Control Of Limit Cycle Oscillations Research Articles

Study on Mechanical Vibration Control of Limit Cycle Oscillations in the Van der Pol Oscillator by means of Nonlinear Energy Sink

Study on Mechanical Vibration Control of Limit Cycle Oscillations in the Van der Pol Oscillator by means of Nonlinear Energy Sink

Feedback control of limit cycle oscillations and transonic buzz, using the nonlinear transonic small disturbance aerodynamics

In this paper, a systematic method to suppress transonic buzz with feedback is presented. A trailing edge control surface in the form of part-span flap was used only to modify and control the unsteady aerodynamic loading on the wing. The flap rotation was used to provide feedback, which consisted of a weighted linear combination of the amplitudes of the principal modes of the structure, referred to as the control law. A linear, optimal feedback control law, that is synthesized systematically based on pseudo-spectral time domain analysis, may be used in principle, to assess its capacity to actively suppress the buzz in the transonic flow domain by using a servo-controlled control surface to modify the unsteady, nonlinear aerodynamic loads on the wing. Thus, it is essential that a set of feasible control laws are first constructed. In this paper, this is done by applying the doublet-lattice method. Restrictions, such as near-zero structural damping in the flap mode, were imposed on the aeroelastic model to facilitate the occurrence of transonic buzz. The feasible set of control laws were then assessed using the nonlinear transonic small disturbance theory and an optimum control is selected to suppress the buzz. The essential differences of the behaviour of the closed-loop system in nonlinear transonic flow, when compared to the applications of linear optimal control in linear potential flow, are presented and discussed.

Tracking Control of Limit Cycle Oscillations in an Aero-Elastic System

Limit cycle oscillations (LCOs) affect current fighter aircraft and are expected to be present on next generation fighter aircraft. Current efforts in control systems designed to suppress LCO behavior have either used a linear model, restricting the flight regime, require exact knowledge of the system dynamics, or require uncertainties in the system dynamics to be linear-in-the-parameters and only present in the torsional stiffness. Furthermore, the aerodynamic model used in prior research efforts neglects nonlinear effects. This paper presents the development of a controller consisting of a continuous robust integral of the sign of the error (RISE) feedback term with a neural network (NN) feedforward term to achieve asymptotic tracking of uncertainties that do not satisfy the linear-in-the-parameters assumption. Simulation results are presented to validate the performance of the developed controller.

Control of limit cycle oscillations in a multiple‐sampled digitally controlled buck converter

SummaryDigital control in switching power converters has been proposed and researched in recent years. However, one of the problems which arise in these circuits is that of quantization‐induced limit cycle oscillations, which are generally considered to be undesirable. In this work, we investigate the addition of new control terms in the feedback loop of the system, in order to actively prevent these limit cycles from occurring. Firstly, the addition of a sinusoidal signal is considered, and then a more complicated signal which focuses on interrupting how the system switches between duty cycle levels is presented. The methods are effective in removing the limit cycle oscillations which arise in the system. Copyright © 2013 John Wiley & Sons, Ltd.

Control of Limit Cycle Oscillations of a Two-Dimensional Aeroelastic System

Linear and nonlinear static feedback controls are implemented on a nonlinear aeroelastic system that consists of a rigid airfoil supported by nonlinear springs in the pitch and plunge directions and subjected to nonlinear aerodynamic loads. The normal form is used to investigate the Hopf bifurcation that occurs as the freestream velocity is increased and to analytically predict the amplitude and frequency of the ensuing limit cycle oscillations (LCO). It is shown that linear control can be used to delay the flutter onset and reduce the LCO amplitude. Yet, its required gains remain a function of the speed. On the other hand, nonlinear control can be effciently implemented to convert any subcritical Hopf bifurcation into a supercritical one and to significantly reduce the LCO amplitude.

Passive Control of Limit Cycle Oscillations in a Thermoacoustic System Using Asymmetry

In this paper we investigate oscillations of a dynamical system containing passive dynamics driven by a positive feedback and how spatial characteristics (i.e., symmetry) affect the amplitude and stability of its nominal limit cycling response. The physical motivation of this problem is thermoacoustic dynamics in a gas turbine combustor. The spatial domain is periodic (passive annular acoustics) which are driven by heat released from a combustion process, and with sufficient driving through this nonlinear feedback a limit cycle is produced which is exhibited by a traveling acoustic wave around this annulus. We show that this response can be controlled passively by spatial perturbation in the symmetry of acoustic parameters. We find the critical parameter values that affect this oscillation, study the bifurcation properties, and subsequently use harmonic balance and temporal averaging to characterize periodic solutions and their stability. In all of these cases, we carry a parameter associated with the spatial symmetry of the acoustics and investigate how this symmetry affects the system response. The contribution of this paper is a unique analysis of a particular physical phenomena, as well as illustrating the equivalence of different nonlinear analysis tools for this analysis.

Output Feedback Modular Adaptive Control of a Nonlinear Prototypical Wing Section

The paper presents nonlinear adaptive control systems for the control of limit cycle oscillations of a prototypical wing section with structural nonlinearities using only output feedback. The chosen model describes the plunge and pitch motion of a wing. The model includes plunge and pitch nonlinearities, and has a single control surface for the purpose of control. Using a canonical representation of the aeroelastic system, a modular output feedback adaptive control system consisting of an input-to-state stabilizing controller and a passive identifier (an observer and adaptation law) is derived. In the closed-loop system, asymptotic stabilization of the pitch and plunge motion is accomplished. Simulation results show that the control system is effective in regulating the state vector to the origin in spite of large parameter uncertainties.

Control of a Nonlinear Wing Section Using Leading- and Trailing-Edge Surfaces

The control of nonlinear aeroelastic response of a wing section with a continuous stiffening-type structural nonlinearity is examined through analytical and experimental studies. Motivated by the limited effectiveness of using a single, trailing-edge control surface for the suppression of limit-cycle oscillations of a typical wing section, improvements in the control of limit-cycle oscillations are investigated through the use of multiple control surfaces, namely, an additional leading-edge control surface. The control methodology consists of a feedback linearization approach that transforms the system equations of motion via Lie algebraic methods and a model reference adaptive control strategy that augments the closed-loop system to account for inexact cancellation of nonlinear terms due to modeling uncertainty. Specifically, uncertainty in the nonlinear pitch stiffness is examined. It is shown through simulations and experiments that globally stabilizing control may be achieved by using two control surfaces.

Control Analysis for Autonomously Oscillating Biochemical Networks

It has hitherto not been possible to analyze the control of oscillatory dynamic cellular processes in other than qualitative ways. The control coefficients, used in metabolic control analyses of steady states, cannot be applied directly to dynamic systems. We here illustrate a way out of this limitation that uses Fourier transforms to convert the time domain into the stationary frequency domain, and then analyses the control of limit cycle oscillations. In addition to the already known summation theorems for frequency and amplitude, we reveal summation theorems that apply to the control of average value, waveform, and phase differences of the oscillations. The approach is made fully operational in an analysis of yeast glycolytic oscillations. It follows an experimental approach, sampling from the model output and using discrete Fourier transforms of this data set. It quantifies the control of various aspects of the oscillations by the external glucose concentration and by various internal molecular processes. We show that the control of various oscillatory properties is distributed over the system enzymes in ways that differ among those properties. The models that are described in this paper can be accessed on http://jjj.biochem.sun.ac.za.

Identification and Control of Limit Cycle Oscillations in Aeroelastic Systems

Nonlinearities in the aeroelastic system induce pathologies such as the observed store-induced limit cycle oscillations found with certain high-performance aircraft configurations. Many prior studies, including efforts by these authors, focus on the nonlinear behavior of the uncontrolled, nonlinear aeroelastic system. These studies are briefly reviewed. More importantly, there is limited study for the active control of these nonlinear aeroelastic systems. Although a linear controller may stabilize the nonlinear system under some circumstances, empirical evidence suggests that these control methods -will prove unreliable in strongly nonlinear regimes and that stability is not guaranteed. Herein, the authors describe the development of control strategies appropriate for these nonlinear systems. A nonlinear controller, and the resulting closed-loop stability, based on a partial feedback linearization are discussed. The approach depends upon the exact cancellation of the nonlinearity and, as a co_nsequence, the authors introduce an adaptive method in which guarantees of stability are evident. The authors present experimental results obtained using the adaptive controller.

Experiments on Control of Limit-Cycle Oscillations in a Typical Section

The experimental application of active control to reduce or eliminate limit-cycle oscillations in a typical section airfoil is presented. The test rig consists of a three-degree-of-freedom typical section which has free play in the e ap restoring stiffness. Such a free play was intended to mimic that associated with control surface mechanism backlashinarealsystem.Controliseffectedby meansofanactuatoractingonthee ap.AlinearquadraticGaussian optimization scheme is used to design a compensator that will accomplish three goals: 1 ) reduce or eliminate limitcycle oscillations, 2 ) increase the e utter boundary, and 3 ) be robust to variations in the e ow velocity. Although the typical section isa nonlineardynamicsystem, thecontrol system design wasbased on thelineartypical section with no freeplay. The results presented indicatethat each ofthesegoalswas accomplished. More specie cally, limit-cycle oscillations were eliminated, the e utter velocity was increased by 17%, and the control system was stable over a wide range of e ow conditions.

Control of limit cycle oscillations in second-order recursive digital filters using constrained random quantization

Limit cycles occur in recursive digital filters due to quantization of fixed point products. A common method of preventing these limit cycles from degrading the performance of the filter is to increase the internal wordlength of the filter beyond the input encoding accuracy, increasing the cost of the filter. This paper proposes two techniques which suppress limit cycles. One involves constrained random quantization of the output of the B <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</inf> multiplier of a standard second-order digital filter section. A second technique detects and eliminates dc and half sampling rate limit cycles. These techniques control all kinds of limit cycles produced by recursive filters with zero input, at the cost of a modest increase in circuit complexity.