Intelligent Control and Automation, 2011, 2, 351-363
doi:10.4236/ica.2011.24040 Published Online November 2011 (http://www.SciRP.org/journal/ica)
Improved NCTF Control Method for a Two-M ass Rotary
Positioning Systems
Mohd Fitri Mohd Yakub, B. A. Aminudin
Department of Mechanical Precision Engineering, Malaysia-Japan International Institute of Technology (MJIIT),
Universiti Teknologi Malaysia International Campus (UTM IC), Kuala Lumpur, Malaysia
Received July 28, 2011; revised September 5, 2011; accepted September 12, 2011
Abstract
This paper describes an improvement of the existing nominal characteristic trajectory following (NCTF) as a
practical control method for a two-mass rotary point-to-point (PTP) positioning systems. Generally, the
NCTF controller consists of a nominal characteristic trajectory (NCT) and a PI compensator. A notch filter is
added as a part of the compensator to eliminate the vibration due to the mechanical resonance of the plant.
The objective of the NCTF controller is to make the object motion follow the NCT and end at its origin. The
NCTF controller is designed based on a simple open-loop experiment of the object. The parameters identifi-
cation and an exact model of the plant are not necessary for controller design. The performance response of
improved NCTF controller is evaluated and discussed based on results of simulation. The effect of the design
parameters on the robustness of the NCTF controller to inertia and friction variations is evaluated and com-
pared with conventional PID controller. The results show that the improved NCTF controller has a better
positioning performance and is much more robust than the PID controller.
Keywords: Improved NCTF, Two-Mass System, Notch Filter, Vibration, Simulation
1. Introduction
Precision positioning systems play an important role in
industrial engineering applications such as advanced
manufacturing systems, semiconductor manufacturing
systems and robot systems. Point-to-point (PTP) posi-
tioning systems, either of one-mass or multi-mass sys-
tems, are used to move an object from one point to an-
other point either in angular or linear position. For ex-
ample, in application with one-mass system, such as
CNC machines, PTP positioning is used to accurately
locate the spindle at one or more specific locations to
perform operations, such as drilling, reaming, boring,
tapping, and punching. In multi-mass systems applica-
tion, such as in spot-welding robot, which has a long arm
for linear system or long shaft in rotary system, PTP po-
sitioning is used to locate the manipulator from one loca-
tion to another.
PTP positioning systems requires high accuracy with a
high speed, fast response with no or small overshoot and
to be robust to parameter variations and uncertainties.
Therefore, the most important requirements in PTP posi-
tioning systems are the final accuracy and transition time
whereas the transient path is considered as the second
important. In PTP applications, parameter varies with the
payload and some friction may cause the instability of
the performances [1]. In this case, the system perform-
ance is expected to be the same or as close as its per-
formance when the system is in normal condition. Thus,
robustness is also an important requirement in order to
maintain the stability of the positioning systems. A
nominal characteristic trajectory following (NCTF) con-
troller as a practical controller for point-to-point posi-
tioning systems had been proposed. The NCTF controller
consists of two elements namely a nominal characteristic
trajectory (NCT) and a PI compensator. It had been re-
ported that the NCTF had a good positioning perform-
ance and robustness to parameters variations [2].
However, the NCTF controller that has been proposed
is designed based on one-mass rotary system. The
positioning systems can only be assumed as one-mass
positioning system in the case a rigid coupling is used
and there are no flexible elements in between motor and
load. On the other hand, the systems should be modeled
as multi-mass systems when flexible couplings with low
stiffness or other flexible elements are used to connect

M. F. M. YAKUB ET AL. 352
the actuator to other elements.
Some application like in robot industry which have a
long arm for linear system or long shaft in rotary system
will be considered as two-mass or multi-mass systems. In
two-mass systems, low stiffness elements such as coup-
lings or long shaft cause mechanical resonance like vibr-
ation between two masses, which may reduce positioning
accuracy and gives the unstable performance response of
the plant [3]. Therefore, the existing NCTF controller
does not work for two-mass rotary positioning systems.
Therefore, enhancement and improvement design of
NCT and a compensator are required to make the NCTF
controller suitable for two-mass rotary positioning sys-
tems.
In this paper, the improved NCTF controller is expect-
ed to control the position and to reduce the vibration that
cause by long shaft in between a first and second mass of
the system. The performances of the improved NCTF
controller is evaluated and compared with the conventio-
nal PID controller.
The paper is organized as follows: Section 2 describes
the modeling of the systems. Determination of the NCT
and its simplified object is explained in Section 3. Next,
compensator design using the NCT information and the
object response is described in Section 4. Then, the ef-
fectiveness of the improved NCTF controller for two-
mass rotary system is examined through simulations in
Section 5. Finally, conclusions are given in the last Sec-
tion.
2. Model of the Systems
Modeling is the construction of physical or mathematical
simulation of the real system. It is a process of repre-
senting the behavior of the real systems by a collection
of mathematical equations [4]. Figure 1 shows the sim-
plified diagram of a rotary positioning system. It consists
of mechanical and electromechanical components. Two
masses, having the moments of inertia Jm and Jl, are cou-
pled by low stiffness shaft which has the torsion stiffness
Ks and a damping.
The electrical part of the DC motor is derived by using
Kirchoff Voltage Law (KCL):
  
d
d
 
m
memf mmm
it
Vt EtLRit
t (1)
where Vm(t) is input voltage, Eemf(t) is electromagnetic
field, Lm is motor inductance, Rm is motor resistance and

m
it is current. SI units are applicable for all notations.
The motor speed is directly proportional to the applied
voltage, or precisely:
 
ˆ
emfb m
EtK t   (2)
Figure 1. Schematic diagram of two-mass rotary position-
ing systems.
where


mt

 is motor angular speed and ˆb
K
is back-
emf constant. Motor torque characteristic is proportional
to the supplied current:


ˆ
mtm
Tt Kit

(3)
where


m
Tt is motor torque and ˆt
K
is motor-torque
constant. Next, modeling on the mechanical parts of the
system is done by applying Newton’s second law of mo
tion to the motor shaft:
 
d() () ()
d

 
m
mmmmcmc
t
l
J
TtBtKt Kt
t (4)
where m
J
is motor inertia, m is motor viscous
damping and c
B
K
is shaft constant. The torque of the
load is expressed as follows:
 
d() () ()
d
l
llllclc
t
m
J
TtBt Kt Kt
t

  (5)
where l
J
is inertia of the load, is load viscous
damping and
l
B


l
Tt is load torque.
The detailed model of the two-mass rotary positioning
systems is used only for making simulation is shown in
Figure 2. The parameter of the object used only for
making simulation is shown in Table 1.
3. NCTF Control Concept
The structure of the NCTF control system is shown in
Figure 3. The NCTF controller consists of a NCT and a
compensator. The NCTF controller works under the fol-
lowing two assumptions [5]:
1) A DC or an AC servo motor is used as an actuator
of the object.
2) The reference input, θr is constant and θr' = 0.

M. F. M. YAKUB ET AL. 353
Figure 2. Exact model of the two-mass rotary positioning systems.
e
Figure 3. Structure of NCTF control system.
Table 1. Nominal object parameters.
Parameter Value Unit
Motor inertia, Jm 17.16e–6 Kgm2
Inertia load, Jl 24.17e–6 Kgm2
Stiffness, Kc 0.039 Nm/rad
Motor resistance, R 5.5 Ω
Motor inductance, L 0.85e–3 H
Torque constant of the motor, Kt 0.041 Nm/A
Motor voltage constant, Kb 0.041 Vs/rad
Frictional torque, Tf 0.0027 Nm
Motor viscous friction, Bm 8.35e–6 Nms/rad
Load viscous friction, Bl 8.35e–6 Nms/rad
The objective of the NCTF controller is to make the
object motion follow the NCT and end at the origin of
the phase plane (e, e'). Signal up shown in Figure 3,
represents the difference between the actual error rate e'
and that of the NCT. The value of up is zero if the object
motion perfectly follows the NCT. The compensator is
used to control the object so that the value of up, which is
used as an input to the compensator, is zero.
Figure 4 shows an example of object motion con-
trolled by the NCTF controller. The object motion com-
prises two phases: one is the reaching phase and the
other, the following phase. In the reaching phase, the
compensator forces the object motion to reach the NCT
as fast as possible. In the following phase, the compen-
sator controls the object motion to follow the NCT and
end at the origin. The object motion stops at the origin,
which represents the end of the positioning motion. Thus,
the NCT governs the positioning response performance.
The NCTF controller consists of NCT, which is con-
structed based on a simple open-loop experiment of the
object, and PI compensator, which is designed based on
the obtained NCT. Therefore, the design of NCTF con-
troller can be described by the following steps [6]:
1) The object is driven with an open loop stepwise
input and its displacement and velocity responses are
measured.
2) Construct the NCT by using the object responses
obtained during the deceleration process. Since the NCT
is constructed based on the actual responses of the object,
it contains nonlinear characteristics such as friction and
saturation. The NCTF controller is expected to avoid
impertinent behavior by using the NCT.

M. F. M. YAKUB ET AL. 354
Error
,
e
Error rate, e'
NC T
o
Object motion
RP: Reac hing phase
FP: Following phase
FP
RP
Figure 4. NCT and object motion.
3) Design the compensator based on the NCT infor-
mation. The NCT includes information of the actual ob-
ject parameters. Therefore, the compensator can be de-
signed by using only the NCT information.
Due to the fact that the NCT and the compensator are
constructed from a simple open-loop experiment of the
object, the exact model including the friction character-
ristic and the conscious identification task of the object
parameters are not required to design the NCTF control-
ler. The controller adjustment is easy and the aims of its
control parameters are simple and clear.
4. Controller Design for Two-Mass Systems
4.1. NCT Determination
In order to determine the NCT, the actuator is driven
with stepwise inputs, and the load displacement and load
velocity responses of the object are measured. Figure 5
shows the stepwise input, load displacement and load
velocity responses of the object. In this case, the object
vibrates due to its mechanical resonance [7]. In order to
eliminate the influence of the vibration on the NCT, the
object responses must be averaged. Figure 6 shows the
averaged object responses.
The parameter of the object used only for making
simulation is shown in Table 1. In Figure 6, moving
averaged filter is used because of its simplicity [7]. As
the name implies, the moving averaged filter operates by
averaging a number of points from the object responses
to produce each point in the averaged responses. The
averaged velocity and displacement responses are used to
determine the NCT. Since the main problem of the PTP
motion control is to stop an object at a certain position, a
deceleration process (curve in area A of Figure 7) is used.
Variable h in Figure 7 is the maximum velocity, which
depends on the input step height. From the curve in area
A and h in Figure 7(a), the NCT in Figure 7(b) is
determined.
There are two important parameters in the NCT as
shown in Figure 7(b): the maximum error rate indicated
Time
Input, Displacement, Velocity
stepwise
loaddisplacement
load veloc it y
Figure 5. Stepwise input and actual objec t responses.
Time
Input, Di splaceme nt, V elo cit
y
stepwise
aver aged displ a cem ent
aver aged ve l oc it y
Figure 6. Stepwise input and ave r aged object responses.
Time
Input, Displacement, Velocity
stepwise
average d d is placement
aver aged velocity
U
h
A
A
h
r
(a)
Error
,
e
E
rror rate, e
'
A
hA
m
o
h
(b)
Figure 7. NCT determination: (a) Stepwise input and averaged
object responses; (b) Nominal characteristic trajectory.

M. F. M. YAKUB ET AL.355
by h, and the inclination of the NCT near the origin in-
dicated by m.
As discussed in the following section, these parame-
ters are related to the dynamic parameters of the object.
Therefore, the parameters are used to design the com-
pensator.
An exact modeling including friction and conscious
identification processes are not required in the NCTF
controller design. The compensator is derived from the
parameter m and h of the NCT. Since the DC motor is
used as the actuator, the simplified object can be pre-
sented as a following fourth-order system:
2
2
2
2
()
() ()() 2
f
l
o2
f
ff
s
Gs K
Us ssss





  (6)
where θl (s) represents the load displacement of the ob-
ject in rad, U(s), the input to the actuator in volt and K, ζ,
α2 and ωf are simplified object parameters to be deter-
mined. The NCT is determined based on the averaged
object response which is does not include the vibration.
So, it can be assumed that the averaged object response
is a response to the stepwise inputs of the averaged ob-
ject model as follows:
2
2
()
()( )
av sK
Us ss


 (7)
where θav(s) is the averaged load displacement, U(s),
input to the actuator and K and α2 are simplified object
parameters that related to the NCT information. The re-
lations between simplified parameters K and α2 and the
NCT information are [6]:
2m

 (8)
r
h
Ku  (9)
where m is the inclination of the NCT near the origin, h,
is maximum error rate of NCT and ur is a voltage input
to the plant.
4.2. Compensator Design
The following PI and notch filter (NF) compensator is
pro- posed for two-mass systems:
22
22
(2 )
() (2 )
pidcff f
c
oo o
KsKK ss
Gs sss
 
 









(10)
The PI compensator is adopted for its simplicity to
forces the object motion to reach the NCT as fast as pos-
sible and control the object motion to follow the NCT
and end at the origin.
In a two-mass system, the mechanical couplings be-
tween the motor, load, and sensor are not perfectly rigid,
but instead, act like springs. Here, the motor response
may cause overshoot or even oscillation at the resonance
frequency resulting in a longer settling time. The most
effective way to deal with this torsional resonance is by
using an anti-resonance NF.
According to standard frequency analysis, resonance is
characterized by a pair of poles in the complex frequency
plane. The imaginary component indicates the resonant
frequency, while the real component determines the
damping level. The larger the magnitude of the real part,
the greater the damping will be [8]. Figure 8 shows
where the poles and zeros of the system are located on
the s-plane. Figure 8(a) shows the root locus of the sys-
tem without the controller, which results in unstable re-
sponses. In Figure 8(b), the poles marked A are the ones
due to the mechanical resonance. These are cancelled by
the complex zeros marked by B. Although it is assumed
that the NF completely cancels the resonance poles, per-
fect cancellation is not required. As long as the NF zeros
(a)
(b)
Figure 8. System responses: (a) Root locus of the system; (b)
Pole and Zero cancellation of the NF.

M. F. M. YAKUB ET AL. 356
are close enough to the original plant poles, they can
adequately reduce the effect of the later, thereby improve
the system response.
Figure 9 shows the effect of the NF to the system in
time domain.
Figure 10 shows the block diagram of the continuous
closed loop NCTF control system with the simplified
object model near the NCT origin where the NCT is lin-
ear and has an inclination α2 = –m. The proportional and
integral compensator gains are calculated [9].
The signal up near the NCT origin in Figure 10 can be
expressed as the following equation:
22
p
l
ue e e

   


 (11)
A higher ωn and a larger ζ are preferable in the com-
pensator design. The selection of ωn and ζ are chosen to
have 40% of the values of ζ practical, so that the margin
safety of design is 60% [9]. During the design parameter
selection, the designer may be tempted to use large val-
ues of ωn and ζ in order to improve the performance.
However they are constrained by the sampling time of
the systems which may lead the system to instability.
5. Simulation Results
Conventional PID controllers were designed based on a
Ziegler Nichols and Tyres Luyben closed loop method,
using proportional control only. The proportional gain is
increased until a sustained oscillation output occur which
giving the sustained oscillation, Ku, and the oscillation
period, Tu are recorded. The tuning parameter can be
found in Table 2 [10]. The detailed model of the object
used only for making simulations is shown in Figure 2.
In the detailed model of the object, friction and satura-
tion are taken into consideration [11]. The significance of
this research lies in the fact that a simple and easy con-
troller can be designed for high precision positioning
system which is very practical. By improving the NCTF
controller, it will be more reliable and practical for real-
izing high precision positioning systems for two-mass
00.5 11.5 22.5 33.5 44.5 5
-40
-20
0
20
40
60
80
100
Ti me, sec
Load di splacem ent, deg
without NF
with NF
Figure 9. Effect of the NF to the system in time domain.
Figure 10. Simplified NCTF control system at small error e.

M. F. M. YAKUB ET AL.357
Table 2. Controller parameters.
Controller Kp K
i K d ςf ωf ςo ωo
Improved NCTF 4.79e−1 2.65e−1 - 0.7 40 0.9 60
Ziegler Nichols PID 78.696 4918.5 0.31478 - - - -
Tyres Luyben PID 59.618 846.85 0.30282 - - - -
positioning systems compared with conventional PID in
term of controller performances.
The stepwise input is applied to the object. Its load
displacement and load velocity responses due to stepwise
input are shown in Figure 5. The input to the actuator ur
is 12 V. The object response vibrates with a vibrating
frequency ωfd of 40 Hz. The object responses are aver-
aged by using the moving average filter as shown in
Figure 7(a). By using the averaged responses, the NCT
is determined as shown in Figure 7(b). In Figure 7(b),
the inclination of the NCT near the origin, m is 61.6 and
the maximum error rate indicate by h is 156.8 rad/s. Se-
lection of NF parameters are based on Routh-Hurwitz
stability criterion. In order to obtain an always stable
continuous closed-loop system, the following constraint
needs to be satisfied.
2
2oo

   (12)
In order to evaluate the effectiveness of improved
NCTF controller designed for a two-mass system, the
controller is compared with PID controllers, which are
tuned using Ziegler-Nichols and Tyres-Luyben methods.
The PI compensator parameters are calculated from
the simplified object parameters (K and α2) and the de-
sign parameters (ωn and ζ). Table 2 shows the parame-
ters of the compensator of the improved NCTF controller
and PID controller.
For simulation purpose, the exact model of the object
and its nominal parameters taken from plant identifica-
tion as described in [12]. In order to evaluate the robust-
ness of the improved NCTF control system, the simula-
tions were conducted in three conditions: with normal
load, with increasing the load inertia, and with increasing
the friction as shown in Table 3. All process within 10
second simulation time.
Figure 11 shows step responses to 30 and 90 deg step
input when the improved NCTF controller is used to
control a normal object. The positioning performance is
evaluated based on percentage of overshoot, settling time
and positioning accuracy. Figure 12 shows step re-
sponses to 30 and 90 deg step input to control the object
Table 3. Object parameter comparison.
Object Inertia Friction
Normal load Jl = 14.17 × 10–6 kg·m2 τfmax = 0.0027
2 × Jl τfmax
Increased inertia load 5 × Jl
10 × Jl
Jl 2 × τfmax
Increased friction object 10 × τfmax
Table 4. Positioning performance comparison, increased object inertia.
Controller OS
(%) Ts (sec) ess (deg)
30
deg
input
Z-N
T-L
NCTF
38.3
17.4
0
1.246
1.485
0.761
1.16
0.01
0.08
Jl 90
deg
input
Z-N
T-L
NCTF
47.6
19.6
6.4
1.023
1.135
0.335
1.15
0
0
30
deg
input
Z-N
T-L
NCTF
83.2
18.7
6.9
1.46
1.396
0.91
0.94
0.2
0.07
2 × Jl 90
deg
input
Z-N
T-L
NCTF
83.7
22
7.2
1.067
1.118
0.44
0.92
0.82
0.45
unstable 30
deg
input
Z-N
T-L
NCTF
31.2
33.9
1.144
0.89
0.45
0.14
unstable
5 × Jl 90
deg
input
Z-N
T-L
NCTF
36.6
8.5
1.111
0.765
0.81
0.52

M. F. M. YAKUB ET AL. 358
00.5 11.5 22.5 33.5 44.5 5
-10
0
10
20
30
40
50
time, sec
Load displacement,
30 deg
00.5 11.5 22.5 33.5 44.5 5
-1
0
1
2
3
time, sec
Control signal,
V
Zeigler-Nichols
Tyres-Luyben
NCTF
Zeigl er-Nichols
Tyres-Luyben
NCTF
(a)
00.5 11.5 22.5 33.5 44.5 5
-2
0
2
4
6
8
time, sec
Control signal,
V
00.5 11.5 22.5 33.5 44.5 5
-50
0
50
100
150
time, sec
Load Displacement,
90 deg
Zeigler-N icho ls
Tyres-Luyben
NCTF
Zeigler-N icho ls
Tyres-Luyben
NCTF
(b)
Figure 11. Step response comparisons, nominal object: (a) Step response 30 deg; (b) Step response 90 deg.
with the increase in the load twice of nominal object (2 ×
Jl).
Figure 13 shows step responses to 30 and 90 deg step
input to control the object with the load increase five
time of the normal object (5 × Jl). The positioning per-
formances based on simulations for normal and increased
object inertia are presented in Table 4. Figures 14 and
15 show step responses to 30 and 90 deg step input to
control the object with the increase in twice and ten
times (2 × τfmax and 10 × τfax) the maximum friction
m

M. F. M. YAKUB ET AL.359
00.5 11.5 22.5 33.5 44.5 5
-10
0
10
20
30
40
50
60
time, sec
Load displacement,
30 deg
00.5 11.5 22.5 33.5 44.5 5
-1
0
1
2
3
time, sec
Control signal,
V
Zeigler-N ichols
Tyres-Luyben
NCTF
Zeigler-N ichols
Tyres-Luyben
NCTF
(a)
00.5 11.5 22.5 33.5 44.5 5
-50
0
50
100
150
200
time, sec
Load di splacement,
90 deg
00.5 11.5 22.5 33.5 44.5 5
-2
0
2
4
6
8
time, sec
Control s ignal ,
V
Zeigler-Nichols
Tyres-Luyben
NCTF
Zeigl er-Nichol s
Tyres-Luyben
NCTF
(b)
Figure 12. Step response comparison, increased inertia object (2 × Jl): (a) Step response 30 deg, (b) Step response 90 deg.
factor. The positioning performances based on simula-
tions for normal and increased friction factor are pre-
sented in Table 5. Figure 16 shows the object motion
follows the NCT for 30 deg step input.
In nominal object, the improved NCTF controller
gives the smallest percentage of overshoot and has the
fastest settling time compared with both PID controllers.
The improved NCTF controller gives a better positioning
accuracy than PID designed with Ziegler-Nichols but
less accuracy than Tyres-Luyben PID controller. With
increased object inertia, improved NCTF controller still
gives the fastest settling time and smaller overshoot than
PID controllers. Improved NCTF controller also has a
table response, even if the control signal is saturated, s

M. F. M. YAKUB ET AL. 360
00.5 11.5 22.5 33.5 44.5 5
-10
0
10
20
30
40
50
time, sec
Load dis p la ce men t,
30 deg
00.5 11.5 22.5 33.5 44.5 5
-2
-1
0
1
2
time, sec
Cont r o l si gnal ,
V
Zeigler-Nichols
Tyres-Luyben
NCTF
Zeigler-Nichols
Tyres-Luyben
NCTF
(a)
00.5 11.5 22.5 33.5 44.5 5
-50
0
50
100
150
time, sec
Load displacement,
90deg
00.5 11.5 22.5 33.5 44.5 5
-1
0
1
2
3
4
5
time, sec
Contr ol signal
V
Zeigler-Nichols
Tyres-Luyben
NCTF
Zeigler-Nichols
Tyres-Luyben
NCTF
(b)
Figure 13. Step response comparison, increased inertia object (5 × Jl): (a) Step response 30 deg, (b) Step response 90 deg.
meanwhile the use of PID controllers result in unstable
responses. So, improved NCTF controller is much more
robust to inertia variation compared with PID controllers.
With increased friction, the improved NCTF controller
gives smallest percentage of overshoot as well as the
fastest settling time compared with PID controllers. The
positioning accuracy does not change significantly due to
friction variation and saturation of the control signal.
Hence, it is proven by simulations that the improved
NCTF controller is much more robust to friction varia-
tion compared to PID controllers, even if the saturation
o
f the controller signal occurs.

M. F. M. YAKUB ET AL.361
00.5 11.5 22.5 33.5 44.5 5
-10
0
10
20
30
40
50
time, sec
Load displacement,
30 deg
00.5 11.5 22.5 33.5 44.5 5
-20
0
20
40
60
80
100
120
140
time, sec
Load displacement,
90 deg
NCTF
Zeigler-Nichol s
Tyres-Luyben
Zeigle r-Nichols
Tyres-Luyben
NCTF
Figure 14. Step response comparison, increased friction object (2 × τt).
00.5 11.5 22.5 33.5 44.5 5
-10
0
10
20
30
40
50
time, sec
Load displacement,
30 deg
00.5 11.5 22.5 33.5 44.5 5
-50
0
50
100
150
time, sec
Load displacement,
90 deg
Zeigler-N icho ls
Tyres-Luyben
NCTF
Zeigler-N icho ls
Tyres-Luyben
NCTF
Figure 15. Step response comparison, increased friction object (10 × τt).

M. F. M. YAKUB ET AL. 362
00.5 11.5 22.5 33.5 44.5 5
-10
0
10
20
30
40
time, sec
Displacement,
30 deg
-0.1 00.1 0.20.3 0.40.5 0.6
-20
-15
-10
-5
0
5
Error , rad
Error ra te, rad /s
NCT
PI
NCTF
Figure 16. Object motion for 30 deg step input.
Table 5. Positioning performance comparison, increase friction object.
Controller Overshoot
(%)
Settling time
(sec)
Ess
(deg)
30
deg
input
Z-N
T-L
NCTF
36.
15.7
6.8
2.505
2.054
1.642
2.01
0.01
0.05
2 × ft 90
deg
input
Z-N
T-L
NCTF
42.1
18.4
2.53
1.763
1.315
0.489
2.16
0.01
0.42
30
deg
input
Z-N
T-L
NCTF
38
20.1
5.2
8.908
6.482
5.216
4.65
0.04
0.14
10 × ft 90
deg
input
Z-N
T-L
NCTF
36.9
16
3.5
8.773
6.6
5.193
5.85
0.01
0.66
6. Conclusions
The improvement of NCTF controller as a new practical
control for two-mass positioning systems has been intro-
duced and discussed. The improved NCTF controller con-
sists of the NCT and the PI with notch filter compensator.
The NCT is constructed using the object response data in a
simple open-loop experiment and the compensator pa-
rameters are designed based on the NCT. The effective-
ness of the improved NCTF controller is examined by
simulation and it showed that the improved NCTF con-
troller is much more effective and robustness then the
conventional PID controller for positioning systems.
7. Acknowledgements
This research is supported by Ministry of Higher Educa-
tion Malaysia under Vot 78606 and Malaysia-Japan In-
ternational Institute of Technology (MJIIT), Universiti
Teknologi Malaysia (UTM).
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M. F. M. YAKUB ET AL.363
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