Multirate integration algorithms for real-time simulation of mechanical systems with interacting subsystems

The topic of this thesis is the development and implementation of multirate integration algorithms for real-time simulation of mechanical systems with interacting subsystems.; Two new multirate algorithms based on the Nordsieck form of the Adams-Bashforth-Moulton algorithm have been developed and shown to be reliable and accurate. The first algorithm employs a fixed step size, third-order predictor, fourth-order corrector Nordsieck scheme as the underlying integrator, and a recursive organization of computations. The partitioning of the system of Ordinary Differential Equations (ODE) has to be performed apriori, based on the structure of the mechanical system modeled and engineering knowledge of the problem being solved. This algorithm is therefore appropriate for well known systems of ODE with clearly separable subsystems. The second multirate algorithm implemented uses the Nordsieck predictor-corrector formulas of order one through twelve with variable step size as the underlying integrator. The only restriction imposed on the partitioning of the complete set of ODE is the possibility to independently compute the derivatives for each subsystem. These subsystems are integrated separately under the administration of a subsystem manager which decides the order of integration and transfers the necessary information among subsystems. This algorithm can benefit most from the modular structure of the systems of differential equations describing the behavior of mechanical systems with interacting subsystems.; Three numerical examples were used to validate the new multirate integrators. Speed increases of more than 40% were obtained for multirate simulations of a complex model of the Caterpillar 950F Wheel Loader, as compared with the single rate simulations using the same algorithm, which resulted in faster than real-time performances on low-cost personal computers.