R.-F. Fung

APPLICATION OF VSC IN POSITION CONTROL OF A NONLINEAR ELECTROHYDRAULIC SERVO SYSTEM

Abstract The hydraulic servomechanism is widely used in manufacturing machinery, heavy-duty machine and the automobile industry. The variable structure control (VSC) is one of the major approaches in dealing with the nonlinear systems. In this paper, we apply the technique of the variable structure control to an electrohydraulic servo control system which is described by a third-order nonlinear equation with time-varying coefficients. First, we construct a two-phase variable structure controller to get the precise position control of an electrohydraulic servo system. Second, we compare the performance among three different types of VSC controllers. Finally, the jerks of the state trajectories will be discussed in the simulation results.

Inverse dynamics of a toggle mechanism

Abstract The inverse dynamics problem aimed at determining the driving forces that produce a specific motion is presented. It is necessary to know the velocities and accelerations to be able to estimate the inertia forces which provide the basis to calculate the required actuating forces. A constrained multibody technique is employed to calculate the position, velocity and acceleration of the toggle mechanism. For the multibody dynamic analysis, Hamiltons principle and Lagrange multiplier method are applied to formulate the equations of motion. By using geometric relationships the differential-algebraic equations can be reduced to pure differential equations form and Runge-Kutta numerical method is used to perform numerical simulations. The results of kinematic and dynamic analysis are presented and compared for the four-point type and the five-point toggle mechanisms.

NONLINEAR DYNAMIC STABILITY OF A MOVING STRING BY HAMILTONIAN FORMULATION

Abstract In this paper, the stability behavior of an axially moving string is examined in the presence of parametric and combination resonances. The Galerkin discretization utilizing stationary string eigenfunctions is used to transform the partial differential equation governing transverse response into a set of coupled ordinary differential equations. Hamiltonian formulation and averaging method are used to yield a set of autonomous equations. The conditions of parametric and summed resonances are obtained over specific ranges between the natural and exciting frequencies. Explicit results of the stability boundaries for the first and secondary principal parametric and the first summation resonances and the bifurcation paths of the nontrivial amplitudes are obtained.