Abstract

Balancing on a horizontally compliant surface is examined by comparing the task with successively more complex dynamic models. 1, 2 and 3 DOF systems are used to examine the balance strategies (state feedback control laws) needed to maintain stability. The 1 and 2 segment systems use a spring attached at the lowest point of the (lower) segment to model horizontal compliance. Velocities are neglected and only position and angular displacement state variables of the system are fed back to achieve balanced, marginally stable closed loop systems. Regions of stability in the feedback gain space are compared using the Routh-Hurwitz criterion, root locus and other graphical techniques. Boundaries of the stable regions in the feedback gain space are provided by the inequalities satisfied by the gains for positivity of the leading column of the Routh array. Knowledge and feedback of horizontal foot position is not important since it is possible to achieve stability by neglecting it entirely. Verf.-Referat