Linear quadratic regulator simulation , polynomial method

Uses the polynomial control method for optimal control. Apply to a motor plus load (servo problem) with structural resonance.

A similar example to this using classical control is given in the book "Feedback" by T.J.Moir, published by Springer Nature Feb 2020.

This is much closer to a real world problem that is encountered in many problems. It has a motor plus load with position output cascaded with a second-order structural resonance term. This makes a 4th order system combined together.

G(s)=K/( s(1+sTm) ) x ( wn^2/(s^2+2.zeta wn.s + wn^2) )

Needs spectral factorization and a Diophantine equation to get the solution G/H polynomials.