Control ENG HW_Part_47

Control ENG HW_Part_47 - P(s) = (10/s)(1 + 0.5 s + 1/s )...

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P(s) = (10/s)(1 + 0.5 s + 1/s ) P(s) = 10/s + 5 + 10/s 2 P(t) = 10 + 5 δ(t) + 10 t Q – 10.3. An ideal PD controller has the transfer function P/e = K C ( τ D s + 1) An actual PD controller has the transfer function P/e = K C ( τ D s + 1) / (( τ D /β) s + 1) Where β is a large constant in an industrial controller If a unit-step change in error is introduced into a controller having the second transfer function, show that P(t) = K C ( 1 + A exp(-βt/ τ D )) Where A is a function of β which you are to determine. For β = 5 and K C =0.5, plot P(t) Vs t/ τ D . As show that β b ∞, show that the unit step response approaches that for the ideal controller. Soln: P/e = K C ( τ D s + 1) / (( τ D /β) s + 1) For a step change, e(s) = 1/s P(s) = K C s( τ D s + 1) / (( τ
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Control ENG HW_Part_47 - P(s) = (10/s)(1 + 0.5 s + 1/s )...

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