a General symbol for an arbitrary constant

a Symbol for a cross-sectional area [p. 7]

b Symbol for a dimension, usually thickness [p. 7]

b Primary feedback (units of e) [p. 92]

b2 Secondary feedback [p. 100]

e Actuating signal (volts or p.s.i.g., or mm of motion, etc.) [p. 92]

e1, e2 specific values of e [p. 95]

f General symbol for a function, i.e., f(t) is a function of time

{fn(t)}n=1,2,…. Q Ensemble of functions of time [p. 37]

f Frequency (Hz) [p. 64]

fq DEC frequency (Hz) [p. 135]

{gn(t)}n=1,2,… Q Ensemble of responses to {fn(t)} [p. 37]

h General symbol for heat flow (Btu/sec) [p. 4]

hmax maximum heat flow (Btu/sec) [p. 70]

hL Heat loss at conveyor apertures (Btu/sec) [p. 76]

hS Heat loss at stack (Btu/sec) [p. 76]

h(t) Unit step function [p. 17]

i General symbol for an input [p. 28]

io Amplitude of a periodic input, i.e., i = io sin ωt [p. 28]

j

m Manipulated variable (numeric) [p. 70]

mh, mc, mc2 Manipulated variable in the heating and cooling functions of heating-cooling process control [pp. 116, 117]

Mean value of m(t) in DEC (numeric) [p. 135]

mn Where 1 < n < Q. Intermediate value of manipulated variable in a Q position system, i.e., 0 < mn < +1 (numeric) [p. 165]

mQ(=0) Lowest value of manipulated variable in a Q position system (numeric) [p. 180]

n The general term in an ensemble

p Magnitude of the deadspace in a multiposition controller (units of e) [p. 153]

q Quantity of heat (Btu) [p. 4]

q Magnitude of the lost motion in the characteristic of a discontinuous control element (units of e) [p. 100]

q′ (=q/H1) Magnitude of lost motion rated in units of the controlled variable θ (units of θ) [p. 106]

δq Small increment in the lost-motion magnitude (units of θ) [p. 104]

r Reference input (units of e) [p. 92]

s Laplace complex variable (= ζ + jω) (sec−1) [p. 41]

t General symbol for time (usually, sec) Note: θ(t) indicates θ as a time-varying function; similarly, m(t), etc.

ta Time of switching operation (sec) [p. 23]

tc Cooling time (sec) [p. 134]

te Elapsed time since last switching operation (sec) [p. 71]

teo, teq Auxiliary cycling time variables in a quasicontinuously controlled process (sec) [p. 171]

th Heating time (sec) [p. 134]

to On time (sec) [p. 134]

tp Off time (sec) [p. 134]

tq Periodic time (sec) [p. 135]

tq Minimum value of tq (sec) [p. 145]

ty Time corresponding to temperature θy (sec) [p. 83]

Δ1t−Δ4t, etc. Arbitrary increments in t that correspond with increments

Δ1θ−Δ4θ, etc. in θ (sec) [p. 83]

Δot Overshoot recovery time (sec) [p. 134]

Δut Undershoot recovery time (sec) [p. 134]

u Disturbance input (units of θ) [p. 79]

v (=ωT) Algebraically convenient variable for frequency of a periodic input [p. 55]

x General symbol for a dimension [pp. 64, 65]

x An arbitrary constant [p. 84]

y (= θr− θ) Error in the control of a process (units of θ) [p. 107]

Mean value of y in DEC [p. 124]

yd Error due to overcompensated secondary feedback (b2 > q). A component of y (units of θ) [p. 114]

yp Error due to deadspace magnitude p (units of θ) [p. 180]

z Arbitrary constant [p. 18]

Switching condition for bang-bang controllers (numeric) [p. 159]

zi Incoming quality level [p. 163]

zo Outgoing quality level [p. 163]

A Amplitude of a phasor [p. 29]

A RIE sensitivity (units of e and units of θ) [p. 91]

A Conveyor aperture area (ft2) [p. 76]

AS Actuating signal comparator [p. 92]

B Arbitrary constant [p. 67]

Btu British thermal unit

C Thermal capacitance (Btu/°F) [p. 4 et seq.]

Cn(n = 1, 2, …) Thermal capacitance at specified locations (Btu/°F) [p. 59]

Cc Capacitance of coating [p. 61]

Cm Capacitance of mercury [p. 61]

CE Control element [p. 92]

D(d/dt) Heaviside operator [p. 4 et seq.]

D Block-diagram symbol for a control element’s characteristic [p. 92]

DEC Dynamic equilibrium cycling [p. 111 et seq.]

G General symbol for a forward transfer function [p. 56]

G(D) Transfer operator [p. 35]

G(s) Transform of transfer function [p. 42]

G(jω) Transfer function [p. 35]

H General symbol for feedback transfer function

H1 PFE sensitivity (units of e and units of θ) [p. 92]

H2 SFE sensitivity (units of θ) [p. 100]

J Imaginary component [p. 35]

K1, K2 Arbitrary constants [pp. 77, 86 et seq.]

L Arbitrary dimension [p. 75]

Laplace transform [p. 43]

M Mass (lb) [p. 4 et seq.]

N Disturbance-input element attenuation (numeric) [pp. 76,...