The transfer function is H(s) = (1.2s+0.18)/(s3 + 0.74s2 + 0.92s) and C(s) = (K(s+1))/ s A) A disturbance input W(s) =W/sk , where W is a constant, into the feedback controller as shown below. We set R(s) = 0. What type of disturbance input W(s)(step, ramp, or parabola) can the system reject (i.e., the steady-state error ess is a nonzero constant)? (B) Suppose you want to design the controller C(s) to produce a closed-loop response to a reference step input that has no more than 30% maximum overshoot (Mp ≤ 0.30) and a peak time of no more than 8 sec (tp ≤ 8). Given the specifications on Mp and tp , compute the constraints on the damping ratio ζ and the damped natural frequency ω, assuming that the closed-loop system is approximated as a 2nd-order underdamped system. Sketch the allowable regions in the complex plane (the s-plane) that these constraints define, and shade in the regions where the poles should not be placed.
The transfer function is H(s) = (1.2s+0.18)/(s3 + 0.74s2 + 0.92s) and C(s) = (K(s+1))/ s
A) A disturbance input W(s) =W/sk , where W is a constant, into the feedback
controller as shown below. We set R(s) = 0. What type of disturbance input W(s)(step, ramp, or parabola) can the
system reject (i.e., the steady-state error ess is a nonzero constant)?
(B) Suppose you want to design the controller C(s) to produce a closed-loop response to a
reference step input that has no more than 30% maximum overshoot (Mp ≤ 0.30) and a peak time
of no more than 8 sec (tp ≤ 8). Given the specifications on Mp and tp , compute the constraints
on the damping ratio ζ and the damped natural frequency ω, assuming that the closed-loop system
is approximated as a 2nd-order underdamped system. Sketch the allowable regions in the
complex plane (the s-plane) that these constraints define, and shade in the regions where the poles
should not be placed.
The question contains a unity feedback system behaving as a feedback controller with transfer functions H(s) and C(s) as given and a reference input R(s) and disturbance input D(s), and the output response is Y(s).
Detailed handwritten solution for parts A and B given in Step 2.
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