Question

Consider the causal CT systems with transfer functions

H₁(s) = s + 1/(s + 2) (s² + s + 16)
H₂(s) = s/(s + 10) (s + 1)
H₃(s) = 1/(s - 1) (s +1)
H₄(s) = s/(s + 1) (s² + s + 16)
Write magnitude and phase expressions for their Bode plots and sketch their asymptotes. Verify using MATLAB.

Answer 1

The student's question involves formulating magnitude and phase expressions for Bode plots of given causal CT systems' transfer functions and verifying them using MATLAB.

Step-by-step explanation:

The student is asking for the magnitude and phase expressions for the Bode plots of four causal continuous-time (CT) systems with given transfer functions and to sketch the asymptotes of these plots. Additionally, the student is asked to verify these plots using MATLAB, a popular engineering software for mathematical computations.

• H1(s) = s + 1/(s + 2)(s² + s + 16)
• H2(s) = s/(s + 10)(s + 1)
• H3(s) = 1/(s - 1)(s +1)
• H4(s) = s/(s + 1)(s² + s + 16)

Each H(s) is a rational function representing the system's frequency response. To sketch the Bode plot asymptotes, we need to factorize each transfer function into its component form and plot the magnitude and phase for each factor. Common components include poles and zeros, which will influence the slope of the asymptotes.