Numerical solution of dynamical systems with equality state-space constraints

Numerical solution of dynamical systems with equality state-space constraints

ten Dam, A.A.

National Aerospace Laboratory NLR

1990-02-07

Numerical simulation of constrained dynamical systems is known to exhibit stability problems even when the unconstrained system can be simulated in a stable manner. We show that not the constraints themselves, but the transformation of a continuous set of equations to a discrete set of equations is the true source of the stability problem. Furthermore, it is shown that there exists no need to introduce the index terminology to characterize difficulties with respect to numerical integration of differential algebraic equations. In fact, we show that use of the appropriate formulation automatically results in stable numerical integration of dynamical systems described by a set of differential and algebraic equations. New theories are presented that allow for stable numerical integration of constrained djmaraical systems. The derived numerical methods are robust with respect to errors in the initial conditions and to errors made during the integration process. As a consequence, perturbations in the initial conditions are allowed. The new theory is extended to the case of constrained mechanical systems. Simulation results are presented that show the use of the theory here developed in simulation studies.

dynamical systems
constraints
dynamic models
robot dynamics
manipulators
computerized simulation
Euler-Lagrange equation
numerical integration
algorithms
control theory
Newton-Raphson method
Numerical stability

http://resolver.tudelft.nl/uuid:36782ec7-2823-4376-8a45-388a0b977670

Nationaal Lucht- en Ruimtevaartlaboratorium

Campus only

NLR Technical Publication 89419 U

Aerospace Engineering Reports

report

(c) 1990 National Aerospace Laboratory NLR