Page 16 - Journal Cover.pdf

12 | Matrood & Nassar

simulation of the two-mass system. It is seen that the control K ( θ 1 – θ 2 )
system has fast speed response and robust stability. Ekhlas
Hameed Karam [8] (2013) suggested a simple and efficient B ( ̇ – ̇ )
1
2
hybrid PID with simple fuzzy controller (FC) in order to
improve the performance of the different PID controllers. Motor Load
The suggested method applied on single link flexible joint
robot. The new hybrid connection PID-FC methods make θ 1 Shaft θ 2
the output response of the tested plant more accurate in T 1 J 1
tracking the desired input with zero or very small steady state J 2 T 2
error. Shahgholian, etal. (2014) [9] presented a speed Fig. 2: Free body diagram of torsional system

control strategy for the torsional vibration systems. The state
feedback strategy with integral control based on the detailed J θ= ∑T
̈
small-signal model was applied to design the speed For motor: (1)
controller for the two-mass resonant system. The integral
̇
̈
̇
control exhibited no steady state error in the response to the J 1 θ1=T 1–K θ1 –B θ 1+ K θ2 +B θ 2 (2)
step input. Korkmaz, etal. (2014) [10] used the modified For load:
Proportional-Integrative-Derivative control system to ̈ ̇ ̇
enhance the performance of the ship shaft control system and J 2 θ2=K θ1+B θ 1–K θ2 –B θ 2 –T 2 (3)
to adjust the torsional vibration. The performance of the Rearranging the above equations yields:
̈
̇
̇
traditional PID controller was improved by moving J 1 θ1=T 1 – K( θ1 – θ2)–B (θ1 – θ2) (4)
̈
̇
̇
derivative and proportional blocks on feedback path. In this J 2 θ2 = K( θ1 – θ2) +B (θ1 – θ2 ) –T2 (5)
study, main motor, shaft and inertial load system were Where:
'
modeled by Newtons Second law, and the model was J 1 and J 2 we polar mass moment of inertia of motor and
simulated by using Matlab-Simulink software. Torsional load respectively. K and B are shaft stiffness inherent
vibration analysis was confirmed because of the resulting damping. T 1 and T 2 are motor and load torques respectively.
risk. θ1 and θ2 are the angles of motor and load respectively.
The goal of this research is to reduce system oscillations by θ1 – θ2 is Shaft twist.
controlling shaft torsional vibration through the application When torque is applied to a mass it will begin to accelerate,
of certain dual loop controllers such as PID – D and PD – I. in rotation. When the system starts rotation the motor will
A comparison showed that PD – I controller made better generate some torque which transmits through the shaft to
stability response than PID – D controller. This research is the load which in t urn will accelerate the system as a result
organized as follows: of continues rotation until approaches to the required
In section II, the torsional rotating system model is constant speed.
derived. The PID – D and PD – I dual loop controllers are This torque has noise components which increase as the
proposed. In section III. Simulation and control results are deformation increases. When combining the torsional
deduced in section IV. Finally, conclusions are presented in rotating system with a feedback system, the frequencies of
section V. the entire system can be interacted causing high frequency
noise which in turn can produce more torsional oscillations
through the system [11].
II. MATHEMATICAL MODELING OF TORSIONAL
ROTATING SYSTEM
III. DUAL LOOP CONTROLLER (DLC)
A two degree of freedom (2DOF) torsional rotating
system is considered which consists of electric motor, shaft The two main controllable variables related to the
and load. The analysis is based on equation of motion torsional vibration in this study are θ1 and θ2 associated with
'
derived from Newtons Second law of motion as "The sum of the terminal points at J1 and J2 to form a complete mechanical
applied torques is equal to the inertia forces". The equation network. This controller uses two feedback sensors. The
of motion for 2DOF rotating system is inserted after drawing advantages of this controller is to reach the control law or the
Free-body diagram. Fig. 1 shows the physical model of feedback signal to the system as a filtered signal without
torsional rotating system. The free body diagram is drawn in noise and torque components. DLC can be constructed by
Fig. 2. using two feedback signal devices forming two loops, one of
them is the inner loop while the other represents the outer
loop. The inner loop connected to the output of motor
K , B
velocity or position with either derivative controller (D)
Motor Load
with a suitable gain or proportional – derivative controller
Shaft (PD) so it acts like a low pass filter while the outer loop is the

normal feedback controlled signal with conventional
(PID) controller [8] or (I) controller [12] respectively to
T 1 J 1 J 2 T 2
accumulate a position error moving away any inaccuracy in
the transmission part, thereby assuring system accuracy and
Fig. 1: Physical model of torsional system