Consider that GM = KM = 1, GP = K/(τ1s+1), and GD = KD/(τ1s+1). a) Wri

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Consider that GM = KM = 1, GP = K/(τ1s+1), and GD = KD/(τ1s+1). a) Write the transfer function for a setpoint change, Y′(s)/Ysp′(s), given that GC1 = K1, GC2 = K1 /τIs and GC3 = K1τDs. b) Write the transfer function for a setpoint change, Y′(s)/Ysp′(s), given that GC1 = K1, GC2 = K1 and GC3 = K1(1 + τDs)(1 + 1/τIs). c) Consider the following values: τ1 = 2, τI = 1, τD = 5, K1 = 3, K = 2. Write the expressions and plot (not sketch!) the response for both system a) and system b) to a step change of Ysp′ = S(t).

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Consider that

G_{M} = K_{M} = 1, G_{P} = K / (τ_{1} s + 1)

, and

G_{D} = K_{D} / (τ_{1} s + 1)

. a) Write the transfer function for a setpoint change,

Y^{'} (s) / Y_{s p}^{'} (s)

, given that

G_{C 1} = K_{1}, G_{C 2} =

K_{1} / τ_{I} s

and

G_{C 3} = K_{1} τ_{D} s

. b) Write the transfer function for a setpoint change,

Y^{'} (s) / Y_{s p}^{'} (s)

, given that

G_{C 1} = K_{1}, G_{C 2} =

K_{1}

and

G_{C 3} = K_{1} (1 + τ_{D} s) (1 + 1 / τ_{I} s)

. c) Consider the following values:

τ_{1} = 2, τ_{I} = 1, τ_{D} = 5, K_{1} = 3, K = 2

. Write the expressions and plot (not sketch!) the response for both system a) and system b) to a step change of

Y_{s p}^{'} =

S (t)

.

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