An experimental evaluation of the PID controller represented by the delta operator

Digital controller based on delta operator for high‐frequency DC–DC switching converters

“…As T s tends to zero, A = b 2 ; B = − 2 b 2 ; C = 0; D = − 2 a 1 ; and E = 1, indicating that with an increase in the switching frequency, the coefficients of the PID controller, b 2 and a 1 , tremendously increase [22] and, in turn, causes the coefficients of the D‐PID controller (i.e. A , B , and D ) to increase so enormously that they might not be properly represented without increasing the controller's word length.…”

“…In [22], a digital‐proportion integration differentiation (D‐PID) controller based on a delta operator was studied for DC–DC switching converters of a lower switching frequency ( f s ≃ 20 kHz). However, only was the effect of the finite word length explored in [22], the system stability and the transfer function convergences in between continuous, and the discrete domain when using shift and delta operators were not mentioned, which are more important at a higher switching frequency. Thus, a digital controller using a delta operator is proposed herein for HFD DC–DC converters to improve both the system stability and control accuracy and reduce the hardware cost.…”

Asymptotic tracking and dynamic regulation of SISO non‐linear system based on discrete multi‐dimensional Taylor network

“…and Q 1 is the proper dimensional matrix of zeros except for the elements of the second row and the second column. Proof: Substituting (24) into (20) yields the closed-loop system which ensures (26).…”

“…With its unique structure, the output goes in the form of linear combination of finite difference and product of the input, which is more suitable for computer implementation [24,25]. Like proportional-integralderivative (PID) controller peer, the MTN controller functions well in eliminating the dependence on the system model and lowering its design complexity [26].…”