Answers to Problems I 353 10.4 A feedback optimizing controller must be used to hold minimum con- ductivity, but the process must be made self-regulating first. This can be accom- plished by feeding solvent from one storage tank while flowing into another, switching when the feed t,ank is empty. 10.5 i2t neutrality, the pH is 9.366. The slope of the curve at that point is 9,330. 10.6 Equation (10.22) and the answers to Prob. 10.2 and 10.3 indicate that the dynamic gain is independent of temperature and concentration. Chapter 11 11.1 For V/F = 5, D/Ii’ = 0.471, x = 0.0822, dy/d(D/P) = -0.5. 11.2 For V/F = 2.5, D/F = 0.393, x = 0.196, dy/d(D/F) = -0.2. 11.3 For constant V/P, B = F(1 - z)/(l - z). For constant V, B = F[l - ?,(a - bF)]. 11.4 Let z1 and z2 be the mole fractions of propane and isobutane, respectively, in the feed; then D = 1f(0.929z1 + 0.912z2 + 0.068). 11.5 Optimum V/F for z = 0.50 is about 8. 11.6 Optimum V/I;’ for 2 = 0.60 is about 7; V/F can be programmed with z or with D/b’ as shown in Fig. 11.20. 11.7 h,l, = 0.688. Chapter 12 IQ.1 Lim y = Kw, Lim y = z; Lim x = w, Lim x = z/K. L/F+CC L/F+0 L ,'F+ m L /F+ 0 12.2 Relative humidity is 64 percent. 12.3 -1 maximum of 2.907 lb of water is vaporized for every pound of steam condensed. d masimum of 5.814 lb of solution can be fed for each pound of steam. 12.4 Mother liquor to feed ratio is 0.535 lb/lb. 12.5 Heavy distillate is O.O21F, light distillate is 0.709P; reflus is 0.54F, and vapor flow is 1.27E’. 12.6 Heavy distillate is manipulated to control interface level in the decanter. Because reflus flow is less than that of light distillate, it can be accurately manipu- lated for composition control; decanter level is then controlled by manipulation of light distillate. Vapor and reflus flow interact in their effect on bottoms com- position. They can be determined from feed composition by I’ = F(9zc - ze), L = 1’(8zc - 22B). Two bottoms-composition controllers are necessary, their outputs mn and mc taking the place of the unknown feed compositions in the pre- vious equations. Then the decoupling control system manipulates heat input and reflus with a forward loop from feed rate: V = F(9mc - mE), 1, = ZF(8mc - 2me). [...]... constant-speed, 134 Multicapacity process, 38-44 Multiple-loop control, 153-180 adaptive control systems, 170-179 cascade control, 154-160 ratio control, 160-167 selective control loops, 167-170 Multipliers, in adaptive systems, 172 in decoupling systems, 200-202 in feedforward systems, 209 for gain compensation, 172, 223, 2 2 4 in ratio control, 162-164 Multivariable process (see Process control, multivariable)... Neutralization process, 275-282 testing of, 58, 59 Noise, in analytical measurements, 83 in flow measurements, 67 in liquid-level measurements, 74 Nonlinear controllers, continuous, 144-148 for pH control, 148, 149, 278 discontinuous, 149 for pH control, 279 dual-mode, 136 -144 on-off, 131 with differential gap, 132 proportional time, 133 , 134 three-state, 134 , 135 Nonlinear dynamic elements, 128 -131 Nonlinearity,... 96 with dual-mode control, 139 -143 with feedforward control, 222 with nonlinear controllers, 136 -138 , 146 with reset saturation, 96-98 Shrink and swell in drum boilers, 245 Sine wave, 7, 8 Single-capacity process, 18-24 Speed control, 167, 168 Square-root extractors, 46 for cascade flow control, 159 in feedforward systems, 210 in flow-ratio systems, 163, 164 Stability, in nonlinear systems, 125, 126... non-self-regulating, 18-20 Index Process, self-regulating, 20-24 single-capacity, 18-24 two-capacity, 24-31 Process control, multivariable, 181-202 controlled and manipulated variables, pairing, 188-198 controlled variables, choosing, 182-188 decoupling control systems, 198202 Process gain, 51-53 Process model, for decoupling systems, 198-202 of distillation, 289-295 dividers in, 214 for feedforward control, 206-211... 15-17 load response with, 17, 102 of sampled process, 113- 116 Proportional-time control, 133 -136 Pumps, centrifugal, 51, 251-253 metering, 250 positive-displacement, 250, 251 R Rangeability, in pH -control systems, 278-282 in ratio -control systems, 163, 164 Raoult’s law 326 Ratio contral, 160-167 dividers in, 160 of flow, 161-167 of fuel and air, 242, 243 I Ratio control, infinite rangeability, 163, 164... feedforward control, 206 Mathematical model (see Process model) Matrix of relative gains, 189-192 Minimum-time control, 138 -141 Mixing, in composition control, 80-83 hot and cold fluids, 234, 235 in jacketed tank, 78 Mode of control (see Controllers) Modulation (see Proportional-time control) Moisture, in air, 330, 331 in solids, 343-346 Mother liquor, 336, 337 Motor, diaphragm, 65 electric, constant-speed, 134 ... feedback, 107-109 with feedforward control, 217 with integral control, 15 with linear controllers, 93-95 with nonlinear controllers, 146 with proportional control, 10-12 with proportional-plus-reset control, 17, 102 in sampled systems, 117 with three-mode control, 102, 103 Load-response criterion, 93, 94 Locus of minimum debit, 227 Loop gain, variable, 125-126 M Manual control, 19 Manual reset, 10 Mass... multicapacity processes, 39-43 in flow loops, 62-67 of interacting capacities, 39, 40 of a jacketed tank, 76 in pressure loops, 69 thermal, in exothermic reactors, 265 of valves, 65-67 variable, 23 Time delay, in dual-mode control, 141 in sampling systems, 114, 115 Time-shared control, 110 (See also Direct digital control) Transfer, auto-manual, 98, 99 in digital control systems, 119 energy, control of... band, 9 Proportional control, for batch processes, 286 bias in, 10 in cascade loops, 158-160 of dead time, 9-12 of dead time plus capacity, 31-33 of first-order lag, 24 of integrating processes, 19 load response with, 10-12 of two-capacity processes, 27-29 Proportional-plus-derivative control, of dead time plus capacity, 33, 34 of two-capacity processes, 29-31 Proportional-plus-reset control, of dead time,... first-order lag, 23 of hysteresis, 129 of integrating processes, 19 of an integrator, 13, 14 in liquid level of boilers, 245 of multiple capacity, 41 Phase shift, of positive feedback, 266 of proportional-plus-derivative control, 33 of proportional-plus-reset control, 16 of sampling element, 113 of second-integral controllers, 166, 167 of a three-mode controller, 99 of unstable reactors, 266 Piping resistance, . 124 on-off, 131 with differential gap, 132 in dual-mode systems, 137 -141 limit cycle due to, 131 with proportional time, 133 , 134 with reset and derivative, 135 three-state, 134 , 135 peak-seeking,. 278 discontinuous, 149 for pH control, 279 dual-mode, 136 -144 on-off, 131 with differential gap, 132 proportional time, 133 , 134 three-state, 134 , 135 Nonlinear dynamic elements, 128 -131 Nonlinearity, 124-128 in. 134 Multicapacity process, 38-44 Multiple-loop control, 153-180 adaptive control systems, 170-179 cascade control, 154-160 ratio control, 160-167 selective control loops, 167-170 Multipliers, in adaptive systems,