Analog proportional-derivative controllers sometimes are formulated with a transfer function of the form:where ? = 0.05 to 02. The ideal PD transfer function is obtained when ? = 0. G1(s) = Kc(?DS + 1)(a) Analyze the accuracy of this approximation for step and tamp responses. Treat a as a parameter and let ? ? 0.(b) Why might it be difficult to construct an analog device with exactly this ideal transfer function?(c) Is there any advantage in not being able to obtain the ideal transfer function?

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TOS +1 aTps +1, Ga(s) =