RME30002 Control and Automation
Assignment
Due on Monday, Week 9 (1 May 2023)
1. A force F is applied to the mass 2 in Figure 1, where 1 2 are the
spring constants, 1 is the damping constant and 2 is the friction coefficient,
1 2 are the displacement. Find the transfer function 1/.
Figure 1
(5 Marks)
2. Consider the torsional mechanical system in Figure 3(a). The torque due to the
twisting of the shaft is –; the damping torque due to the breaking device is – ; the disturbance torque is (); the input torque is (); and the moment
of inertia of the mechanical system is J. the transfer function of the torsional
mechanical system is:
() = 1 �
2 + � � � + �
A closed loop control system for the system is shown in Figure 3(b).
Suppose the desired angle = 0°, = 6, = 1, = 0.9.
(a) Determine the open loop response () of the system for a unit step
disturbance () using MATLAB (set () = 0).
(b) With the controller gain 0 = 46, determine the closed loop response ()
to a unit step disturbance () by calculating the value of percentage
overshoot, peak time and settling time (2% criterion),
(c) Using Matlab, plot the unit step response of the closed-loop system and
estimate the percentage overshoot from the plot. Compare the result with
part (b).
(d) Co-plot the open loop versus the closed loop response to the disturbance
input. Discuss your results and make an argument for using closed loop
feedback control to improve the disturbance rejection properties of the
system.
2
Figure 2
(8 Marks)
3. The shoulder joint of a robotic arm uses a DC motor with armature control and
a set of gears on the output shaft. The model of the system is shown in Figure
3 with disturbance torque () which represents the effect of the load.
(a) When the desired angle input is a step ( ) /d s A sθ = and the load disturbance
is zero, determine the steady-state errors when ( )cG s K= and ( ) /cG s K s=
(b) When ( ) 0d sθ = and the load disturbance is ( ) /dT s M s= , determine the
steady-state errors when ( )cG s K= and ( ) /cG s K s= .
(c) Discuss the effects of the controller.
Figure 3
(7 Marks)
References:
1. “Modern Control Engineering”, Ogata.
2. “Modern Control Systems”, Dorf.
3. “Automatic Control Systems”, Kuo.