14.1. (a) (b) (c) Discuss the topics in Table 13.3 that are influenced by cascade control, explaining how cascade improves performance for each. (d) For the mixing system in Figure 13.4 and a disturbance in the feed con- centration, discuss how you would add one sensor to improve control performance through cascade control. In your own words, discuss each of the cascade design criteria. Give a process example in which cascade control is appropriate. Identify the elements of the cascade block diagram in Figure 14.4 that are process, instrumentation, and control calculations. SP (s)- E(s) SP(s) Gel(s) Feedback process "speed" Feedback fraction process dead time Inverse response Magnitude of disturbance effect Disturbance dynamics Sensor Filter Final element Controller execution period Controller tuning Modelling errors Limitations on manipulated variables Secondary loop Case CVml(s) E(s) TABLE 13.3 Summary of factors affecting single-loop PID controller performance Key factor Typical parameter Kp Feedback process gain 0 +T 0 0 + T Td @d Numerator term in transfer function, (Ts+1) with T < 0 |KADI 0d Tf/(0 +T) Gc2(s) At + CVm2(s) KcKp T TD (0 + T) (0+T) min < MV(t) < max Kp 0 A 1.0 1.0 1.0 1.0 B 1.0 4.0 4.0 1.0 C 1.0 0.5 1.5 1.0 D 0.1 0.5 1.5 1.0 T G,(s) Td G2(s) Gi(s) MV(s) Gp2(s) D Gaz(s) CV (s) Gpl D D Gal(s) FIGURE 13.4 Schematic of process with model parameters for Example 13.1. FIGURE 14.4 Block diagram of cascade control. Effect on control performance The key factor is the product of the process and controller gains. For example, a small process gain can be compensated by a large controller gain. Note that the manipulated variable must have sufficient range. Control performance is always better when this term is small. Control performance is always better when this term is small. Control performance degrades for large inverse response. CV(s) Control performance is always better when this term is small. Control performance is best when the disturbance is slow (the time constant is large). Feedback control is effective for low-frequency disturbances and is least effective at the resonant frequency. Disturbance dead time does not influence performance. Measurement should be accurate. Dynamics should be fast with little noise. Attenuates higher-frequency components of measurement. Reduces the variability of the manipulated variable, but degrades controlled-variable performance as filter time constant is increased. Dynamics should be fast without sticking or hysteresis. Range should be large enough for response to demands. Control performance is best when this parameter is small. Continuous PID tuning correlations can be used by modifying the dead time, 0' = 0 + At/2. These terms are determined from tuning correlations based on control objectives (see Chapters 7, 9, and 10). Errors in the process model parameters lead to poorer control performance and, potentially, instability. Tuning should consider the estimate of model errors. Limitations on manipulated variables reduce the operating window (the range of achievable conditions). An active limit would cause steady-state offset from the set point.