperature, T(t) does likewise, as depicted in Figure IV. At ta there exist a positive error, which is small. Thus the control action provided by the integral controller is small. Examining the error plot versus time, at time ta, the derivative of the error is large and positive. The PID controller notices the large slope of the error curve, and attempts to adjust the output in such a way as to correct an out of control process. At tb the error is positive and greater than the error at ta. Moreover in addition to the excess action taken by the derivative mode, the controller output is also being further saturated from the increased response of the integral and

proportional modes. The slope of the error curve at tb however is negative and the derivative mode begins to subtract from the other two control elements. As a result of this affair the system takes longer to reach the set point. Previously, only the design of a controller has been considered. Although this is an important element, in order for a controller to be effective, it must be fitted appropriately to the process at hand. This is commonly referred to as tuning. Only the qualitative aspects of tuning will be considered. Recall that Kc=100/PB. Generally, an increase in the gain, Kc, will tend to cause the controller to react faster, but if the gain is too large the response could display an unwanted undulation and lead to instability [4]. Usually some median value for Kc is

preferred to optimize the proportional control. This approach is effective for both PI and PID controllers. Decreases in the reset rate (recall the definition of reset rate),I, will cause the controller to respond slowly and sparingly. For very small values of I, the controlled variable will return very slowly to the set point upon any system load perturbations or set point changes [4]. A qualitative generalization regarding the affect of the derivative rate, D, is more complicated. Ordinarily small values for D rectify the response by offsetting large error deviations, reducing the response time, and reducing the degree of oscillatory response. Large values of D, usually amplify noise and should be avoided. Commonly just as with the proportional gain, a median

value for D is chosen. References 1) Shilling, David G. Process Dynamics and Control, Holt, Rinehart, and Winston, Inc. New York, NY, 1963. 2) Babatunde, A. Ogunnaike; Ray, W. Harmon. Process Dynamics, Modeling, and Control, Oxford University Press, New York, NY, 1994. 3) Stephanopoulos, George. Chemical Process Control: An Introduction to Theory and Practice, Prentice Hall, Englewood Cliffs, NJ, 1984. 4) Seborg, Dale E.; Edgar, Thomas F.; Mellichamp, Duncan A. Process Dynamics and Control, John Wiley and Sons, Inc. New York, NY, 1989. 5) Smith, Carlos A.; Corripio, Armando B. Principles and Practice of Automatic Process Control, John Wiley and Sons, New York, NY, 1985. 6) Perry, Robert H.; Green, Don W.; Maloney, James O.; Perry s Chemical Engineers Handbook, 7th ed,

McGraw-Hill, New York, NY, 1997.