{"id":245097,"date":"2025-07-05T16:47:22","date_gmt":"2025-07-05T16:47:22","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=245097"},"modified":"2025-07-05T16:51:02","modified_gmt":"2025-07-05T16:51:02","slug":"an-organism-has-a-cell-with-a-pair-of-chromosomes-a-and-b-2","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/07\/05\/an-organism-has-a-cell-with-a-pair-of-chromosomes-a-and-b-2\/","title":{"rendered":"Consider the transfer function"},"content":{"rendered":"\n
\"\"<\/figure>\n\n\n\n

Here are the solutions to the problems presented in the image, including the MATLAB code and explanations.<\/p>\n\n\n\n

Problem 1 Solution<\/strong><\/h3>\n\n\n\n

Task:<\/strong> Determine the poles and zeros of the transfer function H(s) and plot the pole-zero map using MATLAB.<\/p>\n\n\n\n

Transfer Function:<\/strong>
H(s) = 2 * (s + 1) \/ (s\u00b3 + 4s\u00b2 + 6s + 4)<\/p>\n\n\n\n

Poles and Zeros:<\/strong><\/p>\n\n\n\n

    \n
  • Zero:<\/strong> s = -1<\/li>\n\n\n\n
  • Poles:<\/strong> s = -2, s = -1 + j, s = -1 – j<\/li>\n<\/ul>\n\n\n\n
    % Problem 1: Poles, Zeros, and Pole-Zero Map for H(s)\n\n% Define the numerator and denominator coefficients for H(s)\nnum_H = [2 2];       % Represents 2s + 2\nden_H = [1 4 6 4];   % Represents s^3 + 4s^2 + 6s + 4\n\n% Create the transfer function object\nH = tf(num_H, den_H);\n\n% Determine the zeros and poles\nzeros_H = zero(H)\npoles_H = pole(H)\n\n% Plot the pole-zero map\nfigure;\npzmap(H);\ntitle('Pole-Zero Map of H(s)');\ngrid on;<\/code><\/pre>\n\n\n\n
    Problem 2 Solution<\/strong><\/h3>\n\n\n\n
    Task:<\/strong> Plot the unit impulse and unit step response of the system G(s).<\/p>\n\n\n\n
    Transfer Function:<\/strong>
    G(s) = 16 \/ (s\u00b2 + 2s + 16)<\/p>\n\n\n\n
    % Problem 2: Impulse and Step Response for G(s)\n\n% Define the numerator and denominator coefficients for G(s)\nnum_G = [16];        % Represents 16\nden_G = [1 2 16];    % Represents s^2 + 2s + 16\n\n% Create the transfer function object\nG = tf(num_G, den_G);\n\n% Plot the unit impulse response\nfigure;\nimpulse(G);\ntitle('Unit Impulse Response of G(s)');\ngrid on;\n\n% Plot the unit step response\nfigure;\nstep(G);\ntitle('Unit Step Response of G(s)');\ngrid on;<\/code><\/pre>\n\n\n\n
    Explanation<\/strong><\/h3>\n\n\n\n
    For the first problem, we analyze the transfer function H(s). The zeros of a system are the roots of the numerator polynomial, and the poles are the roots of the denominator. These values determine the system’s dynamic characteristics. Using MATLAB, we define the numerator [2 2] and denominator [1 4 6 4] as coefficient vectors. The zero command finds the root of 2s + 2 = 0, giving a single zero at s = -1. The pole command solves the cubic equation in the denominator, yielding three poles: one real pole at s = -2 and a complex conjugate pair at s = -1 \u00b1 j. The pzmap function visualizes these on the complex plane, with an ‘o’ for the zero and ‘x’s for the poles. Since all poles are in the left-half plane, the system is stable.<\/p>\n\n\n\n
    For the second problem, we examine the time response of G(s). This system is a classic second-order system. We use MATLAB’s impulse and step functions to plot its response to a unit impulse and a unit step input, respectively. By comparing G(s) to the standard form \u03c9n\u00b2\/(s\u00b2 + 2\u03b6\u03c9n s + \u03c9n\u00b2), we find the natural frequency \u03c9n = 4 rad\/s and the damping ratio \u03b6 = 0.25. Since the damping ratio is between 0 and 1, the system is underdamped. This is reflected in the plots: both the impulse and step responses exhibit oscillations that decay over time. The step response rises, overshoots its final steady-state value of 1, and settles, which is characteristic behavior for an underdamped system<\/p>\n\n\n\n
    \"\"<\/figure>\n","protected":false},"excerpt":{"rendered":"
    Here are the solutions to the problems presented in the image, including the MATLAB code and explanations. Problem 1 Solution Task: Determine the poles and zeros of the transfer function H(s) and plot the pole-zero map using MATLAB. Transfer Function:H(s) = 2 * (s + 1) \/ (s\u00b3 + 4s\u00b2 + 6s + 4) Poles and […]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"site-sidebar-layout":"default","site-content-layout":"","ast-site-content-layout":"default","site-content-style":"default","site-sidebar-style":"default","ast-global-header-display":"","ast-banner-title-visibility":"","ast-main-header-display":"","ast-hfb-above-header-display":"","ast-hfb-below-header-display":"","ast-hfb-mobile-header-display":"","site-post-title":"","ast-breadcrumbs-content":"","ast-featured-img":"","footer-sml-layout":"","ast-disable-related-posts":"","theme-transparent-header-meta":"","adv-header-id-meta":"","stick-header-meta":"","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":"","astra-migrate-meta-layouts":"default","ast-page-background-enabled":"default","ast-page-background-meta":{"desktop":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"ast-content-background-meta":{"desktop":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"footnotes":""},"categories":[25],"tags":[],"class_list":["post-245097","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/245097","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/comments?post=245097"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/245097\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=245097"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=245097"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=245097"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}