Dynamic analysis and system identification of an LCD glass-handling robot driven by a PMSM

In this paper, Hamilton’s principle is employed to derive Lagrange’s equations of an liquid crystal display (LCD) glass-handling robot driven by a permanent magnet synchronous motor (PMSM). The robot has three arms driven by two timing belts. The dynamic formulations can be expressed by one and four independent variables, which are named as the rigid and flexible models, respectively. In order to verify the dynamic formulation is correct, we reduce the flexible model to the rigid one under some assumptions. In this paper, we adopt the real-coded genetic algorithm (RGA) to identify all the parameters of the robot and PMSM simultaneously. It is found that the RGA can identify system parameters which are difficult to be measured in practical problems, for examples, the inductance, stator resistance, motor torque constant, damping coefficient of the motor and timing belts. In numerical simulations, vibrations due to flexibility of the timing belts are investigated for the angular displacements, speeds, accelerations of arms, and the horizontal and vertical displacements of the robot. The angular displacements of the robot arm and the translational positions of the robot end are obtained in the numerical simulations and experimental results. From their comparisons, it is demonstrated that identification results of the dynamic model with four independent variables present the better matching with experimental results of the system.     

Dynamic modelling of a multi-cable driven parallel platform with guiding devices

ABSTRACT

In this paper, a mathematical model is presented to numerically simulate the dynamical responses in a multi-cable suspension platform taking into account the slack cables and guiding devices. The state change of the cable (slack versus tensioned) is considered and is described mathematically by a complementary condition equation, and the interactions between the guiding wheels and the shaft wall are described by the Heaviside step function. The Lagrange’s equation with constraints is used to derive the dynamic equations of the system, and a non-smooth generalized-α algorithm for non-smooth phenomena of multibody dynamics is applied to numerically solve the equations. The simulation results have shown the dynamic responses of the platform and the cable tension characters when different cables are excited by different longitudinal excitations. Moreover, the results have illustrated how the cable tension differences may affect the pressure on the shaft wall applied by the guiding devices.     

Simple analysis of a fluid queue driven by an M/M/1 queue

In this note we consider the fluid queue driven by anM/M/1 queue as analysed by Virtamo and Norros [Queueing Systems 16 (1994) 373–386]. We show that the stationary buffer content in this model can be easily analysed by looking at embedded time points. This approach gives the stationary buffer content distribution in terms of the modified Bessel function of the first kind of order one. By using a suitable integral representation for this Bessel function we show that our results coincide with the ones of Virtamo and Norros.     

Dynamic mechanism and its modelling of micromachined electrostatic ultrasonic transducers

A tensile-plate-on-air-spring model (or called TDK model for short) for micromachined electrostatic ultrasonic transducers has been developed based on a thorough investigation of their dynamic mechanism. The mechanical stiffness effects caused by the compressibility of air gaps, bending stiffness of the diaphragm and in-plane tension applied to the diaphragm, together with an electrostatic negative stiffness effect are included completely in the model. Desired particular fundamental frequency and bandwidth can be obtained by only properly tailoring the geometry, dimensions and materials of transducers according to the model, which provides thereby a reliable theoretical basis for the understanding and optimised design of such transducers. Project supported by the National Natural Science Foundation of China (Grant No.69974001).     

Asymptotic analysis of a kernel estimator for parabolic stochastic partial differential equations driven by fractional noises

We study a strongly elliptic partial differential operator with time-varying coeffcient in a parabolic diagonalizable stochastic equation driven by fractional noises. Based on the existence and uniqueness of the solution, we then obtain a kernel estimator of time-varying coeffcient and the convergence rates. An example is given to illustrate the theorem.     

Control of a dendritic neuron driven by a phase-independent stimulation

A dendritic neuron model exhibits bistability under continuous weak stimulation – the oscillatory synchronized regime and the quiet regime coexist. Complex nonlinear dynamics is observed when the neuron undergoes not only phase-dependent continuous weak stimulation, but also when it is driven by an external phase-independent stimulation. In the latter case basin boundaries between the synchronized and the quiet regime become complex and fractal. Simple strategies based on control pulses are not sufficient in these circumstances, because it becomes difficult to predict the dynamics of the neuron after the application of the control pulse. Therefore, a new neural control method is proposed. Initially, a weak phase control strategy is applied until fractal basin boundaries evolve into a deterministic manifold. Consequently, a single control pulse is immediately applied and the neuron evolves into the calm state.     

Anticipated BSDEs driven by a single jump process

In this paper, we discuss a class of anticipated backward stochastic differential equations related to a finite continuous time single jump process. We prove the existence and uniqueness of the adapted solution. Moreover, a comparison theorem for the solutions is also established.     

Evasion of a fixed sphere by a dynamical object driven by a bounded force

A solution is obtained of the problem of synthesizing the control of the motion of a dynamical object (a point mass) evading a fixed spherical obstacle under the action of a bounded force. The set of all points for which evasion is possible is constructed in phase space (of arbitrary dimension), and control modes are constructed for bounded (fixed) and unbounded time intervals. The characteristics of the optimal motion, in particular, the time and minimum distance, are determined for specific initial data. The qualitative properties of the controlled motion are established.     

A fluid queue driven by a Markovian queue

We consider an infinite buffer fluid queue receiving its input from the output of a Markovian queue with finite or infinite waiting room. The input is characterized by a Markov modulated rate process. We derive a new approach for the computation of the stationary buffer content. This approach leads to a numerically stable algorithm for which the precision of the result can be given in advance. This revised version was published online in June 2006 with corrections to the Cover Date.     

Heteroclinic chaotic behavior driven by a Brownian motion

In this paper we study the chaotic behavior of a planar ordinary differential system with a heteroclinic loop driven by a Brownian motion, an unbounded random forcing. Unlike the case of homoclinic loops, two random Melnikov functions are needed in order to investigate the intersection of stable segments of one saddle and unstable segments of the other saddle. We prove that for almost all paths of the Brownian motion the forced system admits a topological horseshoe of infinitely many branches. We apply this result to the Josephson junction and the soft spring Duffing oscillator.     

Evolution equations driven by a fractional Brownian motion

In this paper we study nonlinear stochastic evolution equations in a Hilbert space driven by a cylindrical fractional Brownian motion with Hurst parameter and nuclear covariance operator. We establish the existence and uniqueness of a mild solution under some regularity and boundedness conditions on the coefficients and for some values of the parameter H. This result is applied to stochastic parabolic equation perturbed by a fractional white noise. In this case, if the coefficients are Lipschitz continuous and bounded the existence and uniqueness of a solution holds if . The proofs of our results combine techniques of fractional calculus with semigroup estimates.     

Numerical analysis of the motion of a variable-mass particle in an electrostatic field

The paper presents a mathematical model of the process of motion of a charged liquid particle of variable mass in the interelectrode space. The Cauchy problem is formulated for the system of two ordinary nonlinear differential equations describing the radius of the spherical particle r(x) and its velocity v(x). An exact solution of the nonlinear system is obtained by introducing a physically acceptable simplification. Qualitative and quantitative analysis of the results is presented.Translated from Vychislitel'naya i Prikladnaya Matematika, No. 64, pp. 90–94, 1988.     

Dynamics of spiral waves driven by a rotating electric field

We study the behavior of spiral wave under the driving of a rotating electric field. The rotating electric field can drive a spiral wave to be synchronous, depending on four factors: its frequency and amplitude, chirality, and polarized modes. Rotation-synchronization characterized by the rotating direction is focused on. We discuss the behavior of synchronization, such as the dependence of angle-differences between the spiral tip and the electric field on ratio of frequency, the influences of different polarized modes of the electric field, the radius of synchronous spiral wave, and so on. A circularly polarized electric fields (CPEF) can suppress meandering spiral to rigid one and prevent breakup of spiral in medium with low excitability. The phase diagram describing the controllable region in excitability-period plane is presented. The influences of polarized modes of electric field on minimum excitability of medium are also studied.     

Averaging principle for equation driven by a stochastic measure

ABSTRACT

Equation with the symmetric integral with respect to stochastic measure is considered. For the integrator, we assume only σ-additivity in probability and continuity of the paths. It is proved that the averaging principle holds for this case, the rate of convergence to the solution of the averaged equation is estimated.     

Decompositions of stochastic convolution driven by a white-fractional Gaussian noise

Let u=\{u(t,x);(t,x)\in {ℝ}_{+}\times ℝ\}be the solution to a linear stochastic heat equation driven by a Gaussian noise, which is a Brownian motion in time and a fractional Brownian motion in space with Hurst parameterH\in (\mathrm{0},\mathrm{1}): For any givenx\in ℝ(\text{resp}\text{.},t\in {ℝ}_{+}), we show a decomposition of the stochastic processt\to u(t,x)(\mathrm{r}\mathrm{e}\mathrm{s}\mathrm{p}.,x\to u(t,x))as the sum of a fractional Brownian motion with Hurst parameter H/2 (resp., H) and a stochastic process with C^∞-continuous trajectories. Some applications of those decompositions are discussed.     

Output feedback vibration control of a string driven by a nonlinear actuator

In this paper, we design an observer-based output feedback controller to exponentially stabilize a system of nonlinear ordinary differential equation-wave partial differential equation-ordinary differential equation. An observer is designed to estimate the full states of the system using available boundary values of the partial differential equation. The output feedback controller is built via the combination of the ordinary differential equation backstepping which is applied to deal with the nonlinear ordinary differential equation, and the partial differential equation backstepping which is used for the wave partial differential equation-ordinary differential equation. The controller can be applied into vibration suppression of a string-payload system driven by an actuator with nonlinear characteristics. The global exponential stability of all states in the closed-loop system is proved by Lyapunov analysis. The numerical simulation illustrates the states of the actuator, string, payload and the observer errors are fast convergent to zero under the proposed output feedback controller.     

Shape sensitivity analysis of a quasi‐electrostatic piezoelectric system in multilayered media

The optimization of shape and topology of piezo‐patches or layered piezo‐electrical material attached to structural parts, such as elastic bodies, plates and shells, plays a major role in the design of smart structures, as piezo‐mechanic‐acoustic devices in loudspeakers or energy harvesters. While the design for time‐harmonic motions is genuinely frequency‐dependent, as has been reported in the literature in the context of density optimization with the SIMP‐method, time‐varying piezoelectric material has not been investigated with respect to the optimal design so far. Therefore, shape sensitivities for layered piezoelectric material and time‐varying loads and charges are derived in this paper. In particular, we provide the shape‐derivatives for nested piezo‐layers associated with a class of shape functional. More general layers can be dealt with similar approach. Copyright © 2010 John Wiley & Sons, Ltd.