Browsing by Subject "time delay"

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Open Access
Controller design for haptic systems under delayed position and velocity feedback
(2012) Koru, Ahmet Taha
This thesis considers controller design for haptic systems under delayed position and velocity feedback. More precisely, a complete stability analysis of a haptic system, where local dynamics are described by some second-order mechanical dynamics, is presented. Characteristic equation of this system with time delays involves quasipolynomials. By a change of variables in the characteristic equation, stability conditions are obtained analytically and regions are plotted by using Matlab. Next, using two optimization techniques (H∞ and stability margin optimization) optimal choice for the controller gains is proposed. H∞ optimization minimizes tracking error between devices while avoiding large control action inputs. H∞ analysis requires high computational cost for accurate results due to its dependency to frequency domain. On the other hand, stability margin optimization defines a cost function that expresses the trade-off between system bandwidth and robustness with low computational cost. The derived results are tested on a three degree of freedom real-time experimental platform to illustrate the theoretical results. Finally robustness analysis is performed for optimal parameters to find allowable delay perturbations
Open Access
Reduced order modeling of infinite dimensional systems from frequency response data
(2014) Demir, Okan
In this thesis, a system identification method using frequency response data is studied. Identification method is applied to various types of distributed parameter systems, in particular flexible structures. One of the challenging tasks in the control of flexible structures is the estimation of the dominant modes (location of resonant frequencies and associated damping coefficients). In the literature, there are several studies where transfer functions of flexible structures are derived from PDEs (Partial Differential Equations); these are infinite dimensional models. In this study, a numerical method is proposed to identify the dominant flexible modes of a flexible structure with an input/output delay. The method uses a frequency domain approach (frequency response data) to estimate the resonating frequencies and damping coefficients of the flexible modes, as well as the amount of the time delay. A sequential NLLS (Non-Linear Least Squares) curve fitting procedure is adopted. Instead of optimizing over all available data collected on a frequency interval, a data selection scheme that increases the amount of data at each step is followed. Selecting relevant parts of data and optimizing sequentially increasing number of coefficients in every step is the essential part idea behind this approach. The optimization problem solved reduces to a curve fitting problem. It is illustrated that such a Newtonian optimization method has the capability of finding the parameters of a reduced order transfer function by minimizing a cost function involving nonlinearities such as exponential and rational terms. Further model reduction techniques can be applied by analyzing Hankel singular values of the resulting transfer function. Comparisons with other methods solving similar problems are illustrated with examples. Simulation results demonstrate efficiency of the proposed algorithm.