If you consider a derivative control action only, what would be the roots of the characteristic equation? Is the system stable? If yes, determine the range of the derivative controller gain K_d? Can you apply final value of theorem of Laplace Transform to find the steady state error?

Q59;
Is it possible to apply a proportional-derivative (PD) control to convert the marginally stable system considered above to a stable system (i.e., roots having negative real parts.)? Determine the steady state error. Is it possible to meet the desired performance requirements with a PD controller? If yes, what would be the range of the proportional gain K_p and derivative gain K_d? (Hint. by looking at the location of roots on the s-plane or applying the Routh-Hurwitz criterion)