Two-mode control

The previous section shows that two modes control the cold flow structure in Case 1 ... 

Measure the period of oscillation t and set derivative and reset time both to t /2t. (The optimum value of D and R in Table 4.2 is 0.64Td, which is 2Td/x or To/2it.) For a two-mode controller, set R at t<,/2.4. When adjusting a three-mode pneumatic controller with antiwindup, always keep R>2D to retain proportional stability. 

If To is higher than before, increase both D and R if it is lower, decrease them. This may be necessary to compensate for inaccuracy in the dial settings. With a two-mode controller, t will increase by... 

Although there is no need to use a complementary controller on simple processes, it is nevertheless interesting to speculate on its configuration. If the process is a first-order lag, its complementary controller turns out to be proportional-plus-reset. In fact, pneumatic two-mode controllers are made this way, as shown in Fig. 4.13. 

To properly evaluate this response, a two-mode controller will be applied to the same process, but it must be adjusted so that the error will not cross zero during recovery. Thus integrated error is actually lAE, permitting comparison of loops with different damping. A phase... 

It is important to see over what range of processes complementary feedback has an advantage over two-mode control. A single-capacity plus dead-time process will respond to a step load change under complementary feedback as shown in Fig. 4.15. Without going into the derivation of the load response curve, it turns out that the integrated area per unit load change is... 

FZG 4.16. Complementary feedback is superior to two-mode control for processes more difficult than... 

In general, better performance will be obtained on more difficult applications by using delayed reset,4 as shown in Fig. 4.17. This is obviously a compromise between two-mode control and complementary feedback. 

The degree of improvement will vary with the difficulty of the process. On processes that, are fairly easy to control, improvement over two-mode control may be marginal. In fact, derivative would normally be of more value. But where dead time is dominant, or where derivative cannot be used because of noise level, delayed reset may be of considerable worth. 

Two-mode control combines the speed of response of proportional action with the elimination of offset brought about by automatic reset. The proportional mode is just as valuable in a sampled dead-time loop as it was in one without sampling. In fact, proportional action enables any loop whose dead time is less than the sampling interval to he critically damped. Figure 4.22 shows how this is done. 

FIG 4.24. A sampling two-mode controller can be very effective on a continuous process dominated by dead time. 

Find the optimum combination of proportional and reset for a dead-time process from the information given in Table 1.1. Why is it different from the situation described for the two-mode controller in Table 4.2 ... 

Given a process controlled with a two-mode controller whose proportional band is 200 percent and whose reset time is 10 min, estimate the maximum error developed by a step load change of 5 percent. What would the error be if the same load change were made gradually over an interval of 30 min What would the error be if the load change entered as a sine wave of 5 percent amplitude and 2-hr period ... 

Find the optimum settings for two-mode control of a process consisting of a 30-min lag, a 2-min dead time and an analyzer with a 5-min sampling interval. Leave the proportional band in terms of Kp. 

TABLE 5.2 Loop Gain vs. Amplitude for Two-mode Control... 

If limit cycling and offset are both unacceptable, a two-mode controller can be added to the loop. This controller would actuate the three-state device which in turn drives the valve, as shown in Fig. 5.12. Reset action will keep driving the output of the controller out of the dead zone until the error is reduced to zero. Only then will the loop reach a steady state. Proportional action is necessary for stability, for without it, the double integration of reset and motor would cause an undamped cycle. The availability of a proportional band adjustment eliminates the need for an adjustable dead zone, since the two effects are similar. 

A nonlinear two-mode controller seems generally to outperform a linear two-mode controller. The nonlinear function provides an extra margin of stability similar to what can be attained with derivative. In cases where so much noise is superimposed on the measurement that derivative cannot be used, a nonlinear function can be quite valuable. 

FIG 5.22. The nonlinear two-mode controller is superior in all respects on a noisy flow loop. 

It must be remembered that liquid-level processes such as this are non-self-regulatlng. The controlled variable will consequently drift unless feedback is applied. Since integral feedback may not be used alone, because instability would result, a two-mode controller is always used. In the steady state, feedwater flow will always equal steam flow, so the output of the level controller will seek the bias appUed to the computation. If the controller Is to be operated at about 50 percent output, that bias must be 0.5, as indicated in the formula. The controller does not have to integrate its output to the entire extent of the load change with a forward loop in service, but need only trim out the change in error of the computation during that interval. 

As the output of the proportional controller drives the small valve to either of its limits, the dead zone of the two-mode controller is exceeded. Then the large valve is moved at a rate determined by the departure of the control signal from the dead zone and by the values of proportional and reset. When the control signal reenters the dead zone, the large valve is held in its last position. The large valve is of linear character istic, because the process gain does not vary with flow, as some gains do. 

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