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Fig. 18-5. Bang-Bang Control System With Deadband Controller maximum torque. The law in functional form is

Fig. 18-5. Bang-Bang Control System With Deadband Controller maximum torque. The law in functional form is where

= Ofor-9max<9<9BttU = Ifor 9<-9max and 0„„. is the half-width of the deadband.

System Stability. The purpose of any feedback control system is to maintain a definite and known relationship between the desired output and the acutal output of the system. To achieve this goal, the system must respond to any temporary disturbances by eventually decaying to its desired or steady-state value. A linear system is stable if its output remains bounded for every txmnded input. System stability can be investigated by applying a unit step function disturbance torque to the system in steady state and examining the output as time advances. If the variation of the output about the initial steady-state value approaches zero, the system is stable. If the output increases indefinitely with time, the system is unstable. If the output undergoes continuous bounded oscillations, the system is marginally stable. Finally, if the output attains a constant value other than the initial steady-state one, the system has limited stability.

In general, the stability of a system may be deduced by examining the poles of its closed-loop transfer function shown schematically in Fig. 18-6. An examination

DISTURBANCE INPUT, R

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