The following is an extract from the PID Controller Wikipedia article:
A proportional-integral-derivative controller (PID controller) is a control loop feedback mechanism (controller) widely used in industrial control systems. A PID controller calculates an error value as the difference between a measured process variable and a desired setpoint. The controller attempts to minimize the error by adjusting the process through use of a manipulated variable.
The PID controller algorithm involves three separate constant parameters, and is accordingly sometimes called three-term control: the proportional, the integral and derivative values, denoted P, I, and D. Simply put, 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. The weighted sum of these three actions is used to adjust the process via a control element such as the position of a control valve, a damper, or the power supplied to a heating element.
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The PID control scheme is named after its three correcting terms, whose sum constitutes the manipulated variable (MV). The proportional, integral, and derivative terms are summed to calculate the output of the PID controller. Defining u(t) as the controller output, the final form of the PID algorithm is:
u(t)=\mathrm{MV}(t)=K_p{e(t)} + K_{i}\int_{0}^{t}{e(\tau)}\,{d\tau} + K_{d}\frac{d}{dt}e(t)
where
- K_p: Proportional gain, a tuning parameter
- K_i: Integral gain, a tuning parameter
- K_d: Derivative gain, a tuning parameter
- e: Error = SP - PV
- t: Time or instantaneous time (the present)
- \tau: Variable of integration; takes on values from time 0 to the present t.
The PID controller is an important tool in engineering design. You will learn more about it in a lecture, and you will be able to practice the concept through an exercise.