29.17Review 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.

•Linear equations: any function represented by a straight line on a graph may be represented symbolically by the slope-intercept formula y = mx + b. Relevant to proportional control algorithms.

•Zero shift: any shift in the o set of an instrument is fundamentally additive, being represented by the “intercept” (b) variable of the slope-intercept linear formula y = mx + b. Relevant to controller tuning: adjusting the “bias” of a loop controller always adds to or subtracts from its output signal.

•Span shift: any shift in the gain of an instrument is fundamentally multiplicative, being represented by the “slope” (m) variable of the slope-intercept linear formula y = mx + b. Relevant to controller tuning: adjusting the “gain” of a loop controller always multiplies or divides the response of its output for a given input change.

•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.

•Self-balancing pneumatic mechanisms: all self-balancing pneumatic instruments work on the principle of negative feedback maintaining a nearly constant ba e-nozzle gap. Forcebalance mechanisms maintain this constant gap by balancing force against force with negligible motion, like a tug-of-war. Motion-balance mechanisms maintain this constant gap by balancing one motion with another motion, like two dancers moving in unison.

•Self-balancing opamp circuits: all self-balancing operational amplifier circuits work on the principle of negative feedback maintaining a nearly zero di erential input voltage to the opamp. Making the “simplifying assumption” that the opamp’s di erential input voltage is exactly zero assists in circuit analysis, as does the assumption that the input terminals draw negligible current.

•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. 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.

References

“FOUNDATION Fieldbus”, document L454 EN, Samson AG, Frankfurt, Germany, 2000.

“Identification and Description of Instrumentation, Control, Safety, and Information Systems and Components Implemented in Nuclear Power Plants”, EPRI, Palo Alto, CA: 2001. 1001503.

Kernighan, Brian W. and Ritchie, Dennis M., The C Programming Language, Bell Telephone Laboratories, Incorporated, Murray Hill, NJ, 1978.

Lavigne, John R., Instrumentation Applications for the Pulp and Paper Industry, The Foxboro Company, Foxboro, MA, 1979.

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

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

“Moore 353 Process Automation Controller User’s Manual”, document UM353-1, Revision 11, Siemens Energy and Automation, 2003.

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.

“SPEC 200 Systems”, technical information document TI 200-100, Foxboro, 1980.

“SPEC 200 System Configuration”, technical information document TI 200-105, Foxboro, January 1975.

“SPEC 200 System Wiring”, technical information document TI 200-260, Foxboro, 1972.

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.