CEMP-E
TI 810-11
30 November 1998
results in a narrow range of temperature drift from setpoint while the controller changes its output from full
output to minimum output. Too high a sensitivity adjustment causes the control point to continuously
overshoot and undershoot the setpoint. In other control applications, stable control may not be achievable
with a high sensitivity adjustment. A low sensitivity adjustment results in a wide range of temperature drift
from setpoint while the controller changes its output from full output to minimum output, but control is
usually more stable. After the controller sensitivity has been adjusted, changing conditions of load due to
seasonal and other factors tend to make the adjustment less than optimal. This phenomenon is a function
of HVAC system capacity and HVAC system response to load changes. The sensitivity of a proportional
controller to process variable changes is called proportional gain.
(7) As long as the proportional controller is controlling in a stable fashion, at varying load
conditions, at some control point near the setpoint and the proportional gain setting is optimum, the
controller has achieved the most precise control of which it is capable.
d. Proportional plus integral mode (PI).
(1) Many control applications require a controller that can eliminate offset due to load and can
control very close to setpoint. To achieve closer control than is available from the proportional control
mode, some automatic adjustment has to be made to the controller output to change the actuator position
without changing the setpoint or the proportional gain setting. The method used to adjust the controller
output for changes in load is called "integral mode". Integral mode adds a gain component algebraically to
the controller output. This component is time proportional to the difference between the setpoint and the
stable control point produced by the controller's proportional gain. This difference is caused by the offset
due to load and is called steady-state error, which is the error between control point and setpoint when a
balance between the load on the system versus the system capacity output and controller output is
established. Steady-state error differs from the transitory error between setpoint and control point due to an
upset in the process, such as a changing load or a step change in setpoint.
(2) The integral mode adds a component of output to the output of the controller that is produced
by the controller's proportional gain. The size of the component is determined by the integral gain
multiplied by the error. As the error decreases, the size of the component integrated to the output signal
also decreases, and becomes zero when the controller is controlling at the setpoint. This added
component of output causes the valve actuator stroke position to change. The change in valve capacity
resulting from the change in the actuator stroke position upsets equilibrium or prevents equilibrium from
occurring until the control point reaches setpoint. This action causes two things to happen. The resulting
temperature change due to the change in valve actuator stroke position causes the proportional gain to
change its component of output signal at a magnitude proportional to the change in the temperature being
sensed. While this is happening, the error changes because the control point is closer to setpoint, and this
in turn causes the integral gain to make a change in the magnitude of its component of the output signal
due to the changing value of the magnitude of the error between control point and setpoint. There will be
no further change in the proportional-mode or integral-mode output components when the steady-state
error is zero. Because of the combined action of both of these control modes, the controller can reduce the
offset to zero, or nearly zero, and can establish a steady-state equilibrium of HVAC system control at a
value very near setpoint. This type of control is called Proportional-Integral (PI) control.
(3) See figure 2-14 for an illustration of proportional plus integral modes. The upper graph of the
figure is identical to the upper graph of figure 2-13. The lower and middle graphs provide a comparison of
the proportional mode controller output and resulting coil air discharge temperatures (light lines) versus
those of a PI-mode controller (dark lines). In the beginning of the middle graph the integral mode
component is positive and is added to the proportional mode component. This additional pressure closes
the normally-open valve when the outside air temperature reaches setpoint 7 degrees C (45 degrees F),
instead of at point A, at which the coil discharge air temperature is 7 degrees C (45 degrees F) plus half the
controller throttling range or 8 degrees C (7 + 2/2) (47 degrees F (45 + 4/2)). The 8 degrees C (47 degrees
2-17
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