Consider the differential equations, y(t)-y(t) + 6y(t) = u(t) y(t) + 5y(t) + 2y(t)-u(t)+u(t)=0 Find the...

  

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Consider the differential equations, y(t)-y(t) + 6y(t) = u(t) y(t) + 5y(t) + 2y(t)-u(t)+u(t)=0 Find the transfer functions, (s). What assumptions must be made regarding the initial condi- tions? Is the system stable? What are the initial and final values of the system when the input is a unit step? Y(s) Now, take the U(S) transfer function and apply unity negative feedback around it. How has the feedback changed the stability? What are the new initial and final values when the input is a unit step? Y(s) Finally, transform the transfer function back into a differential equation. R(S) Consider the differential equations, y(t)-y(t) + 6y(t) = u(t) y(t) + 5y(t) + 2y(t)-u(t)+u(t)=0 Find the transfer functions, (s). What assumptions must be made regarding the initial condi- tions? Is the system stable? What are the initial and final values of the system when the input is a unit step? Y(s) Now, take the U(S) transfer function and apply unity negative feedback around it. How has the feedback changed the stability? What are the new initial and final values when the input is a unit step? Y(s) Finally, transform the transfer function back into a differential equation. R(S)