Browsing by Subject "Time Delay"

Now showing 1 - 6 of 6

Open Access
Analysis of two types of cyclic biological system models with time delays
(2011) Ahsen, Mehmet Eren
In this thesis, we perform the stability analysis of two types of cyclic biological processes involving time delays. We analyze the genetic regulatory network having nonlinearities with negative Schwarzian derivatives. Using preliminary results on Schwarzian derivatives, we present necessary conditions implying the global stability and existence of periodic solutions regarding the genetic regulatory network. We also analyze homogenous genetic regulatory network and prove some stability conditions which only depend on the parameters of the nonlinearity function. In the thesis, we also perform a local stability analysis of a dynamical model of erythropoiesis which is another type of cyclic system involving time delay. We prove that the system has a unique fixed point which is locally stable if the time delay is less than a certain critical value, which is analytically computed from the parameters of the model. By the help of simulations, existence of periodic solutions are shown for delays greater than this critical value.
Open Access
Design of P and PI controllers for head positioning in hard disk drives with time delay
(2015) Koyuncu, Havva Buket
In today’s high performance positioning applications, due to stringent design objectives, it is very challenging to cope with input-output time delays. In Hard Disk Drive (HDD) servo system, the information flow between process and the controller is under a time delay. Typical state-space based modern control algorithms are not applicable to such infinite dimensional plants. In this thesis several control design objectives are considered and various types of stabilizing controllers are derived for this infinite dimensional plant. The objective of this thesis is to determine alternative simple (low order) controllers to the previously designed H∞ controller and controllers designed from Pade approximations. For this purpose, six different P and P I controllers for the unstable infinite dimensional plant are obtained. Comparisons of the controllers with each other are done and advantages of every approach are demonstrated.
Open Access
Design of PD controlleers for unstable infinitive dimensional plants with time-delay
(2015) Varol, Deniz
In real life, everything is in movement so there are always continuous transfers, transmissions and transports of people, materials, information and energy to other places. These transfers, transmissions and transports occur with a time delay. In control theory, time delays are encountered very commonly as in real life. By considering this fact, four unstable plants with time delays are considered from different application perspectives and five delay values are chosen. For stabilization of these infinite dimensional plants, PD controllers are designed by three different design methods: two of them give different least fragile PD controllers and the other design method gives a gain margin optimizing PD controller. Designed PD controllers and equivalent plants are put in feedback loop and robust performance test results and step responses are obtained and compared.
Open Access
On the analysis of a dynamical model representing gene regulatory networks under negative feedback
(Wiley, 2014-07-25) Ahsen, M. E.; Özbay, Hitay; Niculescu, S. I.
In this work, stability analysis is performed for a cyclic dynamical model of gene regulatory networks involving time delays, under negative feedback. The model considered has nonlinearities with negative Schwarzian derivatives. Sufficient conditions implying global stability of these types of GRNs are obtained. The special case of homogenous gene regulatory networks is also studied; in this case, the proposed stability conditions depend only on the parameters of the nonlinearity function. Illustrative numerical examples complete the presentation.
Open Access
PID controller design for first order unstable time delay systems
(2009) Arslan, Gül Ezgi
In this thesis, problem of designing P, PI and PD-like controllers for switched first order unstable systems with time delay is studied. For each type of controller, the problem is solved in two steps. First, the set of stabilizing controllers for the class of plants considered is determined using different approaches. Then, an appropriate controller inside this set is chosen such that the feedback systems satisfies a desired property, which is for example gain and phase margin maximization or the dwell time minimization. In the first part, we focus on PI controllers and tune the PI controller parameters in order to maximize the gain and phase margins. The observations in this part show that a P controller is adequate to maximize gain and phase margins. Then, we move on to the problem of tuning P, PI and PD-like (first order stable) controller parameters such that the switched feedback system is stabilized and the dwell time (minimum required time between consequent switchings to ensure stability) is minimized. For this purpose, a dwell-time based stability condition of [39] is used for the class of switched time delay systems. We show that a proportional controller can be found with this method, but a PI controller is not feasible. Finally, we focus on the design of PD-like controllers for switched first order unstable systems with time delays. The proposed method finds the values of PD-like (first order stable) controller parameters which minimize an upper bound of the dwell time. The conservatism analysis of this method is done by time domain simulations. The results show that the calculated upper bound for the dwell time is close to the lower bound of the dwell time observed by simulations. In addition, we compare the obtained PD-like controller results with some alternative PD and first order controller design techniques proposed in the literature.
Open Access
Stability analysis and controller design for the heat equation with time delayed feedback
(2010) Çalışkan, Sina Yamaç
In this thesis, the stability analysis for the system defined by the heat equation with time delayed feedback is performed. In the first part of the thesis, stability conditions in terms of LMI conditions which are obtained from the analysis in time domain, are explained. Necessary and sufficient conditions for stability are obtained using a frequency domain analysis. In the second part of the thesis, robust stability conditions are obtained for the system with parametric uncertainty. In the third part, an 퐻∞ controller design procedure is given for this type of plants described by the heat equation with time delayed feedback. Finally, the results are illustrated with simulations.