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See the Thermostat page for the thermostat principles used in the Master controller

Every thermostat can be programmed with its own set of PID parameters. PID parameters are settings the controls the way the room is heated, how fast and how much overshoot is allowed.

A PID algorithm is used for the 24 (0-23) built-in thermostats. PID is a generic control loop feedback mechanism (controller) widely used in industrial control systems: a PID is the most commonly used feedback controller. A PID controller calculates an "error" value as the difference between a measured process variable (room temperature) and a desired set point. The controller attempts to minimize the error by adjusting the process control inputs. In the absence of knowledge of the underlying process, PID controllers are the best controllers. However, for best performance, the PID parameters used in the calculation must be tuned according to the nature of the system – while the design is generic, the parameters depend on the specific system. Every thermostat has an integrated PID algorithm.

The PID controller calculation involves three separate parameters, and is accordingly sometimes called three-term control: the proportional (P), the integral (I) and derivative (D) values, denoted P, I, and D. The proportional value determines the reaction to the current error, the integral value determines the reaction based on the sum of recent errors, and the derivative value determines the reaction based on the rate at which the error has been changing. The weighted sum (“output” or “drive”) of these three actions is used to adjust the process via a control element such as the position of a control valve or the power supply of a heating element. Heuristically, these values can be interpreted in terms of time: P depends on the present error, I on the accumulation of past errors, and D is a prediction of future errors, based on current rate of change.

By tuning the three constants in the PID controller algorithm, the controller can provide control action designed for specific process requirements. The response of the controller can be described in terms of the responsiveness of the controller to an error, the degree to which the controller overshoots the setpoint and the degree of system oscillation.

To limit overshoot of the integral part of the algorithm, an integral threshold (It) can be set.

PID schematic.png