#### PID Explained

Frequently, clients will askÂ whether PID controllers are necessary for the operation of espresso machines.

Technically speaking they are not; however, virtually everyone agrees that PID circuits are a desirable feature.

Traditionally, espresso machine boilers were controlled by electromechanical pressurestats which would signal the electronics when the internal pressure dropped below a predetermined setpoint or rose above another. This allowed for the system to maintain an average pressure and temperature but did so by drifting up and down in an error condition more often than at the setpoint.

PID controllers view and respond to system errors using mathematics. The result is a much flatter response graph and better espresso.

**Proportional ResponseÂ **

The proportional component depends only on the difference between the set point and the process variable. This difference is referred to as the Error term. The proportional gain (Kc) determines the ratio of output response to the error signal. For instance, if the error term has a magnitude of 10, a proportional gain of 5 would produce a proportional response of 50. In general, increasing the proportional gain will increase the speed of the control system response. However, if the proportional gain is too large, the process variable will begin to oscillate. If Kc is increased further, the oscillations will become larger and the system will become unstable and may even oscillate out of control.

**Integral Response**

The integral component sums the error term over time. The result is that even a small error term will cause the integral component to increase slowly. The integral response will continually increase over time unless the error is zero, so the effect is to drive the Steady-State error to zero. Steady-State error is the final difference between the process variable and set point. A phenomenon called integral windup results when integral action saturates a controller without the controller driving the error signal toward zero.

**Derivative Response**

The derivative component causes the output to decrease if the process variable is increasing rapidly. The derivative response is proportional to the rate of change of the process variable. Increasing the derivative time (Td) parameter will cause the control system to react more strongly to changes in the error term and will increase the speed of the overall control system response. Most practical control systems use very small derivative time (Td), because the Derivative Response is highly sensitive to noise in the process variable signal. If the sensor feedback signal is noisy or if the control loop rate is too slow, the derivative response can make the control system unstable.