29.11.2Automatic and manual modes

A more practical pneumatic proportional controller mechanism is shown in the next illustration, complete with setpoint and bias adjustments, and a manual control mode:

Air supply

Auto Manual

Transfer valve

Output

“Bumpless” transfer between automatic and manual modes is a very important feature for any loop controller because it allows human operators to change the mode of the controller without introducing an unnecessary disturbance to the process being controlled. Without provision for bumpless transfer, the output signal of the controller may suddenly change whenever the mode is switched between automatic and manual. This sudden signal change will cause the final control element to suddenly “step” to some new level of e ect on the process.

In this particular pneumatic controller, bumpless auto/manual transfer is accomplished by the operator paying attention to the balance indicator revealing any air pressure di erence between the output bellows and the output adjust pressure regulator. When in automatic mode, a switch to manual mode involves adjusting the output regulator until the balance indicator registers zero pressure di erence, then switching the transfer valve to the “manual” position. The controller output is then at the direct command of the output adjust pressure regulator, and will not respond

29.11.3Derivative control action

Derivative (rate) control action is relatively easy to add to this pneumatic controller mechanism. All we need to do is place a restrictor valve between the nozzle tube and the output feedback bellows, causing the bellows to delay filling or emptying its air pressure over time:

Transfer valve

Output

If any sudden change occurs in PV or SP, the output pressure will saturate before the output bellows has the opportunity to equalize in pressure with the output signal tube. Thus, the output pressure “spikes” with any sudden “step change” in input: exactly what we would expect with derivative control action.

If either the PV or the SP ramps over time, the output signal will ramp in direct proportion (proportional action), but there will also be an added o set of pressure at the output signal in order to keep air flowing either in or out of the output bellows at a constant rate to generate the force necessary to balance the changing input signal. Thus, derivative action causes the output pressure to shift either up or down (depending on the direction of input change) more than it would with just proportional action alone in response to a ramping input: exactly what we would expect from a controller with both proportional and derivative control actions.

29.11.4Integral control action

Adding integral action to our hypothetical pneumatic controller mechanism requires the placement of a second bellows (a “reset” bellows) opposite the output feedback bellows, and another restrictor valve to the mechanism18:

Air supply

Auto Manual

Transfer valve

Output

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 it 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 ine ectual if this new “reset” bellows were allowed to inflate and deflate with no time lag. However, with a time lag provided by the

18Practical integral action also requires the elimination of the bias spring and adjustment, which formerly provided a constant downward force on the left-hand side of the beam to give the output signal the positive o set necessary to avoid saturation at 0 PSI. Not only is a bias adjustment completely unnecessary with the addition of integral action, but it would actually cause problems by making the integral action “think” an error existed between PV and SP when there was none.

The result of these two bellows’ opposing forces (one instantaneous, one time-delayed) is that the lower bellows’ pressure must always lead 3 PSI ahead of the upper bellows’ pressure in order to maintain a pressure di erence of 3 PSI necessary to balance force with the PV and SP bellows (whose pressures di er by 3 PSI). This creates a constant 3 PSI di erential pressure across the reset restriction valve, resulting in a constant flow of air into the reset bellows at a rate determined by that pressure drop and the opening of the restrictor valve. Eventually this will cause the output pressure to saturate at maximum, but until then the practical importance of this rising pressure action is that the mechanism now exhibits integral control response to the constant error between PV and SP:

4 PSI

Lever

7 PSI

Air supply

The greater the di erence in pressures between PV and SP (i.e. the greater the error ), the more pressure drop will develop across the reset restriction valve, causing the reset bellows to fill (or empty, depending on the sign of the error) with compressed air at a faster rate19, causing the output pressure to change at a faster rate. Thus, we see in this mechanism the defining nature of integral control action: that the magnitude of the error determines the velocity of the output signal (its rate of change over time, or dmdt ). The rate of integration may be finely adjusted by changing the opening of the restrictor valve, or adjusted in large steps by connecting capacity tanks to the reset bellows to greatly increase its e ective volume.

19These restrictor valves are designed to encourage laminar air flow, making the relationship between volumetric flow rate and di erential pressure drop linear rather than quadratic as it is for large control valves. Thus, a doubling of pressure drop across the restrictor valve results in a doubling of flow rate into (or out of) the reset bellows, and a consequent doubling of integration rate. This is precisely what we desire and expect from a controller with integral action.