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

where G(s) = system gain, C(s) = system output, N(s) = system input, and s = Laplace transform complex frequency. Use MATLAB to find the roots of the numerator and denominator and factor these into the form

where a_i and b_i = the roots of the numerator and denominator, respectively.

G(s) = C(s) N (s) s +9s +265 +24 s4 + 15s3 +77s + 153s +90