Question

13. a) Explain the working of a pneumatic P+I controller. b) A PI controller is reverse acting with PB = 20% and repeats per minute = 12 and derivative time 0.2 minutes. Determine the time at which the controller output reaches zero percent if the input error ep to the controller varies ep = 0.9t%, t ≥ 0 the controller output at t = 0 was72%.

Answer 1

Consider the pneumatic system shown in Fig. 1 .It consists of several pneumatic components The components, which can be easily identified, are: flapper nozzle amplifier, air relay, bellows and springs, feedback arrangeet etc. The overall arrangement is known as a pneumatic proportional controller. It acts as a controller in a pneumatic system generating output pressure proportional to the displacement e at one end of the link. The input to the system is a small linear displacement e and the output is pressure Po. The input displacement may be caused by a small differential pressure to a pair of bellows, or by a small current driving an electromagnetic unit. There are two springs K2 and Kf
those exert forces against the movements of the bellows A2 and Af. For a positive displacement of e (towards right) will cause decrease of pressure in the flapper nozzle. This will cause an upward movement of the bellows A2 (decrease in y). Consequently the output pressure of the air relay will increase. The increase in output pressure will move the free end of the feedback bellows towards left, bringing in the gap between the flapper and nozzle to almost its original value. We will first develop the closed loop representation of the scheme and from there the input output relationship will be worked out. The air is assumed to be impressible here.Integral action requires the addition of a second bellows (a “reset” bellows, positioned opposite the output feedback bellows) and another restrictor valve to the mechanism.This second bellows takes air pressure from the output line and translates it into force that opposes the original feedback bellows. At first, this may seem counter-productive, for nullifies the ability of this mechanism to continuously balance the force generated by the PV and SP bellows. Indeed, it would render the force-balance system completely ineffectual if this new “reset” bellows were allowed to inflate and deflate with no timelag. However, with a time lag provided by the restriction of the integral adjustment valve and the volume of the bellows (a sort of pneumatic “RC time constant”), the nullifying
force of this bellows becomes delayed over time. As this bellows slowly fills (or empties)
with pressurized air from the nozzle, the change in force on the beam causes the regular output bellows to have to “stay ahead” of the reset bellows action by constantly filling (or emptying) at some rate over time.