Institute for Systems Research

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Dynamic Bifurcations in a Power System Model Exhibiting Voltage Collapse
(1992) Abed, Eyad H.; Alexander, James C.; Wang, H.; Hamdan, Anan M. A.; Lee, Hsien-Chiarn; ISR
Dynamic bifurcations, including Hopf and period-doubling bifurcations, are found to occur in a power system dynamic model recently employed in voltage collapse studies. The occurrence of dynamic bifurcations is ascertained in a region of state and parameter space linked with the onset of voltage collapse. The work focuses on a power system model studied by Dobson and Chiang (1989). The presence of the dynamic bifurcations, and the resulting implications for dynamic behavior, necessitate a re- examination of the role of saddle node bifurcations in the voltage collapse phenomenon. The bifurcation analysis is performed using the reactive power demand at a load bus as the bifurcation parameter. Due to numerical ill-conditioning, a reduced-order model is employed in some of the computations. It is determined that the power system model under consideration exhibits two Hopf bifurcations in the vicinity of the saddle node bifurcation. Between the Hopf bifurcations, i.e., in the "Hopf window," period-doubling bifurcations are found to occur. Simulations are given to illustrate the various types of dynamic behaviors associated with voltage collapse for the model. In particular, it is seen that an oscillatory transient may play a role in the collapse.
On the Kinematics and Control of Wheeled Mobile Robots.
(1987) Alexander, James C.; Maddocks, J.H.; ISR
A wheeled mobile robot is here modelled as a planar rigid body that rides on an arbitrary number of wheels. The connections between the rigid body motion of the robot, and the steering and driving controls of wheels are developed. In particular, conditions are obtained that guarantee that rolling without skidding or sliding can occur. Explicit differential equations are derived to describe the rigid body motions that arise from rolling trajectories. The simplest wheel configuration that permits control of arbitrary rigid body motions is determined. The question of slippage due to misalignment of the wheels is investigated based on a physical model of friction. Examples are presented to illustrate the models.
On the Maneuvering of Vehicles.
(1987) Alexander, James C.; Maddocks, J.H.; ISR
Equations are derived to govern the motion of vehicles which move on rolling wheels. A relation between the centers of curvature of the trajectories of the wheels and the center of rotation of the vehicle is established. From this relation the general kinematic laws of motion are derived. Applications to questions of offtracking (the difference between the trajectories of the front and back wheels of the vehicle) and optimal steering (how to steer around a tight corner) are considered.