Damping with sampling controller

The existence of any dead time whatever in the loop precludes critical damping with integral control. The value of reset time necessary for zero damping was At/2 for both Figs. 4.20a and 4.21o, although their periods of oscillation differed. But as oscillation becomes more sinusoi dal, i.e., as more sampling intervals make up a period, for zero damping R approaches T /27r,just as in a continuous loop. 

Four types of fabric substrates were cyanoethylated the control, acid hydrolyzed, 50 and 100 Mrad. Fabric specimens 19 X 89 mm were sprayed with a fine mist of 2% NaOH solution using a hand spray bottle until a 100% pickup by weight was achieved. The specimens were then left to air dry until just damp. Six samples were then placed on a rack inside the sealed reaction vessel, which had inlet and outlet connections to permit the acrylonitrile vapor to flow through and around the reactive fabric. This vessel was connected to two bubble bottles containing water and acrylonitrile with which to saturate nitrogen gas as it entered the reaction vessel. The water was necessary to swell the cellulose so the acrylonitrile could penetrate. It was determined that varying nitrogen flow rates and reaction time had little effect on the percent add-on. 

Using a digital proportional controller D and zero-order hold with sampling period = 0.5, find the value of controller gain that gives a closedloop damping coefficient of 0.5. 

Again, half this value leaves the loop undamped. Critical damping was obtained with a conventional proportional-plus-reset controller whose settings were related to both dead time and sample interval. But with the sampling controller, reset alone is required, and dead time can have any value less than At — At, without affecting the closed loop. 

Up to this point we have dealt with processes which give worse control performance when sampled-data control is used than when continuous control is used. We have demonstrated this effect quantitatively by showing that ultimate gains and gains that give a desired closedloop damping coefficient decrease as T, is increased. 

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. 

Samples of leaves of corresponding age, harvested from replicate sets of stressed and control plants, were weighed, extracted with boiling isopropanol, followed by chloroform methanol (2 1 then 1 2, v/v) and washed by the procedure of Folch et al. (1957) to separate the lipid fraction. Thin layer chromatography and estimations of lipids were carried out as described previously (L5sel and Lewis, 1974). In studies of incorporation of C-labelled photosynthate into lipids, 0.5 g samples of leaves were laid on damp filter paper in a transparent plastic box, allowed to photosynthesize in for 30 minutes and for... 

Figure 2.9. Schematic of the intermittent contact mode AFM free oscillation with free amplitude Ao far away from sample surface, and damped oscillation with set-point amplitude A,p and phase shift AO during scanning. Asp is chosen by the operator, and feedback control is used to adjust tip-sample distance such that Asp remains at constant value. The choice of Aq and Asp has great influence on tip-sample force interaction and image formation.

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