Martin Hromcik

Signal shaper with a distributed delay: Spectral analysis and design

Input shapers with time delays have proved useful in many applications related to controls for various oscillatory devices, for example flexible manipulators and cranes. In the paper, a novel approach for designing a zero-vibration signal shaper based on equally distributed delay is proposed. The parameter assessment of the shaper is based on the spectral approach. Various characteristics of the shaper are analyzed and compared with the classical zero-vibration shaper with a lumped delay. The analysis shows that the novel shaper is a slower, but more robust alternative to the classical shaper. Besides, the discrete implementation of the shaper is proposed and tested. It includes zero placement based parameter adjustment with the objective to preserve full compensation of the oscillatory mode by the discrete algorithm.

Numerical and symbolic computation of polynomial matrix determinant

The determinant of a polynomial matrix is frequently computed in analysis and/or design of control systems via polynomial approach. The computation can either be done symbolically using general symbolic procedures for determinant (MATHEMATICA/sup TM/, MAPLE/sup TM/) or by special numeric procedures (POLYNOMIAL TOOLBOX FOR MATLAB/sup TM/). This paper aims to compare the performance of the symbolic procedure built-in Mathematica with the best existing numerical routine based on the Fast Fourier Transform algorithm (FFT), coded for this purpose also in Mathematica. The new tailored numerical algorithm appears to be substantially more efficient than the general-purpose symbolic one. As it is also reasonably accurate, it is recommended for industrial applications of polynomial matrices.

Parameterization of input shapers with delays of various distribution

The paper introduces a new concept for composing the input shapers by combining lumped and distributed delays. Particularly, an analytical method is proposed to parametrize zero vibration shapers with delays of various distribution. Involving these delays in the shaper structure, the accommodation part of the shaped response can be smoothened in a predefined manner, retarded spectral properties can be achieved and the response length can be optionally adjusted within the given range. Next, following the analytical developments, a numerical algorithm based on the constrained linear least squares optimization is proposed for direct design of robust distributed delay shapers.

Zero vibration shapers with distributed delays of various types

The paper deals with design and analysis of novel zero-vibration (ZV) signal shapers. The shaper structure is based on replacing the lumped delay of the classical ZV shaper by a series of lumped and either equally or triangularly distributed delays. For the parametrization purposes, the spectral theory of time delay systems is applied with the aid of numerical tool for computation of rightmost part of infinite spectra of shaper zeros. In the analysis performed, the novel shapers show better spectral, step response and robustness features compared to the classical ZV shaper in some aspects. An experimental example is included to demonstrate the novel shaper performance.

On Feedback Architectures With Zero-Vibration Signal Shapers

The classical and recent feedback solutions for signal shapers are reviewed and critically analyzed in this paper. Based on this assessment, a new effective feedback control architecture is proposed, suitable for manipulation of weakly damped flexible structures. More specifically, we propose to include the inverse of a signal shapers dynamics in the feedback path, and we justify this architecture by analysis of important feedback loop channels, namely the feedback responses from input disturbance to output and from reference to output. Both the classical ZV shaper with one lumped delay, and more recent shapers with distributed delays are considered and analyzed. The most appreciated features of suitable distributed-delay shapers are retarded characteristics-the closed-loop spectrum does not exhibit high-frequency roots close to the imaginary axis (in contrast to ZV shapers)-and at the same time reduced sensitivity of the closed loop interconnection to output disturbances. Feedback performance is demonstrated by two laboratory experiments.

Complete Fast Analytical Solution of the Optimal Odd Single-Phase Multilevel Problem

In this paper, we focus on the computation of optimal switching angles for general multilevel (ML) odd symmetry waveforms. We show that this problem is similar to (but more general than) the optimal pulsewidth modulation (PWM) problem, which is an established method of generating PWM waveforms with low baseband distortion. We introduce a new general modulation strategy for ML inverters, which takes an analytic form and is very fast, with a complexity of only O(n log2 n) arithmetic operations, where n is the number of controlled harmonics. This algorithm is based on a transformation of appropriate trigonometric equations for each controlled harmonics to a polynomial system of equations that is further transformed to a special system of composite sum of powers. The solution of this system is carried out by a modification of the Newtons identity via Padé approximation, formal orthogonal polynomials (FOPs) theory, and properties of symmetric polynomials. Finally, the optimal switching sequence is obtained by computing zeros of two FOP polynomials in one variable or, alternatively, by a special recurrence formula and eigenvalues computation.

Spectral features of ZVD shapers with lumped and distributed delays

An interesting spectral property, related to sensitivity of ZVD shaper zeros with respect to small deviations of involved delays, is presented in the paper. Consequences concern namely feedback interconnections as indicated in the report. Compared to the lumped-delay case, the recently proposed distributed delay alternative - ZVD shaper with distributed delay - is a more robust option, as explained and demonstrated by means of roots diagrams. Several examples are presented to demonstrate the phenomena.

Polynomial Toolbox 2.5 and Systems with Parametric Uncertainties 1

Abstract Polynomial Toolbox is a new MATLAB toolbox for systems, signals and control analysis and design using polynomial methods. See www.polyx.cz for more details. This paper demonstrates on several examples how the Polynomial Toolbox solves various robust control problems for plants with parametric uncertainties. Both classical problems such as one-parameter, interval or polytopic uncertainty are discussed as well as cases with complicated uncertainty structure.

Fast Fourier Transform and Linear Polynomial Matrix Equations

Abstract The discrete Fourier transform theory and its computational tools, namely the famous fast Fourier transform routine, are used here to treat linear matrix polynomial equation of special kind. This specific form, though seemingly highly simple, accommodates many other linear equations structures in fact, among others also the so called Diophantine equations which are of high importance in the control theory [9,10]. Performance of the new method is compared to the traditional Sylvester approach and results of numerical experiments follow.

Double oscillatory mode compensation by inverse signal shaper with distributed delays

Signal shaping technique can be distinguished as a very effective tool for suppressing both single and multiple oscillatory modes of a system linked with the shaper. Utilizing the concept of inverse signal shapers placed in the feedback loop, the double oscillatory mode suppression is addressed, considering that the oscillations induced by both the reference signal and the disturbance changes are to be compensated. In order to avoid the closed loop neutrality of the dynamics, the lumped delay that is usually considered in the shaper structure is substituted by a distributed delay. Next to the theoretical analysis, both the numerical and experimental examples are included.