Suppression Of Limit Cycles Research Articles

Multivariable control of the bifurcation and harmonic perturbations to improve the performance of air-handling units

In this research, nonlinear dynamics of an air-ehandling unit (AHU) is studied for tracking objectives, in the presence of harmonic perturbations. Three arbitrary realistic set-paths are considered for the indoor temperature and relative humidity. Two controllers based on feedback linearization (FBL) and pole placement approaches are designed to preserve the dynamic system around the desired tracking paths. It is shown that FBL controller works efficiently in bifurcation control and transforms the quasi-periodic limit cycles into the periodic ones (and consequently comfortable indoor conditions). In addition, FBL controller guarantees suppression of larger periodic limit cycles into the smaller ones, while it requires the lower air and cold water flow rates with less oscillatory behavior (in comparison with the pole-placement controller). However, it is observed that FBL controller fails in bifurcation control when the disturbance frequency increases. Re-tuning the dynamic gains of FBL controller is essential under such conditions.

$l_{2}-l_{\infty}$ Suppression of Limit Cycles in Interfered Two-Dimensional Digital Filters: A Fornasini–Marchesini Model Case

Recently, Ahn proposed an l 2 -l ∞ stability criterion for interfered two-dimensional (2-D) digital filters described by the Roesser model. However, until now, no criteria for interfered 2-D digital filters in the Fornasini-Marchesini (FM) model have been studied. As a continuation of the results, this brief proposes a new criterion for the l 2 -l ∞ suppression of limit cycles in interfered 2-D digital filters in the FM model. The proposed criterion ensures the asymptotic stability and l 2 -l ∞ performance of 2-D digital filters. The effectiveness of the proposed criterion is demonstrated using numerical examples. The work in this brief and that of the Roesser model provide, as an integrity, systematic results on limit cycle suppression for 2-D digital filters in the l 2 -l ∞ sense.

Strictly passive suppression of limit cycles in direct form digital filters with saturation nonlinearity: linear matrix inequality approach

In this paper, we propose a new linear matrix inequality criterion for suppression of limit cycles in state–space direct form digital filters with saturation arithmetic and external interference via a passivity approach. The passive approach is employed to reduce the effect of external interference on the digital filter. The criterion guarantees not only asymptotic stability but also passivity from the external interference to the output vector. This criterion is in the form of linear matrix inequality; hence, it is computationally tractable. An example shows the effectiveness of the proposed criterion. Copyright © 2013 John Wiley & Sons, Ltd.

Implementation of Resonant Controllers and Filters in Fixed-Point Arithmetic

Resonant controllers and filters are useful in voltage-source-converter control systems. Although the trend is toward implementation in floating-point arithmetic, fixed-point arithmetic is still of interest, but requires much greater care in the algorithm design. This paper covers some important issues, namely, choice of structure, design formulas, scaling, sensitivity, quantization-noise amplification, and suppression of overflow limit cycles. The results presented should be particularly helpful as design guidelines to practical engineers in a situation where one often resorts to trial and error.

Suppression of limit cycles in second-order companion form digital filters with saturation arithmetic

A condition for second-order companion form digital filters with time variant nondeterministic saturation overflow arithmetic to be free of limit cycles was previously given by Ooba. The condition corresponds to a region which is a subset of the stability triangle. In the present paper, time invariant deterministic saturation nonlinearities are considered. It is shown that, with such nonlinearities, the system is free of limit cycles in whole of the stability triangle.

A new frequency-domain criterion for elimination of limit cycles in fixed-point state-space digital filters using saturation arithmetic

In [Singh V. Elimination of overflow oscillations in fixed-point state-space digital filters using saturation arithmetic. IEEE Trans Circ Syst 1990;37(6):814–8], a frequency-domain criterion for the suppression of limit cycles in fixed-point state-space digital filters using saturation overflow arithmetic was presented. The passivity property owing to the presence of multiple saturation nonlinearities was exploited therein. In the present paper, a new notion of passivity, namely, that involving the state variables is considered, thereby arriving at an entirely new frequency-domain criterion for the suppression of limit cycles in such filters.

Suppression of limit cycles in a free electron laser

To take complete benefit of the Free Electron Laser (FEL) features, we have developed a feedback control scheme designed to suppress the dynamical instabilities affecting the FEL output intensity. The principle is to stabilize an unstable stationary state that coexists with the unwanted limit cycle. This paper gives a theoretical and experimental description of the stabilized stationary regime of a storage ring FEL in presence of the feedback control. We present a numerical model of the FEL with control, that describes the longitudinal dynamics of the laser pulse in condition of detuning between the FEL and the electron beam. These theoretical results are compared with experiments performed on the Super-ACO FEL. The established feedback control provides stable operation of the FEL.

Suppression of overflow limit cycles in LDI all-pass/lattice filters

In this paper it is shown that zero-input overflow limit cycles can be suppressed in a class of lossless digital integrator (LDI) all-pass filters. This holds for any filter order, provided that saturation overflow characteristics are used at the input of each delay and for certain restrictions for the multiplier values. The results are shown to apply also to lossless digital differentiator (LDD) filters. The restrictions of multiplier values have the effect of excluding certain combinations of poles within the unit circle, most of which are in the left half circle where corresponding LDD filters can be used. Asymptotic stability can be guaranteed for all second-order LDI and LDD filters.

Suppression of limit cycles in the first-order two-dimensional direct form digital filter with a controlled rounding arithmetic

The first-order two-dimensional direct-form digital filter with magnitude truncation is known to be free from limit cycles for a limited range of allowed filter coefficients. In this correspondence, the quantization technique of controlled rounding is used to extend the region of filter coefficients for which suppression of limit cycles can be proved. With controlled rounding a signal is quantized in the direction of a control signal, which is formed by an integer combination of preceding signal values. The absence of limit cycles is proved with a properly chosen Lyapunov function.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Limit cycles due to roundoff in state-space digital filters

A deterministic analysis is presented for limit cycles due to roundoff in state-space digital filters. Two new sufficient conditions are established for the roundoff stability, i.e. suppression of limit cycles, in digital filters. Using these results, restrictions on the location of poles are found for various realizations to be free from roundoff limit cycles. >

Comments on "Suppression of Limit Cycles in Digital filters designed with One Magnitude-Truncation Quantizer

Comments on "Suppression of Limit Cycles in Digital filters designed with One Magnitude-Truncation Quantizer

Suppression of limit cycles in digital filters by random dither

The use of random dither to suppress limit cycles in 2nd-order direct-form digital filter sections is discussed. Experimental comparisons are made, for binary random dither and uniformly distributed random dither, of the average time taken to suppress limit cycles and of the increase in output noise caused by the dither. A new form of dither is introduced, termed bandstop dither. This has the advantage of suppressing limit cycles about as quickly as binary dither yet it causes an increase in output noise of less than 2 dB.

Suppression of limit cycles in digital filters designed with one magnitude-truncation quantizer

A sufficient condition for the absence of zero-input granularity limit cycles in error feedback digital filters designed with one magnitude-truncation quntizer is presented. This sufficient condition Is satisfied, i.e., no limit cycles can exist, in first- and second-order digital filters, if the parameters in the error feedback loop are properly chosen. The roundoff noise in these digital filters is also discussed.

Analysis of non-linear sampled-data systems with transportation lag†

A detailed investigation is made into the effect of inherent transportation lag on the nature of limit cycles sustained in a second-order sampled-data system containing a relay type non-linearity. The effectiveness of the either signals of sinusoidal, triangular and square wave shape to suppress limit cycles is studied in detail and the advantages and disadvantages of each wave shape are discussed. The method of analysis is via the state transition technique and it is advantageously used to evaluate the response of the system until a final steady-state value is attained by the controlled variable. The results conclusively prove that the wave shape and the amplitude of the dithering signal have a pronounced influence on the manner of suppression of limit cycles and the final steady-state error. It is clearly shown that systems with larger values of transportation lag call for stronger dithering signals in order to quench the limit cycles that would otherwise persist with a time period which is an integral ...