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lab1-SYSC3600

# lab1-SYSC3600 - response of system with initial condition...

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e response of a system with initial condition y(t0) = 6 response of a system with initial condition y(t 0 ) = 2 system with initial condition y(t0) = 6 and a delayed input u(t-5) SYSC3600: LAB1 Hesham Alshaebi 100698585

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2.2 Step response, static gain, and the “time constant” After taking simulating the three different case on the 1 st order differential equation (1) the following have been observed: ( ) =- + ( ) dy t dt yt1τ kτx t (1) τ which is the system time constant controls the output decay of the system. As the value of τ gets bigger the decay of the system gets slower. In other words the system takes longer to reach its steady state. k controls the output gain of the system. The 2% settling time is the time where 98% of the system decay occurs. At this point the value of the output approximately equals k*Vin. This is illustrated in figure 1 below.
Figure : The simulation plot of a first order system 2.3 Response to a delayed input Setting a time delay td in the input will delay the output by the same amount of delay. Figure 2 below shows an input delayed by 10 unites of time. The output response in the plot has been delayed by the same amount.

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lab1-SYSC3600 - response of system with initial condition...

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