Tolerable delay-margin improvement for systems with input–output delays using dynamic delayed feedback controllers Dushmanta Kumar Das ⇑ , Sandip Ghosh, Bidyadhar Subudhi Center of Industrial Electronics and Robotics, Department of Electrical Engineering, National Institute of Technology, Rourkela 769008, India article info Keywords: Time-delay system Continuous pole placement technique Dynamic state feedback controller abstract This paper presents investigations on a dynamic state feedback controller with state delays that improves tolerable delay margin for systems with input–output delays. Using an iter- ative pole placement technique for time-delay systems, the effect of introducing state delay in the controller dynamics is studied. It is observed that such a controller improves the tolerable delay margins compared to its static or even simple dynamic counterpart. Ó 2013 Elsevier Inc. All rights reserved. 1. Introduction Time-delay is inherent to many feedback control systems owing to the fact that information takes finite time to get trans- ported. Often, delays appear in the feedback loop due to the time taken in (i) measuring outputs (ii) computing control ac- tions and (iii) actuating the plant. Such delays in the feedback loop are, in general, destabilizing [1]. However, it is also possible that purposeful use of artificial delays in the controller may improve stability of certain systems, e.g., (i) use of an appropriate delay leads to chattering stability in a milling process [2], (ii) use of delay may yield better purchasing and stocking decisions in supply chain management [3]. Such stabilizing effect of delays is a motivation to many researchers to exploit the possibilities of using them with benefits. This paper considers the problem of stabilizing systems with Input and Output (IO) delays as shown in Fig. 1. Time taken in measuring the output signal and thereby receiving at the controller is called as the output delay (s s ), whereas the sending time for the control signal from the controller to the actuator is the input delay (s a ). For such systems, if one uses a static feedback controller then the delay in the feedback loop may be represented as s total ¼ s a þ s s [4]. For an illustration, consider a scalar system of the form _ xðtÞ¼ axðtÞþ uðt  s a Þ; ð1Þ It is well known that using a static state feedback controller of the form uðtÞ¼ k s xðt  s s Þ, where k s is the control gain, system (1) can be stabilized till a s a þ s s ð Þ < 1 [5]. However, if one uses an observer based controller of the form _ ^ xðtÞ¼ a^ xðtÞþ k^ xðt  s a Þþ l^ xðt  s s Þ lxðt  s s Þ; ð2Þ where ^ xðtÞ is the estimate of the state, l is the observer gain, then the scalar system (1) can be stabilized till as a < 1 and as s < 1 [5], which is an improvement over the static feedback one. However, implementing such a controller is difficult since 0096-3003/$ - see front matter Ó 2013 Elsevier Inc. All rights reserved. http://dx.doi.org/10.1016/j.amc.2013.12.073 ⇑ Corresponding author. E-mail addresses: dushmantakumardas29@gmail.com (D.K. Das), sandipg@nitrkl.ac.in (S. Ghosh), bidyadhar@nitrkl.ac.in (B. Subudhi). Applied Mathematics and Computation 230 (2014) 57–64 Contents lists available at ScienceDirect Applied Mathematics and Computation journal homepage: www.elsevier.com/locate/amc