Question

In control systems analysis, transfer functions are developed that mathematically relate the dynamics of a system’s input to its output. A transfer function for a robotic positioning system is given by ?(?) = ?(?) ?(?) = ?3+12.5?2+50.5?+66 ?4+19?3+122?2+296?+192 . Where, ?(?) = system gain, ?(?) = system output, ?(?) = system input, and ? = Laplace transform complex frequency. Now, use Bairstow’s method to determine the roots of the numerator and denominator and factor these into the form ?(?) = (?+?1)(?+?2)(?+?3) (?+?1)(?+?2)(?+?3)(?+?4) . Where, ?? and ?? = the roots of the numerator and denominator, respectively. [Hints: To perform the evaluation of complex roots, Bairstow’s method divides the polynomial by a quadratic factor ?2 − ?? − ?. Use initial guesses of ? = ? = −1, for determining the roots of both numerator and denominator, and perform up to four iteration.]

Answer 1