Question: The forward path transfer function of a control system with unity feedback is K s(s+ a)(s +30) G(s) = where a and K are

The forward path transfer function of a control system with unity feedback is K s(s+ a)(s +30) G(s) = where a

The forward path transfer function of a control system with unity feedback is K s(s+ a)(s +30) G(s) = where a and K are real constants. (a) Find the values of a and K so that the relative damping ratio of the complex roots of the characteristic equation is 0.5 and the rise time of the unit-step response is approximately 1 s. (b) With the values a and K found in part (a) determine the actual rise time using MATLAB simulation. (c) With the values a and K found in part (a) determine steady-sate errors of the system when the reference input is: i. a unit-step function, and ii. a unit-ramp function

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