Asymptotic behavior of the solution of the moving oscillator problem is examined for large values of the spring stiffness for the general case of nonzero beam initial conditions. In the limit of infinite spring stiffness, the moving oscillator problem for a simply supported beam is shown to be not equivalent in a strict sense to the moving mass problem; i.e., beam displacements obtained by solving the two problems are the same, but the higher-order derivatives of the two solutions are different. In the general case, the force acting on the beam from the oscillator is shown to contain a high-frequency component, which does not vanish, or even grows, when the spring coefficient tends to infinity. The magnitude of this force and its dependence on the oscillator parameters can be estimated by considering the asymptotics of the solution for the initial stage of the oscillator motion. For the case of a simply supported beam, the magnitude of the high-frequency force linearly depends on the oscillator eigenfrequency and velocity. The deficiency of the moving mass model is noted in that it fails to predict stresses in the bridge structure. Results of numerical experiments are presented.

Electronic cam follower motion control is a class of master-slave type mechanism where the slave axis motion must follow the master axis coordinate (process variable) according to a given cam profile while the master axis motion has a time varying speed. Time-domain repetitive control design can be well applied to the electronic cam slave control under constant nominal master’s axis speed. This approach won’t perform well when the master’s axis nominal speed varies, however. Recent research has suggested transforming the slave dynamics into the angle domain. By treating the rotational speed as a parameter which can be measured in real time, the resulting angle domain time varying plant is modeled as an affine linear parameter varying system. A continuous two parameter robust linear parameter varying repetitive controller with modified repetitive signal generator is proposed and compared with the time varying model reference approach. Simulation results show perfect asymptotic tracking performance with piecewise constant parameter profiles and graceful performance degradation with continuously varying parameter profiles.