A graphical method is presented for determining the motion of a freely oscillating system of one degree of freedom stabilized by a controlling device which applies control force in proportion to the displacement of the system, to its rate of change of displacement, or both. The controlling member is assumed to have limitations on its maximum deflection and on its maximum rate of movement. Several examples are presented to illustrate the method.nFrom these examples, it is shown that, at sufficiently small amplitudes, the period and damping of the system correspond to those provided by linear operation of the control whereas, at very large amplitudes, the period and damping approach those of the uncontrolled system. At intermediate amplitudes, if the deflection of the control is limited, a smooth transition between these two conditions of period and damping takes place whereas, if the rate of control movement is limited, the damping may be reduced below that of the uncontrolled system. In some cases, limiting the rate of control movement may produce instability over a range of amplitudes.nIf the control produces primarily an increase in damping, the control remains effective in producing damping even at amplitudes several times that at which saturation effects are first encountered. This effect may be useful in reducing the power requirements of yaw dampers for airplanes.
展开▼
