Ramp disturbances

Use Laplace transform techniques to solve Example 6.7 where a ramp disturbance drives a first-order system. 

Similar expressions can be derived for responses to ramp disturbances. If the disturbance is a decaying exponential, then this is equivalent to an extra lag on a step disturbance, and the response can be evaluated by using the formulas for non-equal-sized tanks. The improvement in achievable attenuation from replacing a step by an exponential disturbance of time constant r or a ramp reaching a new steady value after r is approximately t J n + 1)t. ... 

The ramp disturbances are imposed on the process using each of the three control structures. The temperature and valve-position controllers are tuned by running relay-feedback tests. Deadtimes of 1 min are used in these loops. Temperature controller TCI is tuned at the normal design feed flow rate (4000 kmol/h), and Tyreus-Luyben tuning give Kc = 31 and Ti = 9.2min. 

Notice that the TCI controller does not hold the T35 temperamre at 101 °C during the period when the feed is ramping down or up. A PI controller will produce offset when subjected to a ramp disturbance. This offset occurs in all control structures during the ramp load disturbances. This offset problem could be reduced by using a lag-compensated PI controller for TCI. 

Temperature is controlled by manipulating reboiler duty at all times with this structure, so tight temperature control is expected. Figure 15.8 confirms this expectation. The second graph on the left shows how the temperature on Stage 35 (T35) varies as the ramp disturbances in feed flow rate enter the system. A comparison with Figure 15.7a shows that the dynamic deviations in T35 are smaller using the VPC structure than those observed in... 

Figure 15.10 gives a direct comparison of the performances of the three control structures for the same ramp disturbances. The dashed lines are for the two-temperature control structure. The dotted lines are for the VPC control structure. The solid lines are for the recycle control structure. 

Figure 15.10 Comparison of alternative control structures ramp disturbances.

The ramp disturbances used in the previous section are gradual, and therefore do not test the performance of the control structure as severely as step disturbances. Figures 15.11-15.15 give results for a series of step changes in throughput for the three control structures. Feed flow rates are dropped from 4000 to 3000 kmol/h at time equal 0.5 h, then to 2000 kmol/h at 4h, and finally to 1500 kmol/h at 8h. 

Positive step change in concentration (C, = 1.1 moi/1) Positive step change in temperature (Tj = 438.6 K) Negative step change in concentration (C, =0.9 mol/1) Positive slope ramp disturbance change in concentration (slope of C, = 0.1/60... 

The effect of DT on the system performance has been studied by exciting the system with different ramp disturbances (with the same final values) and applying RTE with different DT values. Figure 2 summarises some of the MOF profiles obtained. Charts a and b correspond to disturbances that favour the steady state objective function, being the opposite for charts c and d. 

Figure 2 Response of RTE system for different ramp disturbances and the influence of DT.

Statistical process control and automatic process control (APC) are complementary techniques that were developed for different types of problems. As indicated in earlier chapters, APC takes corrective action when a controlled variable deviates from the set point. The corrective action tends to change at each sampling instant. Thus, for APC there is an imphcit assumption that the cost of making a corrective action is not significant. APC is widely used in the process industries, because no information is required about the sources and types of process disturbances. APC is most effective when the measurement sampling period is relatively short compared to the process settling time, and when the process disturbances tend to be deterministic (that is, when they have a sustained nature such as a step or ramp disturbance). 

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