TY - JOUR
T1 - Band-Passing Nonlinearity in Reset Elements
AU - Karbasizadeh, Nima
AU - Ahmadi Dastjerdi, A.
AU - Saikumar, N.
AU - Hassan HosseinNia , S.
PY - 2023
Y1 - 2023
N2 - This article addresses nonlinearity in reset elements and its effects. Reset elements are known for having less phase lag based on describing function (DF) analysis compared to their linear counterparts; however, they are nonlinear elements and produce higher-order harmonics. This article investigates the steady-state higher-order harmonics for reset elements with one resetting state and proposes an architecture and a method of design that allows for band-passing the nonlinearity and its effects, namely, higher-order harmonics and phase advantage. The nonlinearity of reset elements is not entirely useful for all frequencies, for example, they are useful for reducing phase lag at crossover frequency regions; however, higher-order harmonics can compromise tracking and disturbance rejection performance at lower frequencies. Using the proposed “phase shaping” method, one can selectively suppress the nonlinearity of a single-state reset element in a desired range of frequencies and allow the nonlinearity to provide its phase benefit in a different desired range of frequencies. This can be especially useful for the reset elements in the framework of the “constant in gain, lead in phase” (CgLp) filter, which is a newly introduced nonlinear filter, bound to circumvent the well-known linear control limitation—the waterbed effect.
AB - This article addresses nonlinearity in reset elements and its effects. Reset elements are known for having less phase lag based on describing function (DF) analysis compared to their linear counterparts; however, they are nonlinear elements and produce higher-order harmonics. This article investigates the steady-state higher-order harmonics for reset elements with one resetting state and proposes an architecture and a method of design that allows for band-passing the nonlinearity and its effects, namely, higher-order harmonics and phase advantage. The nonlinearity of reset elements is not entirely useful for all frequencies, for example, they are useful for reducing phase lag at crossover frequency regions; however, higher-order harmonics can compromise tracking and disturbance rejection performance at lower frequencies. Using the proposed “phase shaping” method, one can selectively suppress the nonlinearity of a single-state reset element in a desired range of frequencies and allow the nonlinearity to provide its phase benefit in a different desired range of frequencies. This can be especially useful for the reset elements in the framework of the “constant in gain, lead in phase” (CgLp) filter, which is a newly introduced nonlinear filter, bound to circumvent the well-known linear control limitation—the waterbed effect.
UR - http://www.scopus.com/inward/record.url?scp=85132322045&partnerID=8YFLogxK
U2 - 10.1109/TCST.2022.3178043
DO - 10.1109/TCST.2022.3178043
M3 - Article
SN - 1063-6536
VL - 31
SP - 333
EP - 343
JO - IEEE Transactions on Control Systems Technology
JF - IEEE Transactions on Control Systems Technology
IS - 1
ER -