共查询到20条相似文献,搜索用时 15 毫秒
1.
In this paper, a four-dimensional system of autonomous ordinary differential equations depending on a small parameter is considered. Suppose that the unperturbed system is composed of two planar systems: one is a Hamiltonian system and another system has a focus. By using the Poincaré map and the integral manifold theory, sufficient conditions for the existence of periodic solutions and invariant tori of the four-dimensional system are obtained. An application of our results to a nonlinearly coupled Van der Pol–Duffing oscillator system is given. 相似文献
2.
The control of lightweight and high speed manipulators requires special strategies to prevent and damp the vibrations caused
by the inertial components of motion, especially when dealing with flexible-links mechanism. In this paper a constrained MPC
(Model Predictive Control) system is proposed as an effective control strategy for position and vibration control of flexible
links mechanism. Here this control system is applied to an electric actuated four-link planar mechanism with three flexible
links laying on the horizontal plane. The effectiveness of this controller is evaluated by the means of exhaustive numerical
simulations. 相似文献
3.
An isotropic flexible shaft, acted by nonlinear fluid-induced forces generated from oil-lubricated journal bearings and hydrodynamic
seal, is considered in this paper. Dimension reductions of the rotor system were carried out by both the standard Galerkin
method and the nonlinear Galerkin method. Numerical simulations provide bifurcation diagrams, spectrum cascade, orbits of
the disk center and Poincaré maps, to demonstrate the dynamical behaviors of the system. The results reveal transitions, or
bifurcations, of the rotor whirl from being synchronous to non-synchronous as the unstable speed is exceeded. The non-synchronous
oil/seal whirl is a quasi-periodic motion. In the regime of quasi-periodic motion, the “windows” of multi-periodic motion
were found. The investigation shows that the nonlinear Galerkin method has an advantage over the standard one with the same
order of truncations, because the influences of higher modes are considered by the former. 相似文献
4.
This paper employs differential transformation (DT) method to analyze and control the dynamic behavior of a gyroscope system. The analytical results reveal a complex dynamic behavior comprising periodic, subharmonic, quasiperiodic, and chaotic responses of the center of gravity. Furthermore, the results reveal the changes which take place in the dynamic behavior of the gyroscope system as the external force is increased. The current analytical results by DT method are found to be in good agreement with those of Runge?CKutta (RK) method. In order to suppress the chaotic behavior in gyroscope system, the sliding mode controller (SMC) is used and guaranteed the stability of the system from chaotic motion to periodic motion. Numerical simulations are shown to verify the results. The proposed DT method and controlling scheme provide an effective means of gaining insights into the nonlinear dynamics and controlling of gyroscope systems. 相似文献
5.
Aiming at the problems in parameter identification of an electronic throttle, this paper proposes a novel hybrid optimization algorithm to search the optimal parameter values of the plant. The parameter identification of an electronic throttle is considered as an optimization process with an objective function minimizing the errors between the measurement and identification, and the optimal parameter values of the plant are searched by using a hybrid optimization algorithm. The proposed hybrid optimization algorithm, effective combination of parallel chaos optimization algorithm (PCOA) and simplex search method, preserves both the global optimization capability of PCOA and the accurate search ability of simplex search method. Simulation and experiment results have shown the good performance of the proposed approach. 相似文献
6.
A novel robust hybrid tracking control for robotic system is proposed. This hybrid control scheme combines computed torque control (CTC) with neural network, variable structure control (VSC) and nonlinear H ?? control methods. It is assumed that the nominal system of robotic system is completely known, which is controlled by using CTC method. Neural network is designed to approximate parameter uncertainties, VSC is used to eliminate the effect of approximation error, and H ?? control is employed to achieve a desired robust tracking performance. Based on Lyapunov stability theorem, it can be guaranteed that all signals in closed loop are bounded and a specified H ?? tracking performance is achieved by employing the proposed robust hybrid control. The validity of the control scheme is shown by computer simulation of a two-link robotic manipulator. 相似文献
7.
Zuo-Lei Wang 《Nonlinear dynamics》2010,59(3):455-462
This work is concerned with projective synchronization of hyperchaotic Lü system and Liu system by add-order method. Different
controllers are designed to projective-synchronize the two nonidentical chaotic systems, active control is used when parameters
are known, while the adaptive control law and the parameter update rule are derived via adaptive control when parameters are
uncertain. Moreover, the convergence rates of the scheme can be adjusted by changing the control coefficients. Finally, numerical
simulations are also shown to verify the results. 相似文献
8.
Based on the dynamic model, a novel nonlinear tracking controller is developed to overcome the nonlinear dynamics and friction
of a planar parallel manipulator. The dynamic model is formulated in the active joint space, and the active joint friction
is described with the Coulomb + viscous friction model. A nonlinear tracking controller is designed to eliminate the tracking
error by using the power function. The nonlinear tracking controller is proven to guarantee asymptotic convergence to zero
of both the tracking error and error rate with the Barbalat’s lemma. The trajectory tracking experiment of the proposed controller
is implemented on an actual five-bar planar parallel manipulator both at the low-speed and high-speed motion. Moreover, the
control performances of the proposed controller are compared with the results of the augmented PD (APD) controller. 相似文献
9.
This paper discusses the synchronization and anti-synchronization of new uncertain unified chaotic systems (UUCS). Based on the idea of active control, a novel active Pinning control strategy is presented, which only needs a state of new UUCS. The proposed controller can achieve synchronization between a response system and a drive system, and ensure the synchronized robust stability of new UUCS. Numerical simulations of new UUCS show that the controller can make chaotic systems achieve synchronization or anti-synchronization in a quite short period and both are of good robust stability. 相似文献
10.
To overcome the shortcomings of extreme time-consuming in solving the Reynolds equation, two efficient calculation methods,
based on the free boundary theory and variational principles for the unsteady nonlinear Reynolds equation in the condition
of Reynolds boundary, are presented in the paper. By employing the two mentioned methods, the nonlinear dynamic forces as
well as their Jacobians of the journal bearing can be calculated saving time but with the same accuracy. Of these two methods,
the one is called a Ritz model which manipulates the cavitation region by simply introducing a parameter to match the free
boundary condition and, as a result, a very simple approximate formulae of oil-film pressure is being obtained. The other
one is a one-dimensional FEM method which reduces the two-dimensional variational inequality to the one-dimensional algebraic
complementary equations, and then a direct method is being used to solve these complementary equations, without the need of
iterations, and the free boundary condition can be automatically satisfied. Meanwhile, a new order reduction method is contributed
to reduce the degrees of freedom of a complex rotor-bearing system. Thus the nonlinear behavior analysis of the rotor-bearing
system can be studied time-sparingly. The results in the paper show the high efficiency of the two methods as well as the
abundant nonlinear phenomenon of the system, compared with the results obtained by the usual numerical solution of the Reynolds
equation. 相似文献
11.
The problem of time minimization of a holonomic scleronomic mechanical system on a prescribed trajectory between two specified
positions in configuration space is solved. The generalized force with restricted coordinates is taken as the controlling
force. The application of the Green theorem (the well-known Miele method in flight mechanics) has shown that at every instant
at least one control is at its boundary and possesses controlling functions with interruptions. It is assumed that at least
one generalized coordinate exists that is monotonous during the interval of movement. An algorithm for numerical computation
is presented for assessing the boundary of the admissible domain in the state space, thus, solving the problem of finding
the optimal control as a function of time. Numerical integration is, therefore, carried out forward from the start point and
backward from the end point by the use of the Runge-Kutta method. The mentioned procedure is illustrated in the example of
time minimization for a manipulator which has its tip moving in a straight line. The application of the presented method simplifies
solving of this type of problem compared to other methods, for instance, dynamic programming. 相似文献
12.
In this paper, a novel adaptive interval type-2 fuzzy sliding mode control (AIT2FSMC) methodology is proposed based on the
integration of sliding mode control and adaptive interval type-2 fuzzy control for chaotic system. The AIT2FSMC system is
comprised of a fuzzy control design and a hitting control design. In the fuzzy control design, an interval type-2 fuzzy controller
is designed to mimic a feedback linearization (FL) control law. In the hitting control design, a hitting controller is designed
to compensate the approximation error between the FL control law and the interval type-2 fuzzy controller. The parameters
of the interval type-2 fuzzy controller, as well as the uncertainty bound of the approximation error, are tuned adaptively.
The adaptive laws are derived in the sense of Lyapunov stability theorem, thus the stability of the system can be guaranteed.
The proposed control system compared to adaptive fuzzy sliding mode control (AFSMC). Simulation results show that the proposed
control systems can achieve favorable performance and robust with respect to system uncertainties and external disturbances. 相似文献
13.
In this paper, we make a systematic analysis of the dynamics of a predator–prey system with type-II functional response, in which the predator growth rate is affected by the presence of a super predator. The main aim of this research is to study the consequences of the presence of a super predator on the system dynamics. The existence and stability of the different possible equilibrium points are studied, and we conclude that the maximum consumption rate of a super predator plays a key role in determining the eventual state of the ecosystem. A detailed bifurcation analysis is carried out through numerical simulations, and we observe that theoretically it is possible to control the dynamics of the system by manipulating the consumption rate of the super predator. 相似文献
14.
Jerzy Warminski 《Nonlinear dynamics》2010,61(4):677-689
Vibrations of nonlinear coupled parametrically and self-excited oscillators driven by an external harmonic force are presented
in the paper. It is shown that if the force excites the system inside the principal parametric resonance then for a small
excitation amplitude a resonance curve includes an internal loop. To find the analytical solutions, the problem is reduced
to one degree of freedom oscillators by applications of Nonlinear Normal Modes (NNMs). The NNMs are formulated on the basis
of free vibrations of a nonlinear conservative system as functions of amplitude. The analytical results are validated by numerical
simulations and an essential difference between linear and nonlinear modes is pointed out. 相似文献
15.
A rotor-active magnetic bearing (AMB) system subjected to a periodically time-varying stiffness with quadratic and cubic nonlinearities
under multi-parametric excitations is studied and solved. The method of multiple scales is applied to analyze the response
of two modes of a rotor-AMB system with multi-parametric excitations and time-varying stiffness near the simultaneous primary
and internal resonance. The stability of the steady state solution for that resonance is determined and studied using Runge-Kutta
method of fourth order. It is shown that the system exhibits many typical non-linear behaviors including multiple-valued solutions,
jump phenomenon, hardening and softening non-linearities and chaos in the second mode of the system. The effects of the different
parameters on the steady state solutions are investigated and discussed also. A comparison to published work is reported. 相似文献
16.
In this effort, a six-degree-of-freedom (DOF) model is presented for the study of a machine-tool spindle-bearing system. The
dynamics of machine-tool spindle system supported by ball bearings can be described by a set of second order nonlinear differential
equations with piecewise stiffness and damping due to the bearing clearance. To investigate the effect of bearing clearance,
bifurcations and routes to chaos of this nonsmooth system, numerical simulation is carried out. Numerical results show when
the inner race touches the bearing ball with a low speed, grazing bifurcation occurs. The solutions of this system evolve
from quasi-periodic to chaotic orbit, from period doubled orbit to periodic orbit, and from periodic orbit to quasi-periodic
orbit through grazing bifurcations. In addition, the tori doubling process to chaos which usually occurs in the impact system
is also observed in this spindle-bearing system. 相似文献
17.
Antonio Algaba Fernando Fernández-Sánchez Manuel Merino Alejandro J. Rodríguez-Luis 《Nonlinear dynamics》2012,69(4):2289-2291
A paper, ??Existence of attractor and control of a 3D differential system,?? was published in the journal Nonlinear Dynamics. The author tries to prove the existence of horseshoe chaos by means of the Shilnikov criterion. To do that, he uses the undetermined coefficient method to analytically demonstrate the existence of heteroclinic orbits in a Lorenz-like system. Unfortunately, his proof is not correct for two reasons. Firstly, he considers an odd function to represent the heteroclinic orbit whereas such an orbit joining two saddle-focus equilibria can never have that symmetry. Secondly, he looks for a structurally unstable Shilnikov heteroclinic orbit by means of uniformly convergent series expansions: This would imply that the dynamical object found is structurally stable. 相似文献
18.
Determination of the global responses characteristics of a piecewise smooth dynamical system with contact 总被引:2,自引:0,他引:2
Jun Jiang 《Nonlinear dynamics》2009,57(3):351-361
In this paper the global response characteristics of a piecewise smooth dynamical system with contact, which is specifically
used to describe the rotor/stator rubbing systems, is studied analytically. A method to derive the global response characteristics
of the model is proposed by studying each piece of the equations corresponding to different phases of the rotor motion, i.e.,
the phase without rubbing, the phase with rubbing and the phase of self-excited backward whirl. After solving the typical
responses in each phase and deriving the corresponding existence boundaries in the parameter space, an overall picture of
the global response characteristics of the model is obtained. As is shown, five types of the coexistences of the different
rotor responses and deep insights into the interactive effect of parameters on the dynamic behavior of the model are gained. 相似文献
19.
Nonlinear Dynamics - In this paper, a Leslie predator–prey system with ratio-dependent and state impulsive feedback control is investigated by applying the geometry theory of differential... 相似文献
20.
This paper aims to study a class of differential equations with parametric Gaussian colored noise. We present the general
framework to get the solvability conditions of the approximate stationary probability density function, which is determined
by the Fokker-Planck-Kolmogorov (FPK) equations. These equations are derived using the stochastic averaging method and the
operator theory with the perturbation technique. An illustrative example is proposed to demonstrate the procedure of our proposed
method. The analytical expression of approximate stationary probability density function is obtained. Numerical simulation
is carried out to verify the analytical results and excellent agreement can be easily found. The FPK equation for the probability
density function of order ε
0 is used to examine the almost-sure stability for the amplitude process. Finally, the stability in probability of the amplitude
process is investigated by Lin and Cai’s method. 相似文献