Positioning Control of a Pneumatic Artificial Muscle Driven Stage Using an
Improved NCTF Control
S. H. Chong*. T. F. Tang**. Z Jamaludin***. K. Sato****
*Centre for Robotics and Industrial Automation, Universiti Teknikal Malaysia Melaka, 76100 Melaka, MALAYSIA (email:
**Centre Robotics and Industrial Automation, Universiti Teknikal Malaysia Melaka, 76100 Melaka, MALAYSIA(e-mail:
*** Centre of Smart System and Innovative Design, Universiti Teknikal Malaysia Melaka, 76100 Melaka, MALAYSIA(e-mail:
**** Department of Mechanical Engineering, Toyohashi University of Technology, 1-1 Hibarigaoka, Tempaku-cho,
Toyohashi, Aichi, 441-8580, JAPAN (e-mail: [email protected])
Abstract: This paper presents a practical controller design method for motion control of a pneumatic
artificial muscle (PAM) driven stage. The proposed controller emphasizes simple control structure and
straightforward design procedure, which the controller parameters can be determined easily without the
need of an exact model parameters. Due to small working range of the constructed PAM mechanism, the
actual velocity feedback is removed from the conventional NCTF control structure. The improvements
have been realized on the conventional NCTF controller by adding the acceleration feedback
compensator to increase the damping characteristic of the PAM mechanism, and the reference rate
feedforward is to improve the following characteristic. The design procedure remains simple and
straightforward. The effectiveness of the improved NCTF control is verified experimentally and
compared with the conventional NCTF control in point-to-point positioning and continuous motion
performances. The experimental results proved that the improved NCTF controller achieves better
positioning and tracking performances than the conventional NCTF controller.
Keywords: NCTF control; Pneumatic artificial muscle; Nonlinear control; Positioning systems; Point-to-
point control
1. INTRODUCTION
McKibben pneumatic artificial muscle (PAM) is a
unidirectional pneumatic actuator that duplicates the
behaviour of skeletal muscle. The compactness, excellent
power-to-weight ratio performance and safe in use
characteristic of the PAM are the factors to enhance the PAM
system in positioning accuracy and further extend its
applications in rehabilitation and welfare devices. It has been
applied in various applications, such as the power assist
devices, medical applications, industry machinery, and
robotics (Deaconescu & Deaconescu, 2017; Hosoda,
Takuma, Nakamoto, & Hayashi, 2008; Hussain, Xie, &
Jamwal, 2013; Park et al., 2014). However, the PAM system
exhibits strong nonlinear characteristic, low damping ability
and hysteresis problem. These limitations are led to low
controllability and high difficulty in achieving the precision
system control and limit its application.
Different control methods have been proposed to control the
motion of the PAM mechanisms such as classical
proportional-integral-derivative (PID) control, nonlinear
model-based control and intelligent control. The classical
PID control is easy to design, but it is not robust to the
changes of parameters and insufficient to compensate for the
nonlinearity and hysteresis of the PAM mechanism which
leads to poor accuracy. In (Hao, Yang, Sun, Xiang, & Xue,
2017; Schreiber et al., 2011), a feedforward hysteresis
compensation was added to the PID control, in order to solve
the hysteresis problem. However, the effect of the hysteresis
compensator that modelled in static characteristic becomes
weak in the high tracking frequency.
Nonlinear model-based controllers, such adaptive control, H∞
control, variable structure control, and sliding mode control
(Amar, Mustapha, & Mohamed, 2012; Chou & Hannaford,
1996; Hamerlain, 1995; Medrano-Cerda, Bowler, & Caldwel,
1995; Prieto, Cazarez-Castro, Aguilar, & Cardenas-Maciel,
2017; Tondu & Lopez, 2000; Zhu, Tao, Yao, & Cao, 2009)
have been proposed in controlling the PAM mechanisms. The
unknown parameters of the dynamic model were primarily
modelled using a static approach, but it is restricted the
control efficiency. The performances of these controllers are
based on how accurate the determined model parameters;
thus, it is time consuming to identify the nonlinear
characteristics of the PAM mechanism accurately and cause
impractical in use.
Besides, hybrid and intelligent controls have been widely
used for the PAM mechanism (Anh, 2010; Chandrapal, Chen,
Wang, & Hann, 2012; Khoa, Truong, & Ahn, 2013; Thanh &
Ahn, 2006). The intelligent control was used to adjust the
control parameters via various learning algorithms, in order
to solve the model-based control problem regards to the
unmodeled or unknown parameters. However, the learning
MACE Technical Journal (MTJ), pp. 33-38 MTJ Vol.2(01) [December 2020] eISSN: 2710-6632
33
session is time consuming, and requires greater
computational resources, which it is not practical for real-
time application. Even though it provides a satisfied
positioning performance, the design procedure is not
systematic and required sufficient knowledge of the
intelligent algorithm. Regardless the complexity of the PAM
mechanism, an appropriate control method that is desirable
are simple control structure, straightforward design
procedure, and model-free.
This paper focuses on proposing and improving the
conventional nominal characteristic trajectory following
(NCTF) control for a PAM driven stage. The proposed
controller emphasizes a simple structure and easy design
procedure without acquiring plant parametric modeling. The
effectiveness of the NCTF control has been clarified in
several type of mechanisms and it has showed the promising
positioning control performance in electric-motor driven
typical mechanism with friction, non-contact mechanism, and
pneumatic actuator (Chong, Hashimoto, & Sato, 2011; Chong
& Sato, 2010; Maeda & Sato, 2008; Mohd Nor & Chong,
2013; K Sato & Maeda, 2009; K Sato & Shimokohbe, 2005;
Kaiji Sato, Nakamoto, & Shimokohbe, 2004; Kaiji Sato &
Sano, 2014). However, the conventional NCTF controller
showed slow transient response and tracking performance,
high positioning error, and vibration problem in high tracking
frequency for the PAM mechanism. Therefore, the improved
NCTF controller is introduced by adding an acceleration
feedback compensator and a reference rate feedforward to
improve the positioning accuracy and following
characteristic, respectively. Furthermore, the actual velocity
feedback is removed to solve the vibration problem.
The rest of this paper is organised as follows: Section II
describes the control concept and its design procedure.
Section III presents the experimental setup that used in this
research. The comparative experimental results are evaluated
and discussed in Section IV, and followed by the conclusion
in Section V.
2. CONTROLLER DESIGN AND CONCEPT
2.1 Conventional NCTF Control Concept
Fig. 1 shows use the conventional NCTF control structure.
The NCTF controller is composed of a nominal characteristic
trajectory (NCT) and a PI compensator. The NCT represents
the reference motion trajectory of the control system and is
expressed on phase plane. The NCT is constructed from the
actual response of the mechanism influenced by the friction
and saturation effects in open-loop condition, which the
construction of NCT does not require an exact model and
parameters of the mechanism. The PI compensator is tuned
necessarily to make the mechanism motion follows the NCT
macroscopically and end the motion at the origin of the phase
plane.
On the phase plane, the object motion comprises two phases
which are a reaching phase and a following phase as
presented in Fig. 2. In reaching phase, the PI compensator
leads the motion of the mechanism to follow the NCT
macroscopically and leads the object motion to end at the
origin of the phase plane in the following phase. The PI
compensator works for reduction of the difference of the
NCT and the actual motion when the difference is increased
by the disturbance forces and mechanism characteristic
changes.
2.2 Improved NCTF Control System
Fig. 3 shows the improved NCTF control structure. Based on
the conventional NCTF control structure, the improved
NCTF controller is modified by adding two elements which
are an acceleration feedback compensator and a reference
rate feedforward.
Due to the working range of the PAM mechanism is small
(±2.4 mm), which the velocity response becomes
insignificant to the input of the PI compensator, up. For the
reason, the elimination of static deviation is more important
than the reduction of the difference between the error rate of
the NCT and the actual velocity in the small working range.
Fig. 1: Control structure of the conventional NCTF control
system
Fig. 2: Nominal characteristic trajectory (NCT)
Fig. 3: Control structure of the improved NCTF control
system for the PAM mechanism
(a)
(b)
Fig. 4: (a) Open-loop responses of the PAM mechanism,
and (b) constructed NCT
Fig. 5: Controller compensation in respect to a margin of
safety of 70%
MACE Technical Journal, MTJ Vol.2(01) [December 2020], eISSN: 2710-6632
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In addition, the derivative of the real-time feedback signal
will amplify the noise and results in unnecessary vibration.
Therefore, the actual velocity feedback, x& in conventional
NCTF is removed.
Besides, the constructed PAM system has a low damping
characteristic. The low damping characteristic easily cause
severe vibration and deteriorate accuracy performance of a
system. In order to improve damping effect of the actuator
that tend to reduce vibrations, an acceleration feedback
compensator is designed and added to the plant. Furthermore,
the reference rate, rx& as the feedforward element is added,
which it is useful to increase the rapid movement of the
mechanism in continuous motion. These changes aim to
improve following characteristics.
2.3 Design Procedure of the Improved NCTF Controller
The design procedure of the improved NCTF controller is
added an additional step as compared to the conventional
NCTF controller, and the procedure remains simple and
straightforward as the conventional NCTF controller one.
The improved controller is designed according to the
following procedure.
1) Construction of NCT
The NCT is constructed on the phase plane using the
experimentally measured open-loop displacement
and velocity responses of the actual mechanism
during deceleration motion. Fig. 4(a) shows the
measured open-loop responses when the PAM
mechanism is driven by a step input, ur of 4V. The
final displacement, xf is 2.4 mm. Based on the
measured responses, the NCT is constructed as
illustrated in Fig. 4(b), and the inclination near the
origin, β is 208 s-1.
2) Design of PI Compensator
The PI compensator is determined experimentally
based on the information of the measured open-loop
responses and the NCT. A practical stability limit is
defined as the margin of stability in selecting the PI
gains that bounded under the stable region. The
practical stability limit of the actual mechanism is
found by first driving the mechanism with the
proportional element only. The value of the
proportional gain is increased until continuous
oscillations. The determined maximum proportional
gain is referred as an actual ultimate proportional
gain (Kpu = 0.12 Vs/mm).
Based on the average open-loop response, a
linearized plant model, Gp is estimated as shown in
(1). Based on the closed-loop transfer function in
(2), the equations of practical stability limit, ξpractical,
proportional gain, Kp, and integral gain, Ki can be
calculated using derived equations as shown in (3)
to (5). Fig. 5 illustrates the practical stability limit,
and the PI gains are selected within the stable region
at the 70% of safety margin (ξpractical x 0.3).
1034.0
826.0
1 +=
+=
ss
KG p
τ (1)
+
++
+=−
τ
β
τ
βτ
ββ
ip
iploopclosed
KKs
KKs
KKsKKG
12
(2)
τω
βξ
n
pupractical
KK
2
1+=
(3)
KK n
pβ
τξω 12 −=
(4)
KK n
iβ
τω 2
= (5)
3) Determination of Acceleration Gain
The acceleration gain (Ka = 1 x 10-5 Vs2/mm) is
adjusted experimentally to gain sufficient damping
characteristic after obtained the PI gains.
3. EXPERIMENTAL SETUP
An experimental setup is designed and constructed as a linear
antagonistic structure using two pneumatic artificial muscles
(PAMs) and a mover is located in between the two PAMs
(FESTO DMSP-10-150N-RM-CM) in a horizontal motion,
as shown in Figure 6. One of the PAM generates pulling
force via pressurized air while another one is depressurized at
the same time, in order to pull and push the 2 kg mover along
the horizontal moving direction in a maximum working range
of ±2.4 mm. As an input source, air is injected from the
pressure supply with a pressure of 0.5 MPa and controlled by
a 5/3-way proportional servo valve (FESTO MPYE-5-1/8LF-
010-B). The pressures in the two PAMs are measured for
observing purpose using two pressure sensors (SMC
PSE540A-01) with the resolution of 0.0012 MPa. A linear
encoder (MicroE Systems MII5800-AB-200-5-1-0) with the
resolution of 0.1 μm is used as a single feedback sensor in
this mechanism to measure the displacement of the mover.
For the signal processing, a data acquisition unit is used to
interface with a host computer that installed
MATLAB/Simulink software. The sampling time, Ts is 0.1
ms.
MACE Technical Journal, MTJ Vol.2(01) [December 2020], eISSN: 2710-6632
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4. PERFORMANCE EVALUATION
In this section, the experimental point-to-point positioning
and continuous motion performances of the PAM driven
stage are examined. In order to show the effectiveness of the
improved NCTF controller, its performances are compared
with the conventional NCTF controller. The conventional
NCTF controller is designed through the similar procedure
with only steps 1 and 2 as stated in Section 2. Table 1 shows
the controller gains of both controllers.
Table 1. Controller parameters
Controller Kp
(Vs/mm)
Ki
(Vs2/mm)
β (s1) Ka
(Vs2/mm)
Conventional
NCTF
0.0142 0.0384 208 -
Improved
NCTF
0.0319 0.2424 208 1 x 10-5
Fig. 7 shows the experimental point-to-point positioning
performances of the conventional NCTF control and the
improved NCTF control at step heights of 0.1 mm and 2 mm.
As can be observed, the improved NCTF significantly
improves the transient response in rise time reduction and
settling time reduction, and positioning accuracy as well.
Table 2 presents the average performance index of both
controllers based on 10 experiments. In contrast, the
improved NCTF control demonstrates shorter rise time and
settling time than the conventional NCTF control in point-to-
point performance, which the improved NCTF control
reduced at least 80% of rise time and 66% of settling time
from the conventional NCTF control. This proves the
modified control structure by removed the actual velocity
feedback is effectively improved the transient response for
the PAM mechanism. Due to the fast transient response, the
improved NCTF control exhibits a slightly high overshoot
performance. Besides, the improved NCTF control with
improvements of 22% and 57% at the step heights of 0.1 mm
and 2 mm, respectively. The results proved that the
Fig. 6: PAM driven stage
(a)
(b)
Fig. 7: Experimental point-to-point positioning
performances comparison at (a) 0.1 mm and (b) 2 mm
(a)
(b)
Fig. 8: Experimental tracking performances comparison
at (a) 0.1 mm and (b) 2 mm with frequency of 0.1 Hz
(a)
(b)
Fig. 9: Experimental tracking performances comparison
at (a) 0.1 mm and (b) 2 mm with frequency of 0.5 Hz
MACE Technical Journal, MTJ Vol.2(01) [December 2020], eISSN: 2710-6632
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acceleration feedback compensator increases the damping
effect and results in a better positioning accuracy.
Figs. 8 and 9 show the comparative experimental tracking
performances at 0.1 mm and 2 mm with the frequencies of
0.1 Hz and 0.5 Hz respectively. Tables 3 summarizes the
average of 10 experiments for tracking performance. The
improved NCTF control demonstrates much better tracking
performances than the conventional NCTF control, which the
improved NCTF control has significantly reduced the
tracking errors of the system. As compared to the
conventional NCTF control, the improved NCTF control
decreases about 90% of tracking errors, except at high
frequency and small working range (0.5 Hz and 0.1 mm) with
about 70% of reduction. Furthermore, the improved NCTF
control shows high following characteristic although in the
high frequency of 0.5 Hz, which the following characteristic
is found lack for the conventional NCTF control. In addition,
the conventional NCTF control exhibits the vibration in high
tracking frequency and high working range as shown in
Figure 9(b). This proved that the improved NCTF control has
a high following characteristic and tracking performance in
continuous motion.
Fig. 10 represents the experimental frequency response of the
conventional NCTF and improved NCTF controllers. The
bandwidth of the improved NCTF is 7.05 Hz, while the
conventional NCTF is 0.69 Hz. This result proves the
improved NCTF can performs in higher frequency than the
conventional NCTF. Besides, the phase response shows that
the improved NCTF has a great following characteristic
although in high frequency.
Overall, it can be concluded that, the improved NCTF
controller has demonstrated a high positioning accuracy and a
fast tracking performance. The results showed that the benefit
of the improved NCTF controller in reducing positioning and
tracking errors, and increasing the following characteristic, as
compared to the conventional NCTF controller.
5. CONCLUSIONS
In this paper, the improved NCTF controller has been
proposed as an enhancement of the conventional NCTF
controller for the PAM mechanism. Based on the
conventional NCTF control structure, the improved NCTF
controller has removed the actual feedback velocity and
added an acceleration feedback compensator and a reference
rate feedforward. The improved NCTF is remained the
simple design produce like the conventional NCTF controller
without the need of a detailed model parameters and complex
control theory. The effectiveness control performance of the
improved NCTF controller was experimentally evaluated and
compared with the conventional NCTF controller, including
the positioning and tracking control results. As compared to
the conventional NCTF controller, the improved NCTF
controller reduces 80% of rise time, 66% of settling time, and
57% of positioning error in positioning performance, while
the improved NCTF controller significantly reduces the
tracking errors about 90% in tracking performance. The
experimental results proved that the improved NCTF
controller has demonstrated superior performances in
positioning and tracking motion control over the
conventional NCTF controller. In addition, the improved
NCTF controller showed the capability in performing high
precision motion and fast positioning for the PAM
mechanism.
ACKNOWLEDGEMENT
The authors would like to be obliged to Centre for Robotics
and Industrial Automation, Faculty of Electrical Engineering,
Universiti Teknikal Malaysia Melaka for providing the
laboratory facilities and equipment support. This work is
financially supported by the Fundamental Research Grant
Project (FRGS/1/2016/TK08/FKE-CeRIA/F00308) and the
scholarship of Skim Zamalah from Universiti Teknikal
Malaysia Melaka.
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