Simple proportional control
If the output signal from the controller is directly proportional to the deviation, then the control action is termed simple proportional. If this output signal is used to vary the position of a modulating valve, then there is one, and only one position of the valve for each value of the controlled variable. Figure 13.7 shows this. Offset is thus an inherent feature of simple proportional control. Only when the valve is half open will the value of the controlled variable equal the set point. At all other times there will be a deviation: when the load is a maximum the deviation will be the greatest in one direction, and vice-versa.
Closed open open
Fig. 13.7 The operation of a proportional controller depends on the temperature of the water handled by the valve: the full line is for the case of hot water and the broken one for chilled water.
The terms direct action and reverse action are used to denote the manner in which the final control element moves in response to the signals it receives from the primary sensor element. For example, suppose that a room suffers a heat gain and that this is offset by means of a fan-coil unit fed with chilled water, the output being regulated by means of an
Electrically actuated, motorised, two-port modulating valve. If, when the room temperature rises the controlling thermostat sends an increasing signal to the valve motor this is termed direct acting. Supposing that the signal drives the motor in a direction that closes the valve; it will reduce the flow of chilled water and is clearly wrong. A reversing relay must be added to the control circuit to drive the motor in the other direction, when chilled water is handled and open the valve, upon receiving a signal of increasing strength. The controller is now reverse acting and the broken line in Figure 13.7 shows this. If hot water flows through the fan coil unit in winter, to deal with a heat loss, the relay is kept out of the circuit and the controller acts directly so that a rise in room temperature sends a signal of increasing strength to the motor, causing the valve to move towards its closed position. This is shown by the full line in Figure 13.7.
An alternative view of simple proportional control is obtained by introducing the concept of ‘potential value’ of the controlled variable (due to Farrington (1957)). If there is not a match initially between load and capacity, the controlled variable will gradually change, approaching a steady value at which a match will prevail. This steady value, attainable exponentially only after an infinity of time, is the potential value of the controlled variable. Every time the capacity of the plant is altered there is a change in the potential value. Capacity variation can thus be spoken of in terms of potential correction, <(>: if a deviation of 0 occurs in the controlled variable then a potential correction of <]) must be applied. Simple proportional control can be defined by an equation:
<)) = — kp 0 + Cj (13.1)
Where kp is the proportional control factor and C, is a manual re-set constant that determines the set point of the controlled variable.
Thus, under a constant load condition, sustained deviation is the rule. This offset corresponds to a value of <j> and when, after a load change, the controlled variable has responded to this correction, it settles down with some decaying overshoot and undershoot at a steady value. Such a steady value is the control point. Hence, even though the set point is unaltered (at the mid-point of the proportional band) the control point takes up a variety of values, depending on the load.
To minimise offset kp should be large and increasing its value is known as increasing the control sensitivity, corresponding to narrowing the proportional band. For a given operating condition too much sensitivity (or too narrow a proportional band) can induce hunting, proportional control degenerating to two-position control.
Posted in Air Conditioning Engineering