arXiv subjects

Suat Gumussoy

Publications and source records attributed to Suat Gumussoy.

At least 37 records · Page 2Linked to original sources

arXiv2020

Relative Stability Analysis of Closed-Loop SISO Dead-Time Systems: non-imaginary axis case

We present a numerical method to analyze the relative stability of closed-loop single-input-single-output (SISO) dead-time systems on a given left complex half-plane for all positive delays. The well-known boundary crossing method for the imaginary axis is extended to a given vertical line stability boundary in the complex plane for these type of systems. The method allows to compute the characteristic roots crossing the relative stability boundary and their corresponding delays up to a maximum predefined delay. Based on this method, we analyze the relative stability of the closed-loop system for all positive delays. Both numerical methods are effective for high-order SISO dead-time systems.

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arXiv2020

A Predictor-Corrector Type Algorithm for the Pseudospectral Abscissa Computation of Time-Delay Systems

The pseudospectrum of a linear time-invariant system is the set in the complex plane consisting of all the roots of the characteristic equation when the system matrices are subjected to all possible perturbations with a given upper bound. The pseudospectral abscissa is defined as the maximum real part of the characteristic roots in the pseudospectrum and, therefore, it is for instance important from a robust stability point of view. In this paper we present an accurate method for the computation of the pseudospectral abscissa of retarded delay differential equations with discrete pointwise delays. Our approach is based on the connections between the pseudospectrum and the level sets of an appropriately defined complex function. The computation is done in two steps. In the prediction step, an approximation of the pseudospectral abscissa is obtained based on a rational approximation of the characteristic matrix and the application of a bisection algorithm. Each step in this bisection algorithm relies on checking the presence of the imaginary axis eigenvalues of a complex matrix, similar to the delay free case. In the corrector step, the approximate pseudospectral abscissa is corrected to any given accuracy, by solving a set of nonlinear equations that characterize extreme points in the pseudospectrum contours.

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arXiv2020

Characterization and computation of H-infinity norms for time-delay systems

We consider the characterization and computation of H-infinity norms for a class of time-delay systems. It is well known that in the finite dimensional case the H-infinity norm of a transfer function can be computed using the connections between the corresponding singular value curves and the imaginary axis eigenvalues of a Hamiltonian matrix, leading to the established level set methods. We show a similar connection between the transfer function of a time-delay system and the imaginary axis eigenvalues of an infinite dimensional linear operator $\mathcal{L}_ξ^N$. Based on this result, we propose a predictor-corrector algorithm for the computation of the H-infinity norm. In the prediction step, a finite-dimensional approximation of the problem, induced by a spectral discretization of the operator $\mathcal{L}_ξ$, and an adaptation of the algorithms for finite-dimensional systems, allow to obtain an approximation of the H-infinity norm of the transfer function of the time-delay system. In the next step the approximate results are corrected to the desired accuracy by solving a set of nonlinear equations which are obtained from the reformulation of the eigenvalue problem for the linear infinite-dimensional operator $\mathcal{L}_ξ^N$ as a finite dimensional nonlinear eigenvalue problem. These equations can be interpreted as characterizations of peak values in the singular value plot. The effects of the discretization in the predictor step are fully characterized and the choice of the number of discretization points is discussed. The paper concludes with a numerical example and the presentation of the results of extensive benchmarking.

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arXiv2020

Transfer Function Estimation in System Identification Toolbox via Vector Fitting

This paper considers black- and grey-box continuous-time transfer function estimation from frequency response measurements. The first contribution is a bilinear mapping of the original problem from the imaginary axis onto the unitdisk. This improves the numerics of the underlying Sanathanan-Koerner iterations and the more recent instrumental-variable iterations. Orthonormal rational basis functions on the unit disk are utilized. Each iteration step necessitates a minimal state-space realization with these basis functions. One such derivation is the second contribution. System identification with these basis functions yield zero-pole-gain models. The third contribution is an efficient method to express transfer function coefficient constraints in terms of the orthonormal rational basis functions. This allows for estimating transfer function models with arbitrary relative degrees (including improper models), along with other fixed and bounded parameter values. The algorithm is implemented in the tfest function in System Identification Toolbox (Release 2016b, for use with MATLAB) for frequency domain data. Two examples are presented to demonstrate the algorithm performance.

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arXiv2020

Improving Linear State-Space Models with Additional Iterations

An estimated state-space model can possibly be improved by further iterations with estimation data. This contribution specifically studies if models obtained by subspace estimation can be improved by subsequent re-estimation of the B, C, and D matrices (which involves linear estimation problems). Several tests are performed, which shows that it is generally advisable to do such further re-estimation steps using the maximum likelihood criterion. Stated more succinctly in terms of MATLAB functions, ssest generally outperforms n4sid.

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arXiv2020

Stable H-infinity controller design for time-delay systems

This paper investigates stable suboptimal H-infinity controllers for a class of single-input single-output time-delay systems. For a given plant and weighting functions, the optimal controller minimizing the mixed sensitivity (and the central suboptimal controller) may be unstable with finitely or infinitely many poles in complex right half-plane. For each of these cases search algorithms are proposed to find stable suboptimal H-infinity controllers. These design methods are illustrated with examples.

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arXiv2020

On the Mixed Sensitivity Minimization for Systems with Infinitely Many Unstable Modes

In this note we consider a class of linear time invariant systems with infinitely many unstable modes. By using the parameterization of all stabilizing controllers and a data transformation, we show that H-infinity controllers for such systems can be computed using the techniques developed earlier for infinite dimensional plants with finitely many unstable modes.

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arXiv2020

Remarks on Strong Stabilization and Stable H-infinity Controller Design

A state space based design method is given to find strongly stabilizing controllers for multiple-input-multiple-output plants (MIMO). A sufficient condition is derived for the existence of suboptimal stable H-infinity controller in terms of linear matrix inequalities (LMIs) and the controller order is twice that of the plant. A new parameterization of strongly stabilizing controllers is determined using linear fractional transformations (LFTs).

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arXiv2020

Continuation Based Computation of Root-Locus for SISO Dead-Time Systems

We present a numerical method to plot the root-locus of Single-Input-Single-Output (SISO) dead-time systems on a given right half-plane up to a predefined controller gain. We compute the starting and intersection points of root-locus inside the region and we obtain the root-loci of each root based on a predictor-corrector type continuation method. The method is effective for high-order SISO dead-time systems.

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arXiv2020

On the sensitivity of the H-infinity norm of systems described by delay differential algebraic equations

We consider delay differential algebraic equations (DDAEs) to model interconnected systems with time-delays. The DDAE framework does not require any elimination techniques and can directly deal with any interconnection of systems and controllers with time-delays. In this framework, we analyze the properties of the H-infinity norm of systems described by delay differential algebraic equations. We show that the standard H-infinity norm may be sensitive to arbitrarily small delay perturbations. We introduce the strong H-infinity norm which is insensitive to small delay perturbations and describe its properties. We conclude that the strong H-infinity norm is more appropriate in any practical control application compared to the standard H-infinity norm for systems with time-delays whenever there are high-frequency paths in control loops.

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arXiv2020

Fixed-order strong H-infinity control of interconnected systems with time-delays

We design fixed-order strong H-infinity controllers for general time-delay systems. The designer chooses the controller order and may introduce constant time-delays in the controller. We represent the closed-loop system of the plant and the controller as delay differential algebraic equations (DDAEs). This representation deals with any interconnection of systems with time-delays without any elimination techniques. We present a numerical algorithm to compute the strong H-infinity norm for DDAEs which is robust to arbitrarily small delay perturbations, unlike the standard H-infinity norm. We optimize the strong H-infinity norm of the closed-loop system based on non-smooth, non-convex optimization methods using this algorithm and the computation of the gradient of the strong H-infinity norm with respect to the controller parameters. We tune the controller parameters and design H-infinity controllers with a prescribed order or structure.

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arXiv2020

Computing H-infinity Norms of Time-Delay Systems

In this paper we consider the computation of H-infinity norm of retarded time-delay systems with discrete pointwise state delays. It is well known that in the finite dimensional case H-infinity norm of a system is computed using the connection between the singular values of the transfer function and the imaginary axis eigenvalues of an Hamiltonian matrix. We show a similar connection between the singular values of a transfer function of a time-delay system and the imaginary axis eigenvalues of an infinite dimensional operator $\mathcal{L}_ξ$. Using spectral methods, this linear operator is approximated with a matrix. The approximate H-infinity norm of the time-delay system is calculated using the connection between the imaginary eigenvalues of this matrix and the singular values of a finite dimensional approximation of the time-delay system. Finally the approximate results are corrected by solving a set of equations which are obtained from the reformulation of the eigenvalue problem for $\mathcal{L}_ξ$ as a finite dimensional nonlinear eigenvalue problem.

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arXiv2020

Computing the Pseudospectral Abscissa of Time-Delay Systems

The pseudospectra of a linear time-invariant system are the sets in the complex plane consisting of all the roots of the characteristic equation when the system matrices are subjected to all possible perturbations with a given upper bound. The pseudospectral abscissa are defined as the maximum real part of the characteristic roots in the pseudospectra and, therefore, they are for instance important from a robust stability point of view. In this paper we present a numerical method for the computation of the pseudospectral abscissa of retarded delay differential equations with discrete pointwise delays. Our approach is based on the connections between the pseudospectra and the level sets of an appropriately defined complex function. These connections lead us to a bisection algorithm for the computation of the pseudospectral abscissa, where each step relies on checking the presence of imaginary axis eigenvalues of an appropriately defined operator. Because this operator is infinite-dimensional a predictor-corrector approach is taken. In the predictor step the bisection algorithm is applied where the operator is discretized into a matrix, yielding approximations for the pseudospectral abscissa. The effect of the discretization is fully characterized in the paper. In the corrector step, the approximate pseudospectral abscissa are corrected to any given accuracy, by solving a set of nonlinear equations that characterize extreme points in the pseudospectra contours.

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arXiv2020

Fixed-Order H-infinity Controller Design via HIFOO, a Specialized Nonsmooth Optimization Package

We report on our experience with fixed-order H-infinity controller design using the HIFOO toolbox. We applied HIFOO to various benchmark fixed (or reduced) order H-infinity controller design problems in the literature, comparing the results with those published for other methods. The results show that HIFOO can be used as an effective alternative to existing methods for fixed-order HIFOO controller design.

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arXiv2020

On the Zeros of Quasi-Polynomials with Single Delay

A new numerical method is introduced for calculation of quasi-polynomial zeros with constant single delay. The trajectories of zeros are obtained depending on time-delay from zero to final time-delay value. The method determines all the zeros of the quasi-polynomial in any right half-plane. The approach is used to determine stability analysis of time-delay systems. The method is easy to implement, robust and applicable to quasi-polynomials with high order. The effectiveness of the method is shown on an example.

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arXiv2020

H-infinity Strong Stabilization via HIFOO, a Package for Fixed-Order Controller Design

We report on our experience with strong stabilization using HIFOO, a toolbox for H-infinity fixed-order controller design. We applied HIFOO to 21 fixed-order stable H-infinity controller design problems in the literature, comparing the results with those published for other methods. The results show that HIFOO often achieves good H-infinity performance with low-order stable controllers, unlike other methods in the literature.

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arXiv2020

On Stable H-infinity Controllers for Time Delay Systems

In this paper, we study the stability of suboptimal H-infinity controllers for time-delay systems. The optimal H-infinity controller may have finitely or infinitely many unstable poles. A stable suboptimal H-infinity controller design procedure is given for each of these cases. The design methods are illustrated with examples.

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arXiv2020

Sensitivity minimization by stable controllers for a class of unstable time-delay systems

In this paper sensitivity minimization problem is considered for a class of unstable time delay systems. Our goal is to find a stable controller stabilizing the feedback system and giving rise to smallest H-infinity norm for the sensitivity function. This problem has been solved by Ganesh and Pearson (1986) for finite dimensional plants using Nevanlinna-Pick interpolation. We extend their technique to include possibly unstable time delay systems. Moreover, we illustrate suboptimal solutions, and their robust implementation.

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