PID Control 77 FIG. 8-5. Response to step process change--PID control PID Control PID control infers that the controller algorithm consists of proportional, integral, and derivative control. Before the step change on the left side of Figure 8-5, the process variable and set point are shown to be equal in a PID controller. As such, the output remains at its previous value because no control action is necessary. When the process variable changes, an error (e) develops, and the output is modified by the proportional, integral, and derivative control algorithms. As shown in Figure 8-5, when the step change occurs, the proportional control causes the output to increase in proportion to the error, while the deriva- tive control causes a spike that is proportional to the rate of change of the error to occur. The integral control algorithm exhibits no immediate response, but causes the output to ramp by an amount that is proportional to the error over time. These actions can be represented by the summation of the propor- tional, integral, and derivative control algorithms: OUT(t + 1) = OUT(t) + K p * e + K i * (e * t) + K d * e / t (8-5) The above equation illustrates that the controller output response to an error is dependent upon the sign and magnitude of the error, and the tuning constants K p , K i , and K d . Controller