PID  CONTROLLER LABORATORY

Specifies the quality of the reference signal (setpoint) tracking (SP), e.g. describes the sp->pv relation. To avoid oscillation in time domain step response we should take into account the complementary sensitivity function upper limit. (see the signals notation)

Complementary Sens. function (CSF) upper limit

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

Proper bandwidth

For ideal tracking of reference sp signal the CSF amplitude should be one in the entire frequency range. On the other hand we always want to restrict the bandwidth of the control loop because of three reasons

1. we want to damp noises at high frequencies
2. there can be some un-modeled dynamics of reality at higher frequencies
3. we have the limited sampling rate of controller

Therefore the CSF shape should be as the one shown in the above figure, e.g. from the required frequency CSF should be damped enough. Such design specification can be defined in our applets by mouse click in CSF window.

 Sensitivity function (SF)Input sensitivity function (Si)