what would be the roots of the characteristic equation?

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 Kd? 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 Kp and derivative gain Kd? (Hint. by looking at the location of roots on the s-plane or applying the Routh-Hurwitz criterion)

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