automatic control design a controller URGENT please answer 3

automatic control: design a controller (URGENT)

please answer 3 and 4

Design a PD controller for the given electrical sub-system of a DC-motor whose Percentage Overshoot is not greater than 5% and settling time is 1 second. What is the expected damping ratio of the final system? What is the natural frequency of the final system? Given a first order plant with transfer function G(s) = 1.5/0.01s + 1 What is the steady state value of the open-loop response? Determine the PD controllers for the given plant in question c, based on parameters of 3. Design a P1D controller for the non-linear mechanical system of a magnetic levitation apparatus whose mechanical system can modeled as mi = mg - k_f (i/x)^2 through the following steps. What is the steady state value of the current required? Determine the linearized transfer function of the system? Determine the natural frequency and damping ratio of the system if it is expected to have a percentage overshoot of 5% and settling time of 0.19 seconds. Determine the PID gains.

Solution

For the design of such a system, the transfer function can be reduced to a second order

system by ignoring the effect of the zero and calculating estimates for the required gains

to meet the desired specifications. Then the response can be plotted and the gains can

be tuned using a trial and error approach until the specifications are met. As can be seen

from the transfer function, PD control allows for both the damping ratio and natural

frequency to be controlled separately. For the approximate second order system, the

natural frequency and damping ratio are