Page 17 - Journal Cover.pdf

Matrood & Nassar | 13

stability. Fig. 3 and Fig.4 show block diagrams for (PID – D)
and (I – PD) dual loop controllers respectively.

Fig. 3: Dual-loop PID-D controller

Fig. 5: Simulink module of (2DOF)

The principle of (PID – D) controller is achieved by adding
suitable gain to the motor position feedback. In this study, a
derivative gain with a value about 6 is applied to insure good
damping and stability with the aid of conventional PID
controller as shown in Fig. 6. This controller provides double
loops to control system variables. The PID controller
parameters are selected by trial and error procedure as:
Kp=0.001, KI=0.0004, KD=0.001.

Fig. 4: Dual-loop I-PD controller

IV. SIMULATION AND RESULTS
The main uncontrolled system was analyzed with
(PID – D) and (I – PD) dual loop controllers structures. In
order to verify the effectiveness of the simulations, the
specific parameters of the system are listed in Table 1.
Depending on the mathematical model given in section 2,
the Matlab / Simulink model for (2DOF) rotating system
using a unit step function input signal as an excitation is
shown in Fig. 5.
TABLE 1
SYSTEM PARAMETERS OF THE MODEL [5]
Polar mass moment of inertia 0.0641 kg m
2
of the driving motor ( J 1 ) Fig. 6: Simulink module of (2DOF) rotating system with
Polar mass moment of inertia 0.0523 kg m PID-D controller
2
of the driven object ( J 2 )
Shaft stiffness ( K ) 242 Nm/rad The second type of dual loop controller is constructed by
using motor position feedback inner loop with PD controller
Shaft damping ( B ) 0.15 Nms/rad
and remaining the feed forward I controller. The Simulink
model is built as illustrated in Fig. 7. Referring to the Fig. 7,
The simulation of (2DOF) rotating system is performed in the inner loop PD parameters are selected as 50 and 5
Matlab / Simulink in order to show the behavior and the respectively while the I controller parameter is chosen as 0.1.
effectiveness of such system when applying torque and by
knowing the angle of twist the applied torque can be
modulated for tuning the variation in twist angles.