A negative unity-feedback system has a forward element consisting of an amplifier with adjustable real- valued gain K in cascade with a transfer function 15 (s− 1)(s+3)(s+5) where a polar form sketch of the frequency response G(jw) for radian frequency w > 0 is shown in Figure 3. Im lower limit on gain K G(s) = K₁ K₂ upper limit on gain K 15 +7s²+78-15' Figure 3: Polar Form Sketch of Frequency Response G(jw) for Radian Frequency w > 0 (a) Allowing gain K to sweep from -∞0 to +∞, determine the gain limits K₁ and K₂ as well as the integer values Z₁, Z₂ and Z3 that complete the following table. K₁ K₂ +∞ G(jwo) Z₁ Z₂ Z3 number of closed-loop right-half-plane poles 0 Re

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Linear Control

A negative unity-feedback system has a forward element consisting of an amplifier with adjustable real-
valued gain K in cascade with a transfer function
15
(s− 1)(s+3)(s+5)
where a polar form sketch of the frequency response G(jw) for radian frequency w > 0 is shown in Figure 3.
Im
lower limit
on gain K
G(s) =
K₁
K₂
upper limit
on gain K
15
+7s²+78-15'
Figure 3: Polar Form Sketch of Frequency Response G(jw) for Radian Frequency w > 0
(a) Allowing gain K to sweep from -∞0 to +∞, determine the gain limits K₁ and K₂
as well as the integer values Z₁, Z₂ and Z3 that complete the following table.
K₁
K₂
+∞
G(jwo)
Z₁
Z₂
Z3
number of closed-loop
right-half-plane poles
0
Re
Transcribed Image Text:A negative unity-feedback system has a forward element consisting of an amplifier with adjustable real- valued gain K in cascade with a transfer function 15 (s− 1)(s+3)(s+5) where a polar form sketch of the frequency response G(jw) for radian frequency w > 0 is shown in Figure 3. Im lower limit on gain K G(s) = K₁ K₂ upper limit on gain K 15 +7s²+78-15' Figure 3: Polar Form Sketch of Frequency Response G(jw) for Radian Frequency w > 0 (a) Allowing gain K to sweep from -∞0 to +∞, determine the gain limits K₁ and K₂ as well as the integer values Z₁, Z₂ and Z3 that complete the following table. K₁ K₂ +∞ G(jwo) Z₁ Z₂ Z3 number of closed-loop right-half-plane poles 0 Re
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