TY - JOUR
T1 - Reset control approximates complex order transfer functions
AU - Valério, Duarte
AU - Saikumar, Niranjan
AU - Dastjerdi, Ali Ahmadi
AU - Karbasizadeh Esfahani, Nima
AU - Hossein Nia Kani, Hassan
N1 - Accepted Author Manuscript
PY - 2019
Y1 - 2019
N2 - A controller with the frequency response of a complex order derivative may have a gain that decreases with frequency, while the phase increases. This behaviour may be desirable to ensure simultaneous rejection of high-frequency noise and robustness to variations of the open-loop gain. Implementations of such complex order controllers found in the literature are unsatisfactory for several reasons: the desired behaviour of the gain may be difficult or impossible to obtain, or non-minimum phase zeros may appear, or even unstable open-loop poles. We propose an alternative nonlinear approximation, combining a CRONE approximation of a fractional derivative with reset control, which does not suffer from these problems. An experimental proof of concept confirms the good results of this approximation and shows that nonlinear effects do not preclude the desired performance.
AB - A controller with the frequency response of a complex order derivative may have a gain that decreases with frequency, while the phase increases. This behaviour may be desirable to ensure simultaneous rejection of high-frequency noise and robustness to variations of the open-loop gain. Implementations of such complex order controllers found in the literature are unsatisfactory for several reasons: the desired behaviour of the gain may be difficult or impossible to obtain, or non-minimum phase zeros may appear, or even unstable open-loop poles. We propose an alternative nonlinear approximation, combining a CRONE approximation of a fractional derivative with reset control, which does not suffer from these problems. An experimental proof of concept confirms the good results of this approximation and shows that nonlinear effects do not preclude the desired performance.
KW - Complex order derivatives
KW - Fractional calculus
KW - Micro precision
KW - Reset control
UR - http://www.scopus.com/inward/record.url?scp=85069646584&partnerID=8YFLogxK
U2 - 10.1007/s11071-019-05130-2
DO - 10.1007/s11071-019-05130-2
M3 - Article
AN - SCOPUS:85069646584
SN - 0924-090X
VL - 97
SP - 2323
EP - 2337
JO - Nonlinear Dynamics
JF - Nonlinear Dynamics
IS - 4
ER -