Question

7.3 Let $G(s) = KG\tilde{(s)}$. The Bode plots of $\tilde{G}(s)$ are shown in Fig. P7.3. (a) Find $K$ such that $\omega_c = 10$ rad/s. (b) Find $K$ such that $PM = 50^\circ$. (c) Find $K$ such that $K_v = 20$. (d) Find $K$ such that $20\log|G(j\omega)| \ge 30$ dB for $\omega \in [0, 1]$ rad/s.

          7.3 Let $G(s) = KG\tilde{(s)}$. The Bode plots of $\tilde{G}(s)$ are shown in Fig. P7.3.
(a) Find $K$ such that $\omega_c = 10$ rad/s.
(b) Find $K$ such that $PM = 50^\circ$.
(c) Find $K$ such that $K_v = 20$.
(d) Find $K$ such that
$20\log|G(j\omega)| \ge 30$ dB for $\omega \in [0, 1]$ rad/s.

7.3 Let G(s) = KG(̃s̃)̃. The Bode plots of G̃(s) are shown in Fig. P7.3.
(a) Find K such that = 10 rad/s.
(b) Find K such that PM = 50^∘.
(c) Find K such that Kv = 20.
(d) Find K such that
20log|G(jω)| ≥ 30 dB for ω∈ [0, 1] rad/s.

Added by Linda P.

University Physics with Modern Physics

Hugh D. Young 14th Edition

Instant Answer

Solved by Expert Amit Srivastava

02/26/2022

Step 1

From the Bode plot, we can see that the phase crossover frequency (ωc) is approximately 10 rad/s. To find K, we need to determine the gain at this frequency. At ωc = 10 rad/s, the magnitude of G(jω) is approximately 0 dB. Therefore, K = 1. Show more…

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7.3 Let G(s) = Khat(G)(s). The Bode plots of hat(G)(s) are shown in Fig. P7.3. (a) Find K such that ωc = 10rad/s. (b) Find K such that PM = 50°. (c) Find K such that Kv = 20. (d) Find K such that 20log|G(jω)| >= 30dB for ω in [0,1]rad/s. Find K such that K = 20. d Find K such that 20logGj30dBforE[0,1]rad/s 50 50 Magnitude(dB) 100 -150 -200 -90 -135 Phase(deg) -180 -225 -270 10^-1 10^3 10^4 10^0 10^1 10^2 Frequency(rad/s) Figure P7.3: Bode plots of Problem 7.3