Introduction to Control Systems Engineering
Ql. A small dc motor is described in terms of the following parameters:

R = (mm. = lmH, 1 = 0.01kg ~ m2, b = 0.1 51, = kb = 0.05.

a) Determine the motor transfer function from the input Va(t) to the angular velocity w(t) output.

b) Using Bode plot, design a feedback controller in order to achieve the following specifications:
ts < 20oms; PM > 60°; k, > 10.
Show the improvement by plotting the compensated system alongside the original Bode plot.

c) Using Root locus technique, design a PlD controller to achieve: ts < 20om; 05 < 10%.

d) Choose suitable sampling time, and give a discrete-time realization of the controller, i.e., give
update rules for computer implementation of the PID controller.

e) Plot the step response of the compensated continuous and discrete systems on the same plot.

Introduction to Control Systems Engineering
Ql. A small dc motor is described in terms of the following parameters:

R = (mm. = lmH, 1 = 0.01kg ~ m2, b = 0.1 51, = kb = 0.05.

a) Determine the motor transfer function from the input Va(t) to the angular velocity w(t) output.

b) Using Bode plot, design a feedback controller in order to achieve the following specifications:
ts < 20oms; PM > 60°; k, > 10.
Show the improvement by plotting the compensated system alongside the original Bode plot.

c) Using Root locus technique, design a PlD controller to achieve: ts < 20om; 05 < 10%.

d) Choose suitable sampling time, and give a discrete-time realization of the controller, i.e., give
update rules for computer implementation of the PID controller.

e) Plot the step response of the compensated continuous and discrete systems on the same plot.