For the following system given by the block diagram: a. (5 pts) Determine an expression for...

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For the following system given by the block diagram: a. (5 pts) Determine an expression for the closed-loop transfer function T(s): = y(s) r(s) terms of the parameters a and K. b. (5 pts) Determine values for the design parameters a and K by assuming that the zero of the closed-loop transfer function T(s) can be ignored and therefor approximated as a standard second-order system such that the closed-loop percent overshoot is less than 5% and the settling time is approximately 2.0 seconds when r(t) a unit-step input r(s) ==/ c. (5 pts) What is the steady-state value of the output y(t) for the system as found in part (a) using the parameter values a and K from part (b) in response to r(t) as a unit-step input? d. (5 pts) What are the poles and zeros for the closed-loop system evaluated in part (c)? (5 pts) For the actual system with the effects of the closed-loop zero included, what would be the approximate percent overshoot of the output with a unit step input as e. K(s + a) -200 s+2 r(s) in 1 s+1 y(s) For the following system given by the block diagram: a. (5 pts) Determine an expression for the closed-loop transfer function T(s): = y(s) r(s) terms of the parameters a and K. b. (5 pts) Determine values for the design parameters a and K by assuming that the zero of the closed-loop transfer function T(s) can be ignored and therefor approximated as a standard second-order system such that the closed-loop percent overshoot is less than 5% and the settling time is approximately 2.0 seconds when r(t) a unit-step input r(s) ==/ c. (5 pts) What is the steady-state value of the output y(t) for the system as found in part (a) using the parameter values a and K from part (b) in response to r(t) as a unit-step input? d. (5 pts) What are the poles and zeros for the closed-loop system evaluated in part (c)? (5 pts) For the actual system with the effects of the closed-loop zero included, what would be the approximate percent overshoot of the output with a unit step input as e. K(s + a) -200 s+2 r(s) in 1 s+1 y(s)