Stability Domain Of Systems Research Articles

Torsional behaviors of motor rotor of permanent magnet semi-direct drive system for aerial passenger device

Considering the influence of motor shaft torsional damping, the torsional dynamics equations of a permanent magnet semi-direct drive rotor system in an aerial passenger device are derived. The derivation relies on the coupling between the mathematical model and the gear dynamics model of the permanent magnet motor, and the Lagrange–Maxwell equations are used for streamlined analysis. To protect the motor under extreme working conditions, the influence of supercritical Hopf bifurcation caused by different torsional dampings of the motor shaft on the torsional vibration of the motor rotor is investigated. Based on the Hurwitz criterion, the influence of the linear control gain and nonlinear gain of the washout filter on the system bifurcation point and the limit cycle amplitude of the system is analyzed. Then, from the perspective of the system instability and oscillation caused by friction damping change of the drive motor and the complex electromechanical coupling behavior in the permanent magnet semi-direct drive cutting drive system of the aerial passenger device, the system stability domain is defined. The results can be applied to effectively suppress the torsional vibration of the shaft system in the permanent magnet semi-direct drive system of the aerial passenger device, providing a theoretical guidance for stable operation of the system.

Complexity analysis of technology spillover supply chain with dual business objectives

ABSTRACT Based on the existence of technology spillover effect of manufacturers, considering the manufacturer's commercial goals of profit and market share, a dynamic price game model of technology spillover supply chain with dual commercial goals is established. Based on game theory and nonlinear dynamics theory, the equilibrium point and local stability of the system are analyzed. In addition, the effects of price adjustment rate, balance coefficient of business objectives, and technology spillover on model complexity, the change of manufacturer price and profit were analyzed through numerical simulation. The results show that the price adjustment rate, the balance coefficient of business objectives, and the technology spillover have an impact on the stability and complexity of the manufacturer's price competition model. Rationally controlling the price adjustment rate, and enhancing technological spillovers are beneficial to the healthy development of manufacturers and the healthy competition among manufacturers, maintaining the stability of product market prices, and effectively avoiding market chaos. Moreover, when considering market share, manufacturers can expand the system stability domain.

Bifurcation Analysis and Fractional PD Control of Gene Regulatory Networks with sRNA

This paper investigates the problem of bifurcation analysis and bifurcation control of a fractional-order gene regulatory network with sRNA. Firstly, the process of stability change of system equilibrium under the influence of the sum of time delay is discussed, the critical condition of Hopf bifurcation is explored, and the effect of fractional order on the system stability domain. Secondly, aiming at the system’s instability caused by a large time delay, we design a controller to improve the system’s stability and derive the parameter conditions that satisfy the system’s stability. It is found that changing the parameter values of the controller within a certain range can control the system’s nonlinear behaviours and effectively expand the stability range. Then, a numerical example is given to illustrate the results of this paper.

Hopf Bifurcation Control for Rolling Mill Multiple-Mode-Coupling Vibration Under Nonlinear Friction

Rolling mill system may lose its stability due to the change of lubrication conditions. Based on the rolling mill vertical–torsional–horizontal coupled dynamic model with nonlinear friction considered, the system stability domain is analyzed by Hopf bifurcation algebraic criterion. Subsequently, the Hopf bifurcation types at different bifurcation points are judged. In order to restrain the instability oscillation induced by the system Hopf bifurcation, a linear and nonlinear feedback controller is constructed, in which the uncoiling speed of the uncoiler is selected as the control variable, and variations of tensions at entry and exit as well as system vibration responses are chosen as feedback variables. On this basis, the linear control of the controller is studied using the Hopf bifurcation algebraic criterion. And the nonlinear control of the controller is studied according to the center manifold theorem and the normal form theory. The results show that the system stability domain can be expanded by reducing the linear gain coefficient. Through choosing an appropriate nonlinear gain coefficient, the occurring of the system subcritical bifurcation can be suppressed. And system vibration amplitudes reduce as the increase of the nonlinear gain coefficient. Therefore, introducing the linear and nonlinear feedback controller into the system can improve system dynamic characteristics significantly. The production efficiency and the product quality can be guaranteed as well.

Effect of rolling process parameters on stability of rolling mill vibration with nonlinear friction

Friction-induced vibration is a typical self-excited phenomenon in the rolling process. Since its important industrial relevance, a rolling mill vertical-torsional-horizontal coupled vibration model with the consideration of the nonlinear friction has been established by coupling the dynamic rolling process model and the rolling mill structural model. Based on this model, the system stability domain is determined according to Hurwitz algebraic criterion. Subsequently, the Hopf bifurcation types at different bifurcation points are judged. Finally, the influences of rolling process parameters on the system stability domain are analyzed in detail. The results show that the critical boundaries of vertical vibration modal, horizontal vibration modal and torsional vibration modal will move with the change of rolling process parameters, and the system stability domain will change simultaneously. Among the parameters, the reduction ratio has the most significant effect on the stability of the system. And when rolling the thin strip, the system stability domain may be only enclosed by the critical boundaries of vertical vibration modal and torsional vibration modal. In that case, the system instability induced by horizontal vibration modal would not occur. The study is helpful for proposing a reasonable rolling process planning to reduce the possibility of vibration, as well as selecting an optimal rolling process parameter to design a controller to control the rolling mill vibration.

Nonlinear dynamic modeling in low frequency and control system stability domain determination for a LPE

Algorithms have been presented for the low-frequency nonlinear dynamic modeling and stability domain determination of liquid propellant engines. Also, the considerations that can facilitate the modeling process and remove the drawbacks have been presented. The defined algorithms and the stated considerations have been applied for a particular liquid propellant engine. The equations describing the mentioned engine have been classified into 11 subsystems. The simulations have been performed in the MATLAB Simulink software environment. Each simulated subsystem represents one or several physical subsystems whose interactions have been defined in the overall form of engine configuration. The engine modeling results have been validated by the data of cold and warm tests of the subsystems and engine. In the process of determining the stable operation range of the mentioned engine, by linearizing the obtained nonlinear model, which accompanies the correct determination of model input and output, and by applying the Nyquist criterion, the stability analysis of the regulator and engine systems has been performed control system and the stability margin and the cutoff frequencies have been obtained. Finally, the effects of structural and process parameters of the relevant subsystems on the engine’s stable range of performance have been evaluated.

Study of Impact of Tool Wear on Stable Region for Die Steel Cutting Process

The stability of the process systems has an obvious impact on the cutting quality, seeking cutting process stability region is an important aspect of the cutting mechanism. In this paper, establishing cutting process dynamic analysis model is based on the tool wear and creating the evaluation model about the influence of tool wear on the cutting system stability by power spectral RMS method. Root locus plot of non-uniform load distribution is obtained and the minimum stiffness ratio in the root locus plot is determined. So as to arrive the limit plot in different tool wear cutting system stability domain and determine the flank wear limit in the stable cutting quantitatively and offer the parameter of design and evaluation indicators to cutting system. The results found that with the increase in cutting speed and tool wear intensifies, the system stability is sharp in decline and tool wear is more intense. Obtaining limit diagram of cutting stability domain is suitable for providing a theoretical basis for processing in the different tool wear conditions.

Design and analysis of a model predictive controller for active queue management

Model predictive (MP) control as a novel active queue management (AQM) algorithm in dynamic computer networks is proposed. According to the predicted future queue length in the data buffer, early packets at the router are dropped reasonably by the MPAQM controller so that the queue length reaches the desired value with minimal tracking error. The drop probability is obtained by optimizing the network performance. Further, randomized algorithms are applied to analyze the robustness of MPAQM successfully, and also to provide the stability domain of systems with uncertain network parameters. The performances of MPAQM are evaluated through a series of simulations in NS2. The simulation results show that the MPAQM algorithm outperforms RED, PI, and REM algorithms in terms of stability, disturbance rejection, and robustness.

Stability Domain of Systems of Three Arbitrary Charges

We present results on the stability of quantum systems consisting of a negative charge −q1 with mass m1 and two positive charges q2 and q3, with masses m2 and m3, respectively. We show that, for given masses mi, each instability domain is convex in the plane of the variables \(\). A new proof is given of the instability of muonic ions \(\). We then study stability in some critical regimes where \(\): Stability is sometimes restricted to large values of some mass ratios; the behaviour of the stability frontier is established to leading order in \(\). Finally we present some conjectures about the shape of the stability domain, both for given masses and varying charges, and for given charges and varying masses.

The stability domains of hamiltonian systems

Linear Hamiltonian systems with an arbitrary number of degrees of freedom, which depend smoothly on a vector of real parameters, are investigated. All possible singularities of the boundary of the stability domain of Hamiltonian systems of general position are determined and described for the case of two and three parameters. In the first approximation, the geometry of these singularities (the orientation in the parameter space, angles, etc.) is determined on the basis of the first derivative of the matrix of the system with respect to the parameters, as are the eigenvectors and generalized eigenvectors evaluated at the singular point. A detailed investigation is made of gyroscopic systems as a special case of Hamiltonian systems. As mechanical examples, an account is given of the problem of the stability of the oscillations of a tube through which a fluid is flowing, and of the stability of the motion of a two-body system. The tangent cones to the stability domains of these systems at singular points of the “cusp” and “dihedral angle” type, which arise on the boundaries of these domains, are found.

Comments on "Decision-surface estimate of nonlinear system stability domain by Lie series method"

In the above paper,' Kormanik and Li have given a systematic procedure to obt.ain an analytic expresion for the stability boundary of a seeond-order nonlinear system, whose stable equilibrium point is located at the origin of t,he phase plane. In the present correspon- dence, we would like to make some comments concerning the useful- ness of the methods applied in that, paper. Lie series method has been used by Kormanik and Li1 to obtain a set of points which lie very close t.o exact stability boundary, by simultaneous solution of the system stat,e equations and the modified form of Zubov's partial differential equat.ion ((l) and (5)).* We have worked out. the example reported' on an IBM '7044 com- puter, using Lie series method and obtained the results as reported by the authors. We have also integrat.ed (1) and (5)' simultaneously, using a standard numerical integration technique-Fourth order Runge-Kutt.a method, and obtained the identical results (see Fig. (l)), with much less computational effort and reduced computing time. The total computer t.ime taken including execut.ion and com- pilation, using Runge-Kut,ta method was 20 s. We would accord- ingly like to know t.he claims the authors make about advantages of Lie series method over standard numerical integration techniques. Kormanik and Li1 have considered a simple example of Vander- pol-Oscillator where linlit cycle phenomenon is exhibited. It appears however that the techniques described' will be insufficient to obt.ain regions of attraction for systems having a stable equilibrium point but with phase-plane trajectories as shorn in Fig. 2. The basic problem in Fig. 2 is the computat.ion of t.he domain of at.traction of the equilibrium point.. This kind of problem is encountered while dealing with transient stabilit,y studies in power system, e.g., com- putation of domain of stability for a single machine connected to an infinit,e bus taking t.ransient saliency and damping into account. This same nature of phase plane t.rajectories is also exhibited in some phase-locked loop synchronization studies (I). One important problem encountered in 6he integration process is in the choice of t.he init.ia1 guess for t.he state variables. The authors suggest t.hat, in general, a set of initial values may be chosen as lying on sufficiently closed quadrdic surface around the st.able equilibrium point x = 0, which satisfies (2)' in the for the given +(x). If me t.ake a positive definite +(x), (2)' is always satisfied, as long as we stay within the st.ability domain, i.e., V(x) < 1. So we are un- able to appreciate what the authors wanted to convey by the term, small neighborhood. The necessity for a small neighborhood does not appear to be very stringent as long as above mentioned conditions are met. Furthermore, for the problem relatcd to Fig. 2, one would have

Decision surface estimate of nonlinear system stability domain by Lie series method

The Lie series recursive algorithm for Zubov's partial differential equation is used to generate two sets of points, where one represents the exact asymptotic stability boundary of an equilibrium state of the nonlinear system under consideration and the other is interior to it. Based on these two sets of data as training samples of two classes, a decision hypersurface can be determined such that it is a close approximation of the asymptotic stability boundary.