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Quiz 6 solutions_1

# Quiz 6 solutions_1 - Name Quiz 6(30 pts 1 Sketch the time...

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Name______________________ Quiz 6 1. Sketch the time response of a first order system with τ = 0.1 sec to a step input of amplitude 4.0 if the system starts at y 0 = 1.0. Make sure your sketch shows the amplitudes reasonably correctly at t = 0, τ , and ∞. (Recall that e -1 = 0.37.) ( 29 0 t / y(t ) KA y KA e τ - = + - F(t) = AU(t) = 4 U(t) What is K ? It is related to the static sensitivity of the system, dy/dx. K might be a constant or it might be function of the magnitude of the input x , as shown in the following figure (from Figliola and Beasley). Since this is like a static sensitivity, it does not depend on time. Therefore, it will not change the shape of the time response to a step input. In this problem, we don’t know K . At t = 0, t / e τ - = 1, so y(t) = KA + y 0 – KA = y 0 = 1.0 (consistent with problem statement) At t = ∞, t / e τ - = 0, so y(t) = KA = 4.0 At t = τ , y(t) = 4.0 K (1 - 0.37) - 0.37 = 4.0 K *0.63

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