Analysis of Frequency Response, Zero-Pole Plot, and Cascade Structure for Second-Order Systems
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Comprehensive analysis of second-order systems requires calculating magnitude-frequency and phase-frequency responses, plotting zero-pole diagrams, and implementing cascade structures. The magnitude response can be computed using the absolute value of the transfer function H(jω), while the phase response is obtained through the angle() function in MATLAB. Zero-pole plots visualize system stability using the tf() function to create transfer function objects and pzmap() for visualization. For cascade implementation, two second-order systems can be connected serially using series() function or by multiplying transfer functions directly. The overall transfer function becomes H(s) = H₁(s)×H₂(s), allowing analysis of combined frequency characteristics. This approach enables deeper investigation into system behavior, stability margins, and potential performance optimizations through parameter adjustments in bode() plots and root locus analysis.
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