Showing papers by "Ye-Hwa Chen published in 2005"

Inverse Dynamics of Servo-Constraints Based on the Generalized Inverse

Abstract: The acceleration form of constraint equations is utilized in this paper to solve for the inverse dynamics of servo-constraints. A condition for the existence of control forces that enforce servo-constraints is derived. For overactuated dynamical systems, the generalized Moore-Penrose inverse of the constraint matrix is used to parameterize the solutions for these control forces in terms of free parameters that can be chosen to satisfy certain requirements or optimize certain criterions. In particular, these free parameters can be chosen to minimize the Gibbsian (i.e., the acceleration energy of the dynamical system), resulting in “ideal” control forces (those satisfying the principle of virtual work when the virtual displacements satisfy the servo-constraint equations). To achieve this, the nonminimal nonholonomic form recently derived by the authors in the context of Kane’s method is used to determine the accelerations of the system, and hence to determine the forces to be generated by the redundant manipulators. Finally, an extension to inverse dynamics of servo-constraints involving control variables is made. The procedures are illustrated by two examples.

Nonminimal Kane's Equations of Motion for Multibody Dynamical Systems Subject to Nonlinear Nonholonomic Constraints

Abstract: Nonholonomic constraint equations that are nonlinear in velocities are incorporated with Kane's dynamical equations by utilizing the acceleration form of constraints, resulting in Kane's nonminimal equations of motion, i.e. the equations that involve the full set of generalized accelerations. Together with the kinematical differential equations, these equations form a state-space model that is full-order, separated in the derivatives of the states, and involves no Lagrange multipliers. The method is illustrated by using it to obtain nonminimal equations of motion for the classical Appell–Hamel problem when the constraints are modeled as nonlinear in the velocities. It is shown that this fictitious nonlinearity has a predominant effect on the numerical stability of the dynamical equations, and hence it is possible to use it for improving the accuracy of simulations. Another issue is the dynamics of constraint violations caused by integration errors due to enforcing a differentiated form of the constraint equations. To solve this problem, the acceleration form of the constraint equations is augmented with constraint stabilization terms before using it with the dynamical equations. The procedure is illustrated by stabilizing the constraint equations for a holonomically constrained particle in the gravitational field.

Lattice gas modeling of thermoacoustic oscillations

Abstract: Publisher Summary This chapter explores the application of a lattice-gas method to thermoacoustics. A two-dimensional 9-bit thermal lattice-gas model is applied to simulate self-sustained oscillations in a thermoacoustic resonant tube. The time-evolution of pressure oscillation and the change in temperature with time and space are successfully simulated using the present model. At each lattice node one particle at most is permitted according with the exclusion principle. These particles move at regular time intervals from one lattice node to another along the lattice links, and collide at a lattice node obeying the mass, the momentum and the energy conservation laws for a thermal lattice gas model. The results from this model show qualitatively good agreement with those from other researchers in earlier literature. The work demonstrates that the lattice gas method would be a new powerful approach to investigate some complicated thermoacoustic problems. To reduce model noise and to extend its applications to thermoacoustic refrigerators and other thermoacoustic systems with complex geometric boundaries, an improved lattice gas model and more experimental work would be desirable.