Algorithms used in control blocks combine three types of control calculations: proportional, integral, and derivative. Error signals are based on the difference between the controlled medium and a desired set point; the error signal integrated (or summed) with time (yielding an "amount of error") is the driving force in integral control systems, and the derivative of the error signal by time (yielding a "rate of control") is the driving force in derivative control systems. Ruys (1990) describes these control calculations:
Proportional control signals vary linearly with the error signals. Proportional, or P, control is a simple and effective control technique. Valve or damper position, the output of the controller, is proportional to the error signal. In order for the operator to maintain a required position, a non-zero error signal may be necessary. Unfortunately, P controls are unable to maintain an exact setpoint. P Systems are designed to maintain a control point within a given range. The location of the range is specified by the setpoint; the width of the range is called the "throttling range." Another term used by some vendors is "offset"—the difference between the control point and the setpoint.
Throttling range is a form of proportional gain. If a selected throttling range is too small, the gain is too large and the controller overreacts, resulting in a form of instability known as "hunting." The valve or damper continuously overshoots between open and closed when the controller responds faster than the medium.
Proportional integral, or PI, control is becoming more popular [due to DDC technology] because of the ability to maintain an exact setpoint. Cost and complexity, the major disadvantages of pneumatically performed integration, have been eliminated with DDC technology. Computational methods simplify integration, using an approximation based on repetitive calculation. The more frequent the calculation, the more precise the approximation. The amount of precision is determined by the sampling time between calculations, which is selected to be as small as possible.
The integral signal is simply a total of P calculations multiplied by sampling time. The valve or damper continues to change position unless offset and successive P calculations equal zero. PI control calculates an initial position based on the error signal. Successive calculations are based on previous offsets. These combined calculations continue to refine the operator's position until the offset equals zero.
PID control combines a PI control signal with derivative (D) control, D control is also referred to as "rate control"; the controller responds to reduce the rate of change. Most thermal systems have a small rate of change. Space temperature, return air temperature and mixed air temperatures change very slowly and require nothing to reduce their rates. Discharge air temperature should change quickly when needed and does not benefit from D control.
On the other hand, a static pressure system changes very quickly. A cleanroom begins to depressurize immediately if a door is opened or a fume hood is started. A D controller monitoring this static pressure will respond immediately, while the P control signal changes slowly after a noticeable change in the static pressure is detected; I control is the slowest of all. The D constituent is most significant in the initial seconds after a disturbance in order to speed up the controller's response.
When safety depends on the control systems of a laboratory environment, PID control will eliminate the dangers caused by a slow response. In these critical applications, the control system must be designed carefully. Because PID utilizes three dimensions of control, these systems have three times the potential to become unstable. A control loop consists of many components, and each of the following must be carefully selected for response, accuracy and reliability: sensors, sensor locations, transmitters, controllers, transducers, transmission media (particularly pneumatic tubing) and orators. Additionally, the precision of the controller, as measured by the sampling time, must be evaluated to ensure a fast, stable system.
