Browsing by Subject "Infinite-dimensional system"

Now showing 1 - 5 of 5

Open Access
Multi input dynamical modeling of heat flow with uncertain diffusivity parameter
(Taylor & Francis, 2003) Efe, M. Ö.; Özbay, Hitay
This paper focuses on the multi-input dynamical modeling of one-dimensional heat conduction process with uncertainty on thermal diffusivity parameter. Singular value decomposition is used to extract the most significant modes. The results of the spatiotemporal decomposition have been used in cooperation with Galerkin projection to obtain the set of ordinary differential equations, the solution of which synthesizes the temporal variables. The spatial properties have been generalized through a series of test cases and a low order model has been obtained. Since the value of the thermal diffusivity parameter is not known perfectly, the obtained model contains uncertainty. The paper describes how the uncertainty is modeled and how the boundary conditions are separated from the remaining terms of the dynamical equations. The results have been compared with those obtained through analytic solution. © Taylor and Francis Ltd.
Open Access
On the robust controller design for Hard Disk Drive servo systems with time delays
(IEEE, 2013) Yan, P.; Özbay, Hitay
Due to the existence of various sources of delays, the dynamical model of HDD (Hard Disk Drive) servo systems is actually infinite dimensional, although most of the control algorithms simplified the model with Padé expansions or other finite dimensional approximations. In this paper, a robust loop shaping algorithm is developed for the HDD model with delays by using an h ∞ synthesis approach for infinite dimensional systems. The h∞ controller is derived with a structure of an internal feedback loop including an FIR (Finite Impulse Response) filter and an IIR (Infinite Impulse Response) filter, which facilitates non-fragile implementations. Comparisons to other robust control methods are given and the advantages of this approach are demonstrated in terms of improvement of TMR (track misregistration) and tracking TPI (Track-per-Inch) capability.
Open Access
Remarks on H ∞ controller design for SISO plants with time delays
(2006-07) Gümüşsoy, Suat; Özbay, Hitay
The skew Toeplitz approach is one of the well developed methods to design H ∞ controllers for infinite dimensional systems. In order to be able to use this method the plant needs to be factorized in some special manner. This paper investigates the largest class of SISO time delay systems for which the special factorizations required by the skew Toeplitz approach can be done. Reliable implementation of the optimal controller is also discussed. It is shown that the finite impulse response (FIR) block structure appears in these controllers not only for plants with I/O delays, but also for general time-delay plants.
Open Access
Sensitivity reduction by stable controllers for mIMO infinite dimensional systems via the tangential nevanlinna-Pick interpolation
(IEEE, 2014) Wakaiki, M.; Yamamoto, Y.; Özbay, Hitay
We study the problem of finding a stable stabilizing controller that satisfies a desired sensitivity level for an MIMO infinite dimensional system. The systems we consider have finitely many simple transmission zeros in C +, but they are allowed to possess infinitely many poles in C +. We compute both upper and lower bounds of the minimum sensitivity achievable by a stable controller via the tangential Nevanlinna-Pick interpolation. We also obtain stable controllers attaining such an upper bound. To illustrate the results, we discuss a repetitive control system as an application of the proposed method.
Open Access
Stable controllers for robust stabilization of systems with infinitely many unstable poles
(Elsevier, 2013) Wakaiki, M.; Yamamoto, Y.; Özbay, Hitay
This paper studies the problem of robust stabilization by a stable controller for a linear time-invariant single-input single-output infinite dimensional system. We consider a class of plants having finitely many simple unstable zeros but possibly infinitely many unstable poles. First we show that the problem can be reduced to an interpolation-minimization by a unit element. Next, by the modified Nevanlinna-Pick interpolation, we obtain both lower and upper bounds on the multiplicative perturbation under which the plant can be stabilized by a stable controller. In addition, we find stable controllers to provide robust stability. We also present a numerical example to illustrate the results and apply the proposed method to a repetitive control system.