30 2. Consider a motor G(s) = The input is the voltage in volts and the output is the angle in radians. Design a controller K(s) and if needed a pre-filter F (s) such that • % overshoot in the step response for desired angle of 1rad, is less than 5% • Settling time of the step response for desired angle of 1rad, is less than 3 seconds. s(s+ If there is a step disturbance du applied to the plant, then the controller rejects it. I.e. there is no steady state error in the angle output due to the unit step disturbance du. Clearly and in great detail explain your methodology to achieve this. • If there is a step disturbance dy applied to the output, then the controller rejects it. Explain using math. I.e. there is no steady state error in the angle output due to the unit step disturbance dy. • Controller should be able to handle all the above specifications, if there is a time delay of 0.1 second in providing the input u to the plant. Clearly and in great detail explain your methodology to achieve this. Remember the time delay's TF will be e-0.15 and it can (Pade) approximated as (1+015) • Voltage to the motor should be less than 12Volts, for a step reference of 1 rad. Write down the steps you followed in the sisotool as a numbered list. Include the following in those steps: a. Your error calculations. b. Paste the snapshots of all the root loci diagrams leading to the final one. c. Expression of your final controller K(s). d. The plot of the response y(t) with settling time and overshoot marked in it, due to r(t) of 1 rad. e. The plot of the response y(t) due to step du(t) and dy(t) separately. f. The voltage response due to the reference command r(t) of 1 rad. g. The combined response y(t) due to r(t) of 1 rad, and step du(t). (You'll use the step command, sisotool cannot do this for you, sisotool only does the responses separately).

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30 2 consider a motor g s the input is the voltage in volts and the ou

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30 2. Consider a motor G(s) = The input is the voltage in volts and the output is the angle in radians. Design a controller K(s) and if needed a pre-filter F (s) such that • % overshoot in the step response for desired angle of 1rad, is less than 5% • Settling time of the step response for desired angle of 1rad, is les