Sensitivity function (SF)

Describes the frequency dependent amplitude gain of disturbances that are affecting the measurement of the process variable (PV). To ensure that no disturbances are gained "too much" the sensitivity function upper limit must be taken into account. (see the signals notation)

Sensitivity function (SF) upper limit

Should always be less than some given value Ms (e.g. 1.5), which means that the Nyquist plot cannot enter the protected area given by dark blue 'M-circle'. This specification can be added to the controller design by toggling the corresponding M-circle checkbox in our applets.

Nyquist plot shaping Sensitivity function shaping

Low frequency disturbances damping

Ideal sensitivity function has a zero amplitude at the whole frequency band (all disturbances will be totally damped). Unfortunately, it is impossible to reach this shape thanks to the 'water bed effect' which holds true for any feedback controller. It can be proved that if some frequencies are damped the other ones must be gained. However, we can at least try to damp low frequency disturbances in a specified band as shown in above figure. This design specification can be used in our applets by mouse click in the SF figure.

Water bed effect principle

 Gain and phase margin (Gm, Pm)Complementary sensitivity function (CSF) 

 
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