StepFunctionResponseTimeThe time required for a system to respond to a value thatis 9o% of the step input, yo - Yo, is important and iscalled the rise time of the systemrt/r%Error%Response00.01.0100.0163.20.36836.8286.50.13513.52.390.00.10010.0395.05.00.05050.799.30.0070.00.0100.08
Step Function Response Time • The time required for a system to respond to a value that is 90% of the step input, y∞ - y0 , is important and is called the rise time of the system
SimplePeriodicFunctionInputWhen periodic inputs are applied to a first-order system, the input signalfrequency has an important influence on measuring system time responseand affects the output signal.Consider the first-order measuring system to which an input of the form ofa simple periodic function F(t) = A sin ot is applied for t ≥ O with initialcondition to = t(O)The general solution to this differential equation yields the measurementsystem output signal, that is, the time response to the applied input, y(t)KAy(t)= Ce-1/t +sin(ot - tan- ot)1+(ot)wherethe valueforC depends on the initial conditions
Simple Periodic Function Input • When periodic inputs are applied to a first-order system, the input signal frequency has an important influence on measuring system time response and affects the output signal. • • Consider the first-order measuring system to which an input of the form of a simple periodic function F(t) = A sin wt is applied for t ≥ 0 with initial condition t0 = t(0) • The general solution to this differential equation yields the measurement system output signal, that is, the time response to the applied input, y(t): sin( tan ) 1 ( ) ( ) 1 2 / w w w t KA y t Ce t where the value for C depends on the initial conditions