On-off control action coupled with a sampling and holding mechanism is equivalent to the on-off control action with a stochastically varying dead time. The magnitude of the dead time may take a value between 0 and the interval of the sampling action. Limit band can easily be constructed on the phase plane, encolosing all possible limit cycles and ultimate trajectories. The inner boundary of the limit band is reduced in size by decreasing a fixed dead time along the control loop, while the outer boundary of the limit band is reduced by decreasing the sum on the fixed dead time and the sampling interval. The size of the limit band can also be reduced by introducing a predicting compensater along the control loop. Only for particular initial conditions there exist limit cycles or exactly perioic oscillations of the system output inside the limit band, but almost all trajectories are not periodic and are fluctuating in the limit band.
The result of the tests by using analog computer shows good coincidence with that of the theoretical investigations and also shows that the limit band may provide sufficient information for the design of this type of control systems. The characteristics of the limit band can be predicted by the system paramesers.
