PE Control Systems cheat sheet

4-20 mA loop: 4 mA = 0 % of span (live zero) and 20 mA = 100 %; 0 mA indicates an open circuit, and NAMUR NE43 treats <3.6 mA or >21 mA as a fault.

Differential-pressure flow element: Q = Cd·Ao·sqrt(2·dP/rho); flow is proportional to the square root of dP, so the transmitter or DCS must apply square-root extraction to linearize.

Pt100 RTD: 100 ohms at 0 degC with alpha about 0.00385 ohm/ohm/degC; usable roughly -200 to 650 degC, more accurate and stable than base-metal thermocouples.

Thermocouple type K (Chromel-Alumel, -200 to 1260 degC), J (iron-constantan), T (copper-constantan, cryogenic); output is a small mV Seebeck voltage and requires cold-junction compensation.

Thermocouples use matching extension wire; RTDs use 3-wire or 4-wire connections to cancel lead resistance; analog signals are shielded, twisted pair grounded at one end.

Magnetic flowmeters need a conductive liquid (typically >5 microsiemens/cm), a full pipe, and grounding; they cannot measure hydrocarbons or gases but add no flow obstruction.

Coriolis meters measure mass flow and density directly at about 0.1 % accuracy with no straight-run requirement; vortex meters obey f = St·v/d and need adequate Reynolds number.

Level by differential pressure follows dP = rho·g·h; radar/ultrasonic use time of flight d = c·t/2; displacer units infer level from buoyancy force on a torque tube.

Accuracy stated as percent of span is worse than percent of reading at low signal; turndown (rangeability) = maximum usable reading / minimum usable reading.

Ideal (ISA) PID: u = Kc[e + (1/Ti) integral(e dt) + Td·de/dt]; the parallel form uses independent Kp, Ki, Kd, so always confirm which form a tuning rule assumes.

First-order-plus-dead-time model: G(s) = K·exp(-theta·s)/(tau·s + 1); a dead-time-to-time-constant ratio theta/tau above about 1 limits PID performance and favors feedforward or a Smith predictor.

Ziegler-Nichols continuous cycling PID: Kc = 0.6·Ku, Ti = Pu/2, Td = Pu/8, where Ku is the ultimate gain and Pu the ultimate period; the result is aggressive and oscillatory.

Second-order closed loop: overshoot = exp(-pi·zeta/sqrt(1-zeta^2)); zeta = 1 is critically damped, zeta about 0.7 gives roughly 5 % overshoot, and settling time is about 4/(zeta·omega_n).

Closed-loop stability requires all poles in the left half-plane; the Routh-Hurwitz array gives the stability limit without factoring, and the final value theorem shows integral action removes steady-state offset.

Bode criteria: gain margin is the gain in dB at -180 deg phase, phase margin is the degrees above -180 deg at 0 dB crossover; common targets are GM of 6 dB or more and PM of 45 to 60 deg.

Integral (reset) eliminates offset but adds phase lag; derivative adds lead but amplifies noise, so it is applied to the measurement and filtered with a time constant of roughly Td/8 to Td/10.

Cascade control requires the secondary loop to be at least three to five times faster than the primary, and normally only the primary controller carries integral action.

Feedforward acts on a measured disturbance before error develops; it needs a process model and is always paired with feedback to correct model mismatch and unmeasured disturbances.

Liquid valve sizing: Cv = Q·sqrt(SG/dP) with Q in gpm and dP in psi; gas and steam sizing add the expansion factor Y and compressibility factor Z.

Inherent characteristics are linear, equal percentage, and quick opening; the installed characteristic is the inherent curve modified by how pressure drop varies across the valve with flow.

Equal-percentage trim is the usual default for throttling because it offsets the falling valve pressure drop at high flow, yielding a nearly linear installed characteristic.

Fail-safe action is set by the process safe state: air-to-open actuators with spring return fail closed on air loss, air-to-close actuators fail open.

Cavitation occurs when pressure at the vena contracta drops below vapor pressure and bubbles collapse downstream; allowable dP = FL^2·(P1 - Ff·Pv). Flashing occurs when downstream pressure stays below vapor pressure.

Choked flow is reached when dP exceeds FL^2·(P1 - Ff·Pv); beyond that point additional downstream capacity does not increase flow.

A positioner compares the controller signal with actual stem position and corrects for friction and unbalanced force; an I/P transducer converts 4-20 mA to a 3-15 psi air signal.

Valve rangeability is typically 30:1 to 50:1 for globe valves; oversized valves run near the seat where control is poor, so size for about 60 to 80 % travel at maximum design flow.

Stiction and dead band come from packing friction and actuator hysteresis; they cause limit cycles that no amount of retuning removes, so the valve must be repaired or a positioner added.

Three-element boiler drum level control uses drum level as the feedback trim, steam flow as feedforward, and feedwater flow as the inner loop, which compensates for shrink and swell during load swings.

Compressor anti-surge control opens a recycle valve as flow approaches the surge line; surge is a flow reversal that can destroy thrust bearings within seconds.

pH control is strongly nonlinear near neutrality; the titration gain changes by orders of magnitude, so gain scheduling, reagent split-ranging, or adaptive control is required.

Fired heaters use fuel/air ratio control with cross-limiting: air leads on load increase and fuel leads on load decrease, with O2 trim for combustion efficiency.

Distillation columns are usually controlled by fixing column pressure first, then trimming a tray temperature with reflux flow or reboiler steam; online analyzers are slow and need fast backup feedback.

Exothermic reactors are commonly controlled with a jacket-temperature cascade; loss of cooling is a design-basis hazard, so the cooling valve must fail safe and interlocks must trip feed.

Shell-and-tube heat exchangers have long dead time, so control is usually PI on utility flow or bypass with derivative action avoided; feedforward from process flow improves response.

Selective (auctioneering) control takes the high or low of several controller outputs, for example overriding compressor suction pressure or protecting a pump near the end of its curve.

Ratio control holds one flow at a fixed multiple of a measured wild flow, as in fuel/air, reagent/reactant, and reflux/feed applications.

ISA-5.1 tag: the first letter is the measured or initiating variable (F flow, T temperature, P pressure, L level, A analysis) and later letters give the function (T transmitter, C controller, V valve, I indicator), e.g., FIC-101.

Low-demand SIL bands per IEC 61511 (PFDavg): SIL 1 = 10^-2 to 10^-1, SIL 2 = 10^-3 to 10^-2, SIL 3 = 10^-4 to 10^-3, SIL 4 = 10^-5 to 10^-4.

PFDavg approximations: 1oo1 = lambda_DU·TI/2; 1oo2 is roughly (lambda_DU·TI)^2/3; 2oo3 is roughly (lambda_DU·TI)^2 - redundancy and shorter proof-test intervals reduce PFDavg.

A safety instrumented system must be independent of the basic process control system, with separate sensors, logic solver, and final elements; shared final elements need justification and additional proof testing.

Hazardous location classes: Class I gases and vapors, Class II dusts, Class III fibers; Division 1 means the hazard is present in normal operation and Division 2 only in abnormal cases; Zones 0, 1, 2 are the IEC equivalents.

Protection methods include explosion-proof enclosures (contain the flame), intrinsic safety (limit energy), purging and pressurization, and encapsulation; intrinsic safety is the only method generally accepted for Zone 0.

The safety lifecycle runs PHA/HAZOP, LOPA, SIL assignment, safety requirements specification, design and verification, installation and validation, operation and proof testing, then decommissioning.

Signal wiring practice: shields grounded at one end to prevent ground loops, instrument cable routed separately from power cable, and a 24 V loop driving 4-20 mA tolerates roughly 250 to 600 ohms of total loop resistance.

Lockout/tagout and energy isolation are required before servicing actuators; spring-return actuators store mechanical energy and must be vented, restrained, or blocked before disassembly.