where: Kt = 0.2 N-m/A, Kb = 0.25 V-s/rad, J = 0.3 kg.m2, and b = 0.4 N-m-s/rad
1. (Assume that the torque disturbance D(s) is zero unless mentioned otherwise)
(A-1) Determine the transfer function relating the output position heta (s) to the input voltage Ea(s).
(A-2) To control the output position, a unity feedback signal is compared with an input signal of the required position heta r. The output of the comparator is applied to a controller before being applied to the dc motor input. Plot a block diagram describing this closed-loop control system.
2. Assume a proportional control action with a proportional constant of Kp.
(B-1) Determine the transfer function of the resulted closed-loop second-order system.
(B-2) Assuming Kp = 1, 2, 5 and 10, express the output position as a function of time in response to a unit step input. Analyse the behaviour of the system analytically in terms of damping, rise time, settling time, steady-state error, and stability. 3. Assume a proportional-plus-derivative control action with a proportional constant of Kp, and derivative constant of Kd.
(C-1) Determine the transfer function of the resulted closed-loop second-order system.
(C -2) Assuming Kp = 5 and Kd = 0, 1, 2 and 3, use MATLAB and Simulink to evaluate and plot the output position (from 0 to 10 seconds) in response to a unit step input. Analyse the behaviour of the system in terms of damping, rise time, settling time, steady-state error, and stability. Tabulate your results neatly and draw conclusions. 4.Assume a proportional-plus-integral control action with a proportional constant of Kp and an integration constant of Ki.
(D -1) Determine the transfer function of the resulted closed-loop system.
(D -2) Assuming Kp = 5 and Ki = 0, 1, 5 and 10, use MATLAB and Simulink to evaluate and plot the output position (from 0 to 10 seconds) in response to a unit step input. Analyse the behaviour of the system in terms of damping, rise time, settling time, steady-state error, and stability. 5.Assume a proportional-plus-integral-plus-derivative control action with a proportional constant of Kp, an integration constant of Ki, and a derivative constant of Kd.
(E -1) Determine the transfer function of the resulted closed-loop system.
D(s)
Ea(s)
1/Js
1/s
>0(s)
b
Kb