Design Innovation Paper

Ball and Beam Balancing Mechanism Actuated With Pneumatic Artificial Muscles

[+] Author and Article Information
Željko Šitum

Faculty of Mechanical Engineering and Naval
Department of Robotics and Production System
University of Zagreb,
Ivana Lučića 5,
Zagreb HR-10000, Croatia
e-mail: zeljko.situm@fsb.hr

Petar Trslić

Faculty of Mechanical Engineering and Naval
Department of Robotics and Production System
University of Zagreb,
Ivana Lučića 5,
Zagreb HR-10000, Croatia

1Corresponding author.

2Present address: Centre for Robotics and Intelligent Systems (CRIS), University of Limerick, Castletroy, Limerick, V94 T9PX, Ireland.

Contributed by the Mechanisms and Robotics Committee of ASME for publication in the JOURNAL OF MECHANISMS AND ROBOTICS. Manuscript received May 19, 2017; final manuscript received May 25, 2018; published online June 27, 2018. Editor: Venkat Krovi.

J. Mechanisms Robotics 10(5), 055001 (Jun 27, 2018) (7 pages) Paper No: JMR-17-1156; doi: 10.1115/1.4040490 History: Received May 19, 2017; Revised May 25, 2018

The paper presents the results of modeling and control of an original and unique ball-on-beam system with a pneumatic artificial muscle pair in an antagonistic configuration. This system represents a class of under-actuated, high-order nonlinear systems, which are characterized by an open-loop unstable equilibrium point. Since pneumatic muscles have elastic, nonlinear characteristics, they are more difficult to control. Considering that an additional nonlinearity is added to the system which makes it harder to stabilize. The nonlinear mathematical model has been derived based on the physical model of the ball-on-beam mechanism, the beam rotating by using an antagonistic muscle pair and the pneumatic muscle actuated by a proportional valve. Based on the nonlinear model, the linearized equations of motion have been derived and a control-oriented model has been developed, which is used in the state feedback controller design procedure. The proposed state feedback controller has been verified by means of computer simulations and experimentally on the laboratory setup. The simulation and experimental results have shown that the state feedback controller can stabilize the ball-on-beam system around an equilibrium position in the presence of external disturbances and to track a reference trajectory with a small tracking error.

Copyright © 2018 by ASME
Your Session has timed out. Please sign back in to continue.


Almutairi, N. B. , and Zribi, M. , 2010, “ On the Sliding Mode Control of a Ball on a Beam System,” Nonlinear Dyn., 59(1–2), pp. 221–238. [CrossRef]
Keshmiri, M. , Jahromi, A. F. , Mohebbi, A. , Amoozgar, M. H. , and Xie, W. F. , 2012, “ Modeling and Control of Ball and Beam System Using Model Based and Non-Model Based Control Approaches,” Int. J. Smart Sensing Intell. Syst., 5(1), pp. 14–35. [CrossRef]
Chang, Y. H. , Chan, W. S. , and Chang, C. W. , 2013, “ TS Fuzzy Model-Based Adaptive Dynamic Surface Control for Ball and Beam System,” IEEE Trans. Ind. Electron., 60(6), pp. 2251–2263. [CrossRef]
Petrić, J. , and Šitum, Ž. , 2003, “ Inverted Pendulum Driven by Pneumatics,” Int. J. Eng. Educ., 19(4), pp. 597–602.
Petrić, J. , and Šitum, Ž. , 2003, “ Pneumatic Inverted Wedge,” 6th IFAC Symposium on Advances in Control Education, Oulu, Finland, June 16–18, pp. 229–234.
Åström, K. J. , and Furuta, K. , 2000, “ Swinging Up a Pendulum by Energy Control,” Automatica, 36(2), pp. 287–295. [CrossRef]
Šitum, Ž. , and Herceg, S. , 2008, “ Design and Control of a Manipulator Arm Driven by Pneumatic Muscle Actuators,” 16th Mediterranean Conference on Control and Automation, Ajaccio, France, June 25–27, pp. 926–931.
Martens, M. , and Boblan, I. , 2017, “ Modeling the Static Force of a Festo Pneumatic Muscle Actuator: A New Approach and a Comparison to Existing Models,” Actuators, 6(4), p. 33. [CrossRef]
Tondu, B. , and Lopez, P. , 2000, “ Modeling and Control of McKibben Artificial Muscle Robot Actuators,” IEEE Control Syst. Mag., 20(2), pp. 15–38. [CrossRef]
Carbonell, P. , Jiang, Z. P. , and Repperger, D. W. , 2001, “ Nonlinear Control of a Pneumatic Muscle Actuator: Backstepping Vs. Sliding–Mode,” IEEE International Conference on Control Applications (CCA'01), Mexico City, Mexico, Sept. 5–7, pp. 167–172.
Sárosi, J. , Biro, I. , Nemeth, J. , and Cveticanin, L. , 2015, “ Dynamic Modeling of a Pneumatic Muscle Actuator With Two-Direction Motion,” Mechanism Mach. Theory, 85, pp. 25–34. [CrossRef]
Shen, X. , 2010, “ Nonlinear Model-Based Control of Pneumatic Artificial Muscle Servo Systems,” Control Eng. Pract., 18(3), pp. 311–317. [CrossRef]
Schröder, J. , Erol, D. , Kawamura, K. , and Dillman, R. , 2003, “ Dynamic Pneumatic Actuator Model for a Model-Based Torque Controller,” IEEE International Symposium on Computational Intelligence in Robotics and Automation (CIRA), Kobe, Japan, July 16–20, pp. 342–347.
Dorf, R. C. , and Bishop, R. H. , 2011, Modern Control Systems, 12th ed., Prentice Hall, Upper Saddle River, NJ.


Grahic Jump Location
Fig. 3

Schematic drawing of the ball and beam system actuated with PAMs

Grahic Jump Location
Fig. 1

Ball and beam system actuated with PAMs: (a) photo and (b) schematic diagram

Grahic Jump Location
Fig. 2

(a) Ball position measuring system and (b) beam angle measuring system

Grahic Jump Location
Fig. 4

Transient response of muscle pressures: (a) varying step signal and (b) zoomed part of figure

Grahic Jump Location
Fig. 5

Simulation results of pneumatically actuated ball and beam system

Grahic Jump Location
Fig. 6

Experimental results of pneumatically actuated ball and beam system: (a) balancing the ball to the center, (b) square wave reference signal, and (c) sinusoidal reference signal



Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In