30.7Review of fundamental principles

Shown here is a partial listing of principles applied in the subject matter of this chapter, given for the purpose of expanding the reader’s view of this chapter’s concepts and of their general interrelationships with concepts elsewhere in the book. Your abilities as a problem-solver and as a life-long learner will be greatly enhanced by mastering the applications of these principles to a wide variety of topics, the more varied the better.

•Conservation of mass: mass is an intrinsic property of matter, and as such cannot be created or destroyed. Relevant to the mass balance of a process, meaning that all mass flowing into a process must equal all mass flowing out of a process (unless mass is being accumulated or released from the process). This is relevant to the determination of a process’ characteristic as either self-regulating or integrating: whether the mass balance of the process naturally equalizes or not as the process variable changes value.

•Conservation of energy: energy cannot be created or destroyed, only converted between di erent forms. Relevant to the energy balance of a process, meaning that all energy flowing into a process must equal all energy flowing out of a process (unless energy is being accumulated or released from the process). This is relevant to the determination of a process’ characteristic as either self-regulating or integrating: whether the energy balance of the process naturally equalizes or not as the process variable changes value.

•Negative feedback: when the output of a system is degeneratively fed back to the input of that same system, the result is decreased (overall) gain and greater stability. Relevant to loop controller action: in order for a control system to be stable, the feedback must be negative.

•Amplification: the control of a relatively large signal by a relatively small signal. Relevant to the role of loop controllers exerting influence over a process variable at the command of a measurement signal. In behaving as amplifiers, loop controllers may oscillate if certain criteria are met.

•Barkhausen criterion: is overall loop gain is unity (1) or greater, and phase shift is 360o, the loop will sustain oscillations. Relevant to control system stability, explaining why the loop will “cycle” (oscillate) if gain is too high.

•Time constant: (τ ), defined as the amount of time it takes a system to change 63.2% of the way from where it began to where it will eventually stabilize. Also known as the lag time of a system. The system will be within 1% of its final value after 5 time constants’ worth of time has passed (5τ ). Relevant to process control loops, where natural lags contribute to time constants, usually of multiple order.

•Phase shift: the angular di erence between two sinusoidal waves of the same frequency. Relevant to the analysis of controller trend graphs: zero phase shift between PV and Output is the hallmark of proportional action; lagging phase shift is the hallmark of integral action; leading phase shift is the hallmark of derivative action.

•Di erentiation (calculus): where one variable is proportional to the rate-of-change of two others. Di erentiation always results in a positive phase shift if the input is a wave. Relevant

to the output of a controller, for determining by (leading) phase shift whether derivative action is dominant.

•Integration (calculus): where one variable is proportional to the accumulation of the product of two others. Integration always results in a negative phase shift if the input is a wave. Relevant to the output of a controller, for determining by (lagging) phase shift whether integral action is dominant.

References

Lipt´ak, B´ela G. et al., Instrument Engineers’ Handbook – Process Control Volume II, Third Edition, CRC Press, Boca Raton, FL, 1999.

McMillan, Greg, “Is Wireless Process Control Ready for Prime Time?”, Control, May 2009, pp. 54-57.

Mollenkamp, Robert A., Introduction to Automatic Process Control, Instrument Society of America, Research Triangle Park, NC, 1984.

Palm, William J., Control Systems Engineering, John Wiley & Sons, Inc., New York, NY, 1986. Shinskey, Francis G., Energy Conservation through Control, Academic Press, New York, NY, 1978.

Shinskey, Francis G., Process-Control Systems – Application / Design / Adjustment, Second Edition, McGraw-Hill Book Company, New York, NY, 1979.

St. Clair, David W., Controller Tuning and Control Loop Performance, a primer, Straight-Line Control Company, Newark, DE, 1989.

Ziegler, J. G., and Nichols, N. B., “Optimum Settings for Automatic Controllers”, Transactions of the American Society of Mechanical Engineers (ASME), Volume 64, pages 759-768, Rochester, NY, November 1942.