Integration of MRI/EEG/MEG/SPECT for source localisation

Abstract

For reasons of saturation avoidance and limitation of high frequency noise, the classical PID controller is usually implemented with a lowpass filter on the derivative channel. As pointed out by the author some years ago, this has profound implications for the stability of digital control systems based on discretised analog designs. However, it then ceases to be a PID controller and might be better described as PIL, where L normally stands for phase “lead,” but might in exceptional circumstances be phase “lag.” Such controllers are investigated as eigenvalue assigners for an inherently unstable magnetic levitation (maglev) system and for a first order lag with pure time delay, where the time delay is approximated by a first order Padé approximation for design purposes and then simulated exactly for performance evaluation. Explicit controller designs are derived with all closed loop eigenvalues placed at the same location. It is demonstrated, using root locus arguments, that this gives an optimally stable system in the sense that as any single controller or process parameter is varied with respect to its nominal value, the rightmost eigenvalue, on passage through the nominal parameter setting, is as deep in the left half plane as possible.