natural frequency spanned a range from 22 to 32 rad/sec (35 to 5.1 HZ). The average damping

ratio ranged from 0.18 to 0.32.

 The second-order open-loop dynamic transfer functions were simulated with the

 parameters as determined by the step tests for joints 0 and 1. The results of these simulated

 systems were plotted for comparison with the experimental results of the step tests.

 Representative results from the experimental tests and the simulations are presented in Figures

 6.7 through 6.12. These graphs represent cases for joints 0 and 1 spanning the determined

 natural frequency and damping ratio ranges. A response pattern was evident across all of the

 tests. In each case, the response of the actual joint showed a peak which compared directly to

 the first peak of the simulated system. In some, but not all cases, the actual joint oscillated

 slightly (usually one cycle) before settling to a steady-state value. The simulated systems, on

 the other hand, generally oscillated more.

 This discrepancy indicated nonlinearities in the systems which probably resulted from

 nonlinear servo valve characteristics. Theoretically, a deadband in the valve would deliver a

 much smaller oscillation than would occur for a valve that was purely linear. A region in the

 response of a hydraulic valve in which small changes in the control signals have no effect on

 the direction or amount of fluid flow through the valve is referred to as the deadband of the

 valve. The responses of the servo valve controlled joints of the robot seem to indicate that a

 deadband caused by either an overlap of the valve ports or coulomb friction exists in these

 systems.

 Because design of the robot's control systems was based on linear systems, a linear

approximation of the transfer functions for these joints was necessary. Noting that the step

responses of the systems were best approximated by second-order responses, second-order

systems were chosen to estimate the transfer function of the actual systems. Therefore,

Merritt's assumptions for reducing the electrohydraulic control system to a second-order system

were verified for the cases of joints 0 and 1. These second-order systems were later used to model