Multivariable Nyquist self-tuning: a general approach

Anti-windup scheme for PI temperature control of an open-loop unstable chemical reactor

This paper studies the generation of stable transfer functions for which the real or imaginary part takes prescribed values at discrete uniformly spaced points on the unit circle. Formulas bounding the error between a particular interpolating function and any function consistent with the data are presented, which have the desirable property that the error goes to zero exponentially fast with the number of interpolating points. The paper also examines generation of stable minimum phase transfer functions for which the magnitude takes prescribed values at uniformly spaced points on the unit circle, and presents error bounds for this problem. Connection with the discrete Hilbert transform is made. The effect of uncertainty in the original data is also examined.

We present a new experimental technique for the separation of dynamic chemical signals based on their frequency domain characteristics. Such a technique can be used to create filters that separate slow signals from fast signals from a common input flow stream. The propagation of time-varying chemical waves through networks of microfluidic channels is first examined. Mathematical models and a set of simple experiments are developed that demonstrate that short microfluidic channels behave as linear delay lines. The observed dispersive broadening and delay behavior can be explained in Fourier space in terms of corresponding phase delay, amplitude decay and characteristic transfer functions. Such delay components can be utilized to implement frequency dependent interference filters. An 8th order PDMS bandpass filter chip demonstrating these ideas was constructed. The filter chip has a central frequency of 0.17 Hz and a bandwith of 0.04 Hz at a flow rate of 4 microL h(-1).

This paper presents a systematic development of steady‐state, small‐signal models of interleaved dual boost converter operating in a continuous current mode. These models are derived by employing the well‐known signal flow graph method. This signal flow graph approach provides a means to directly translate the switching converter into its equivalent graphic model, from which a complete behaviour of the converter can easily be studied. Steady‐state performance, small‐signal characteristic transfer functions are derived using Mason's gain formula. The bode plots of audiosusceptibility, input impedance, output impedance, and control‐to‐output transfer functions are determined and illustrated using MATLAB for different values of load resistances, duty ratios. Small‐signal frequency responses obtained from the signal flow graph method are validated with PSPICE simulator results. To validate the signal flow graph modelling equations, sample steady‐state experimental results are provided. Copyright © 2001 John Wiley & Sons, Ltd.

Several techniques are available for characterizing the surface microstructure of smooth components. Often it is necessary to compare the results from two or more of these techniques. This can lead to problems unless it is understood that all measurement techniques are bandwidth limited, and each technique has a characteristic transfer function. We will discuss several techniques in this regard, including the optical profilometer (WYKO), the optical scatterometer (both angle-resolved and TIS), and the mechanical profilometer (Talystep). A number of samples having different microstructure properties were characterized using these techniques, and results will be discussed.

The electrodynamic loudspeaker couples mechanical, magnetic, electric and thermodynamic phenomena. The Thiele/Small (TS) model provides a low frequency approximation, combining passive linear (multiphysical or electric-equivalent) components. This is commonly used by manufacturers as a reference to specify basic parameters and characteristic transfer functions. This paper presents more refined nonlinear models of electric, magnetic and mechanical phenomena, for which fundamental properties such as passivity and causality are guaranteed. More precisely, multiphysical models of the driver are formulated in the core class of port-Hamiltonian systems (PHS), which satisfies a power balance decomposed into conservative, dissipative and source parts. First, the TS model is reformulated as a linear PHS. Then, refinements are introduced, step-by-step, benefiting from the component-based approach allowed by the PHS formalism. Guaranteed-passive simulations are proposed, based on a numerical scheme that preserves the power balance. Numerical experiments that qualitatively comply with measured behaviors available in the literature are presented throughout the paper.

This study describes the use of a biofeedback method for the noninvasive study of baroreflex mechanisms. Five previously untrained healthy male participants learned to control oscillations in heart rate using biofeedback training to modify their heart rate variability at specific frequencies. They were instructed to match computer-generated sinusoidal oscillations with oscillations in heart rate at seven frequencies within the range of 0.01-0.14 Hz. All participants successfully produced high-amplitude target-frequency oscillations in both heart rate and blood pressure. Stable and predictable transfer functions between heart rate and blood pressure were obtained in all participants. The highest oscillation amplitudes were produced in the range of 0.055-0.11 Hz for heart rate and 0.02-0.055 Hz for blood pressure. Transfer functions were calculated among sinusoidal oscillations in the target stimuli, heart rate, blood pressure, and respiration for frequencies at which subjects received training. High and low target-frequency oscillation amplitudes at specific frequencies could be explained by resonance among various oscillatory processes in the cardiovascular system. The exact resonant frequencies differed among individuals. Changes in heart rate oscillations could not be completely explained by changes in breathing. The biofeedback method also allowed us to quantity characteristics of inertia, delay, and speed sensitivity in baroreflex system. We discuss the implications of these findings for using heart rate variability biofeedback as an aid in diagnosing various autonomic and cardiovascular system disorders and as a method for treating these disorders.

It is shown that a p <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">x</sup> m transfer function G(s) with p⩾m can be decomposed as G = (I-ν <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">N</sub> Δ <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">N</sub> ) <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">-1</sup> ...(I-ν <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">r+2</sub> Δ <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">r+2</sub> ) <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">-1</sup> (I-ν <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">r=1</sub> Δ <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">r=1</sub> ) <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">-1</sup> G <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">O</sub> where Δ <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">i</sub> are stable all-pass transfer functions, 1=ν <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</sub> ..=ν <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">r</sub> ≫ν <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">r=1</sub> ..≫ν <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">N</sub> ≫0 are the Hankel-singular-values of GW* <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">-1</sup> where G*G=WW* with W stable and minimum phase. Results on the McMillan degree of G <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Λ</sup> :=(I-ν <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">i</sub> Δ <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">i</sub> )..(I-ν <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">N</sub> Δ <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">N</sub> )G then show that G <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Λ</sup> gives a good low order approximation to G in the sense of relative error.

Simultaneous stabilization using stable system inversion

UDC 517.5 We study the relationship between certain Fibonacci polynomials and the Schwarz lemma within the framework of the complex analysis and control engineering. The Fibonacci polynomials are traditionally associated with combinatorial mathematics and recursive sequences. At the same time, they also play a significant role in the power series expansions of analytic functions. We present a version of the Schwarz lemma based on the first Fibonacci polynomial. By considering the boundary version of the Schwarz lemma, we deduce new inequalities that provide deeper insights into the relationship between these two mathematical concepts. Beyond their theoretical significance, we also present practical implications of our results. Specifically, we show that the deduced results can be applied to get marginally stable discrete-time transfer functions in digital control systems.

Autotuners represent a combination of a relay feedback identification test and some control design method. In this contribution, models with up to three parameters are estimated by means of a single asymmetrical relay experiment. Then a stable low order transfer function with a time delay term is identified by a relay experiment. Autotuning principles then combine asymmetrical relay feedback tests with a control synthesis. Two algebraic control syntheses then are presented in this paper. The first one is based on the ring of proper and stable rational functions R PS. The second one utilizes a special ring R MS, a set of RQ-meromorphic functions. In both cases, controller parameters are derived through a general solution of a linear Diophantine equation in the appropriate ring. A final controller can be tuned by a scalar real parameter m>0. The presented philosophy covers a generalization of PID controllers and the Smith-like control structure. This contribution deals with the implementation of proposed autotuners and presents some illustrative examples. A Matlab toolbox for automatic design and simulation was developed and various simulations performed and analyzed.

Optimal Hankel-norm approximation of stable systems with first-order stable weighting functions

Conditions for a Class of Rational Approximants of Fractional Differentiators/Integrators to Enjoy the Interlacing Property

Stray free switched capacitor loop biquad that realizes different generic transfer functions

l1 Robust Identification of Fractional Transfer Functions