PID tuning for unstable processes based on gain and phase-margin specifications

Set point weighted modified Smith predictor for integrating and double integrating processes with time delay

“…(28) and (29) along with Eqs. (27a) and (27b) can be solved for the controller parameters k d andk τ d .…”

“…Hence, to make the solution simple, the trigonometric term (tan) in Eq. (17) is approximated as [28] tan…”

PID Control of Unstable Processes with Time Delay

“…이 후 Venkatashankar와 Chidambaram [6] 이 De Paor과 O'Malley 방법에서 필요한 수치 해석적 방법 대신 근사적 해법을 이용해 P 제어기 와 PI 제어기를 제안하였고, Poulin과 Pomerleau [7] 는 최대 피크 공진에 기초하여 PI 제어기와 PID 제어기를 제안하였다. Ho와 Xu [8] 는 특정한 이득 여유와 위상여유를 만족하도록 하는 PI 제어기를 제안하였으며, 폐루프 시스템이 나이퀴스트(Nyquist) 안정도 조건을 만족시킴을 보여주었다.…”

PID-Like Controller Tuning for Second-Order Unstable Dead-Time Processes

“…Table 5 presents a stability robustness comparison with other existing PID tuning methods. In particular, the tuning methods presented in Sections 4 and 5 are compared with the R&L method with λ=2.2 (Rotstein & Lewin, 1991), the P&M method (De Paor and O'Malley, 1989), the H&X method with specifications A m =1.3 and φ m =10 o (Ho & Xu, 1998), the P&P method based on the ITAE criterion (Poulin & Pomerleau, 1997) and the J&C method based on the IMC tuning rule with λ=2.5 (Jacob & Chidambaram, 1996), in the special case where d=0.5 and τ S =1. Table 5 show that the DPC method provides more robust controllers than most other methods (except the J&C method with λ=2.5, that gives a significantly slower response in both set point tracking and regulatory control).…”