IFAC PapersOnLine 51-14 (2018) 248–253 ScienceDirect Available online at www.sciencedirect.com 2405-8963 © 2018, IFAC (International Federation of Automatic Control) Hosting by Elsevier Ltd. All rights reserved. Peer review under responsibility of International Federation of Automatic Control. 10.1016/j.ifacol.2018.07.231 © 2018, IFAC (International Federation of Automatic Control) Hosting by Elsevier Ltd. All rights reserved. 1. INTRODUCTION Identification, control even adaptive algorithms usually assume the apriori knowledge of the process time-delay. This knowledge is sometimes very uncertain and the mismatch coming from a lack of precision in mathematical modeling of the plant and/or changes in the plant parameters with time can result instability. It would be desirable to know how the time-delay mismatch influences the basic robustness and performance behaviors of the closed-loop control. Some controller design methodologies, mostly for discrete- time systems, include the time-delay of the plant also into the parameters (Bányász and Keviczky, 1994). Unfortunately relatively few papers (e.g., Hocken et al., 1983; Tzypkin, and Fu, 1993) can be found dealing with the influence of the accuracy of the apriori knowledge or estimate of the time- delay, which is sometimes called the time-delay mismatch problem. Our paper investigates the influence of the time- delay uncertainty on the robust stability and performance. The framework how this issue will be discussed is the generic two-degree of freedom (GTDOF) system topology (Keviczky, 2015), which is based on the Youla- parameterization (Maciejowski, 1989) providing all realizable stabilizing regulators (ARS) for open-loop stable plants and capable to handle the plant time-delay. The advantage of this approach is that it is easy to calculate the "best" reachable optimal regulator depending on the applied H 2 and/or H  norms as criteria. The drawback is that this methodology can be applied only for open-loop stable plants. A GTDOF control system is shown in Fig. 1, where y r ,u , y and w are the reference, process input, output and disturbance signals, respectively. The optimal ARS regulator of the GTDOF scheme (Keviczky and Bányász (1997)) is given by R o = P w K w 1  P w K w S = Q o 1  Q o S = P w G w S + 1 1  P w G w S  z  d (1) where Q o = Q w = P w K w = P w G w S +  1 (2) is the associated optimal Y-parameter (Keviczky and Bányász (2002)) furthermore Q r = P r K r = P r G r S + 1 ; K w = G w S + 1 ; K r = G r S + 1 (3) assuming that the process is factorable as S = S + S  = S + S  z d (4) where S + means the inverse stable (IS) and S  the inverse unstable (IU) factors, respectively. z d corresponds to the discrete time-delay, where d is the integer multiple of the sampling time. Here P r and P w are assumed stable and proper transfer functions (reference models). An interesting result was (Keviczky, and Bányász, 1999) that the optimization of the GTDOF scheme can be performed in H 2 and H  norm spaces by the proper selection of the serial G r and G w embedded filters. P r y r y w S u K r S + + + + + - P w K w 1  P w K w S R o Fig. 1. The generic TDOF (GTDOF) control system 2. ROBUST STABILITY CONDITIONS FOR GTDOF CONTROL SYSTEMS Be M the model of the process. Assume that the process and its model are factorizable as S = S + S  = S + S  z d ; M = M + M  = M + M  z d m (5) where S + and M + mean the inverse stable (IS), S  and M  the inverse unstable (IU) factors, respectively. z d and z d m correspond to discrete time delays, where d and d m are the Copyright © 2018 IFAC 248 Keywords: robustness, stability, performance, time-delay uncertainty Abstract: In a practical control system the process always has a time delay. The uncertainty in the knowledge of the time delay i.e. the delay mismatch strongly influences the quality of the closed-loop control. It can cause unwanted instability and influences the robustness of the control. Stability region applicable for this uncertainty is investigated in this paper in connection with the required performance and robustness. †Institute of Computer Science and Control, Hungarian Academy of Sciences H-1111 Budapest, Kende u 13-17, HUNGARY, (e-mail: banyasz@sztaki.hu , keviczky@sztaki.hu) ‡Department of Automation and Applied Informatics, Budapest University of Technology and Economics, H-1117 Budapest, Magyar Tudósok krt 2, Q/B, HUNGARY, (e-mail: Bars.Ruth@aut.bme.hu) Cs. Bányász†, L. Keviczky† and R. Bars‡ Influence of Time-Delay Mismatch for Robustness and Stability