Understanding Smart Sensors - Nomads.usp

Control Techniques 153otherwise take to reach a new set point determined by the proportional control.Controllers with derivative control have rate amplitude and rate time adjustments.PID control can be implemented in both analog and digital systems [4].The PID control algorithm is defined byT() s = C()/ s R()s =1 (7.1)where: T (s) is the desired transfer function, and R (s) and C (s) are Laplacetransforms of the reference input r (t) and the controlled output c(t) [5].If C (s) is not measured, the system is open loop. Otherwise, a measurementof C (s) is used to provide closed-loop feedback control. Figure 7.2 showsthe location of those parameters in the analog control system [5]. For r (t) varyingwith time, a tracking problem must be solved. For r (t)=constant, the problemis one of regulation. Disturbances in the forward transmission path and thefeedback path can prevent c (t) from ideally following r (t).The process being controlled typically dictates if only proportional, proportionaland integral, or full PID should be implemented. As in most systems,the most appropriate solution is the simplest one that will achieve the desiredresults. Control systems based on digital techniques can improve previous analogsystems. Figure 7.3 shows the simplification that results when a singlerotary encoder provides position, speed, and commutation data in a speedcontrolsystem [6]. The number of connections to the motor is reduced from13 to 8. The speed computation block is used to interpolate the encoder outputsignal for improved resolution.PInputE(s)1SIOutputC(s)SDFigure 7.2 PID control.