PID Controller
Typically the feedback control circuits used in a scanning probe microscope use the widely excepted proportional, integral, derivative algorithem. Figure 4, shows the relationship between the controller input, and the controller output. The input to the PID controller is the error signal from the force sensor, and the controller output is used to actuated a Z piezoelectric ceramic that ultimately controls the relationship between the probe and surface.  Figure 4: The input to the PID controller is the error signal and the output of the controller is the voltage used to drive the Z piezoelectric ceramic. The responsiveness of the controller is set with the coefficients P,I and D in equation 1. In the initial designs of scanning probe microscopes, analog circuits were used and the PID control parameters were set using knobs at the front of electronic boxes. Optimizing the PID parameters involved turning the knobs until the best images were obtained. With the advent of personal computers and high speed digital electronics there are many options for the design of feedback control circuits.
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