positioning control of a pneumatic artificial muscle driven...

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:

[email protected])

**Centre Robotics and Industrial Automation, Universiti Teknikal Malaysia Melaka, 76100 Melaka, MALAYSIA(e-mail:

[email protected])

*** Centre of Smart System and Innovative Design, Universiti Teknikal Malaysia Melaka, 76100 Melaka, MALAYSIA(e-mail:

[email protected])

**** 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

34

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.


35

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


36

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.

REFERENCES

Amar, R., Mustapha, H., & Mohamed, T. (2012).

Decentralized RBFNN type-2 fuzzy sliding mode

controller for robot manipulator driven by artificial

muscles. International Journal of Advanced Robotic

Systems, 9(5), 182–194.

Anh, H. P. H. (2010). Online tuning gain scheduling MIMO

neural PID control of the 2-axes pneumatic artificial

muscle (PAM) robot arm. Expert Systems with

Applications, 37(9), 6547–6560.

Table 2. Average of 10 experiments for point-to-

point positioning performance comparison

Step

height

Performance

index

Conventional

NCTF

Improved

NCTF

0.1 mm Rise time 0.87 s 0.17 s

Settling time 2.48 s 0.84 s

Overshoot 5.5% 19.9%

Steady-state

error 0.9 µm 0.7 µm

2.0 mm Rise time 0.50 s 0.05 s

Settling time 1.17 s 0.38 s

Overshoot 0% 5.1%

Steady-state

error 9.3 µm 4.0 µm

Table 3. Average of 10 experiments for tracking

performance comparison

Input reference Conventional

NCTF Improved NCTF

Freq.

(Hz)

Amp.

(mm)

RMSE

(µm)

Peak

error

(µm)

RMSE

(µm)

Peak

error

(µm)

0.1 0.1 14.3 24.7 0.7 2.3

2.0 187.0 416.0 8.9 35.7

0.5 0.1 73.7 105.5 21.3 34.0

2.0 1164.5 1975.4 89.9 249.2

Fig. 10: Experimental frequency response of the

conventional NCTF and improved NCTF controllers


37

Chandrapal, M., Chen, X., Wang, W., & Hann, C. (2012).

Nonparametric control algorithms for a pneumatic

artificial muscle. Expert Systems with Applications,

39(10), 8636–8644.

Chong, S. H., Hashimoto, H., & Sato, K. (2011). Practical

motion control with acceleration reference for precision

motion - New NCTF control and its application to non-

contact mechanism. Precision Engineering, 35(1), 12–

23.

Chong, S. H., & Sato, K. (2010). Practical controller design

for precision positioning, independent of friction

characteristic. Precision Engineering, 34(2), 286–300.

Chou, C., & Hannaford, B. (1996). Measurement and

Modeling of McKibben Pneumatic Artificial Muscles.

IEEE Trans. Robotics and Automation, 12(1), 90–102.

Deaconescu, T., & Deaconescu, A. (2017). Pneumatic

Muscle-actuated Adjustable Compliant Gripper System

for Assembly Operations. Journal of Mechanical

Engineering, 63(4), 225–234.

Hamerlain, M. (1995). Anthropomorphic robot arm driven by

artificial muscles using a variable structure control. In

IEEE International Conference on Intelligent Robots

and Systems, 1, 550–555.

Hao, L., Yang, H., Sun, Z., Xiang, C., & Xue, B. (2017).

Modeling and Compensation Control of Asymmetric

Hysteresis in a Pneumatic Artificial Muscle. Journal of

Intelligent Material Systems and Structures, 28(19),

2769–2780.

Hosoda, K., Takuma, T., Nakamoto, A., & Hayashi, S.

(2008). Biped robot design powered by antagonistic

pneumatic actuators for multi-modal locomotion.

Robotics and Autonomous Systems, 56(1), 46–53.

Hussain, S., Xie, S. Q., & Jamwal, P. K. (2013). Adaptive

impedance control of a robotic orthosis for gait

rehabilitation. IEEE Transactions on Cybernetics,

43(3), 1025–1034.

Khoa, L. D., Truong, D. Q., & Ahn, K. K. (2013).

Synchronization controller for a 3-R planar parallel

pneumatic artificial muscle (PAM) robot using

modified ANFIS algorithm. Mechatronics, 23(4), 462–

479.

Maeda, G., & Sato, K. (2008). Practical control method for

ultra-precision positioning using a ballscrew

mechanism. Precision Engineering, 32(4), 309–318.

Medrano-Cerda, G. A. ., Bowler, C. J. ., & Caldwel, D. G. .

(1995). Adaptive Position Control of Antagonistic

Pneumatic Muscle Actuators. In in Proc. IEEE/RSJ

International Conference on Intelligent Robots and

Systems, 378–383.

Mohd Nor, R., & Chong, S.-H. (2013). Continuous Motion

NCTF control of a one mass rotary system. In 2nd Int.

Conf. on Elec., Control and Computer Eng., 316–321.

Park, Y.-L., Chen, B., Pérez-Arancibia, N. O., Young, D.,

Stirling, L., Wood, R. J., … Nagpal, R. (2014). Design

and Control of a Bio-inspired Soft Wearable Robotic

Device for Ankle-foot Rehabilitation. Bioinspiration &

Biomimetics, 9(1), 16007–16024.

Prieto, P. J., Cazarez-Castro, N. R., Aguilar, L. T., &

Cardenas-Maciel, S. L. (2017). Chattering existence

and attenuation in fuzzy-based sliding mode control.

Engineering Applications of Artificial Intelligence, 61,

152–160.

Sato, K, & Maeda, G. J. (2009). A practical control method

for precision motion - Improvement of NCTF control

method continuous motion control. Precision

Engineering, 33(2), 175–186.

Sato, K, & Shimokohbe, A. (2005). Robustness evaluation of

three friction compensation methods for point-to-point

(PTP) positioning systems. Robotics and Autonomous

Systems, 52(2–3), 247–256.

Sato, Kaiji, Nakamoto, K., & Shimokohbe, A. (2004).

Practical control of precision positioning mechanism

with friction. Precision Engineering, 28(4), 426–434.

Sato, Kaiji, & Sano, Y. (2014). Practical and intuitive

controller design method for precision positioning of a

pneumatic cylinder actuator stage. Precision

Engineering, 38(4), 703–710.

Schreiber, F., Sklyarenko, Y., Schluter, K., Schmitt, J., Rost,

S., Raatz, A., & Schumacher, W. (2011). Tracking

Control with Hysteresis Compensation for Manipulator

Segments Driven by Pneumatic Artificial Muscles. In

Proceedings of IEEE International Conference on

Robotics and Biomimetics, 2750–2755.

Thanh, T. D. C., & Ahn, K. K. (2006). Nonlinear PID control

to improve the control performance of 2 axes

pneumatic artificial muscle manipulator using neural

network. Mechatronics, 16(9), 577–587.

Tondu, B., & Lopez, P. (2000). Modeling and control of

McKibben artificial muscle robot actuators. IEEE

Control Systems Magazine, 20(2), 15–38.

Zhu, X., Tao, G., Yao, B., & Cao, J. (2009). Integrated

direct/indirect adaptive robust posture trajectory

tracking control of a parallel manipulator driven by

pneumatic muscles. IEEE Transactions on Control

Systems Technology, 17(3), 576–588.


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