Feedback complementary

Shinskey [Ref. 3] uses the term complementary feedback for the dead-time compensator. He also discusses several practical considerations which should guide the design of dead-time compensators for various processing units. The terms complementary feedback was introduced in an interesting paper by Giloi [Ref. 4],... 

Optimized Feedback Control of Dead-Time Plants by Complementary Feedback, by W. Giloi, IEEE, Trans. Appl. and lnd., 83,183 (1964). 

Several authors have postulated a feedback control system that is modeled after the process. This kind of control action is known as complementary feedback, because the characteristics of the controller complement the dynamics of the process. A block diagram showing both process and complementary controller appears in Fig. 4.10. 

FIG 4.11. With complementary feedback, m images r, producing response which appears to be open loop. 

Within the controller, complementary feedback is sending -j-Am gp to the same summing point, such that Am will retain its original value of... 

Figure 1.26 shows the required proportional band for j i-amplitude damping for any combination of dead time and capacity. A band of 100 percent (proportional gain of 1.0) is seen to be required for a process whose Td/ri = 1.2. But with (mmplomentary feedback, the same proportional gain could produce criti( al damping. Complementary feedback is, by this token, of advantage in the most difficult processes. 

In theory, complementary feedback is capable of critically damping a process consisting of pure dead time. Following the lines of the example given for proportional control of dead time in Chap. 1, the advantages of complementary feedback will be demonstrated. For simplicity, let... 

The best value of lOOKp/P is 1.0. At 2.0, the loop becomes undamped, while at <1.0, damping is heavier than critical. Figure 4.12 illustrates the effect of changing gain. So some variation in gain can be tolerated. Unfortunately the same is not true for the complementary feedback term g,. If the positive feedback arrives at a different time than the negative feedback from the process, the loop mill break into oscillations of two periods, which are the sum and the difference of the two dead times. 

Perhaps the most significant features of complementary feedback, as brought out in this example, are ... 

In the case of a dead-time process with perfect complementary feedback, a step disturbance in load would produce an error corrected one dead time later. Figure 4.14 shows the results. 

This indicates that complementary feedback significantly reduces lAE, as well as settling time. 

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... 

A proportional-plus-reset controller applied to the same process, and adjusted to produce 22.5 phase lag, can serve as a reference for compaii son. The values of reset time and proportional band required for )- 4-ainplitude damping were calculated for selected ratios of trated error per unit load chan was then found as the PR product, to compare with that obtainable through complementary feedback. This information is plotted in Fig. 4.16, with coordinates... 

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

It was pointed out earlier that, as in regard to closed-loop gain, complementary feedback was superior for processes more difficult than Td/ri = 1.2. But the comparison was not exactly on the same basis, because the proportional band was selected for J/ -amplitude as opposed to critical damping. The comparison shown in Fig. 4.16 is limited in the same way, but the agreement of the two methods is evident. The intent, has been to prove in two ways that, complementary feedback should be reserved for only the most difficult applications. 

Pure dead time cannot be generated by analog means, therefore a dead-time complementary analog controller will never be available. Dead time can be generated digitally, so the possibility exists for direct digital control systems. But in view of the problems that can be anticipated from a mismatch of process and controller dynamics, complementary feedback is of questionable value for any pure dead-time process. (A similar and more reliable method will be presented later in this chapter.)... 

The foregoing discussion on complementary feedback was based primarily on critically damped response. With a pure dead-time process, this was the best obtainable. But with less difficult processes, lower damping will enhance recovery from load disturbances due to greater controller gain. 

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. 

If Td > At, critical damping cannot be achieved. As with complementary feedback, reducing P by one-half produces zero damping, by one-fourth gives 1. -amplitude damping. 

A sampling integral controller is capable of critically damping a process dominated by dead time, while a continuous controller is not. This line of reasoning parallels that of complementary feedback, i.e., sampling is similar in nature to dead time whereas automatic reset is not. 

Giloi, W. Optimized Feedback Control of Dead-time Plants by Complementary Feedback, Trans. IEEE, May, 1964. 

Response to a set point change will be exponential, appearing as if the loop were open. Since moving the set point causes steam flow to move directly to the correct value, the response is ecactly what was sought with complementary feedback (see Fig. 4.11). 

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