It is possible to implement a stable, non-linear controller, that approximates, in a desired range of frequencies, the behaviour of a complex derivative s^(alpha+j*beta); alpha < 0; beta > 0. The frequency response of this complex derivative has the gain decreasing with frequency, while the phase increases. This additional phase lead provides at the same time rejection of high frequency noise and lower overshoots in time responses when the open-loop gain increases. The describing function of the proposed non-linear approximation is close to the desired frequency response over more than one or two decades, depending on the number of reset poles employed. Larger frequency ranges were not obtained because of numerical problems.
Part of a work developed by Duarte Valério (ULisboa, IST, IDMEC), Niranjan Saikumar, Ali Ahmadi Dastjerdi, Nima Karbasizadeh, S. Hassan HosseinNia (TUDelft, 3mE, PME). This work was supported by NWO, through OTP TTW project #16335, by FCT, through IDMEC, un der LAETA, project UID/EMS/50022/2019, and grant SFRH/BSAB/142920/2018 attributed to the first author.
Duarte Valério (2019). Complex order reset controllers (https://www.mathworks.com/matlabcentral/fileexchange/70366-complex-order-reset-controllers), MATLAB Central File Exchange. Retrieved .