Skip to main content
SpringerLink
Log in

Multidimensional control systems: case studies in design and evaluation

  • Published:
Multidimensional Systems and Signal Processing Aims and scope Submit manuscript

Abstract

Multidimensional control systems have been the subject of much productive research over more than three decades. In contrast to standard control systems, there has been much less reported on applications where the multidimensional setting is the only possible setting for design or produces implementations that perform to at least the same level. This paper addresses the latter area where case studies focusing on control law design and evaluation, including experimental results in one case, are reported. These demonstrate that movement towards the actual deployment of multidimensional control systems is increasing.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13
Fig. 14
Fig. 15
Fig. 16
Fig. 17
Fig. 18
Fig. 19
Fig. 20
Fig. 21
Fig. 22
Fig. 23
Fig. 24
Fig. 25
Fig. 26
Fig. 27
Fig. 28
Fig. 29

Similar content being viewed by others

References

  • Ahn, H.-A., Chen, Y. Q., & Moore, K. L. (2007). Iterative learning control: Brief survey and characterization. IEEE Transactions on Systems Man and Cybernetics Part C, 37(6), 1099–1121.

    Article  Google Scholar 

  • Arimoto, S., Kawamura, S., & Miyazaki, F. (1984). Bettering operation of robots by learning. Journal of Robotic Systems, 2(1), 123–140.

    Article  Google Scholar 

  • Bose, N. K. (1982). Applied multidimensional systems theory. New York: Van Nostrand Reinhold.

    MATH  Google Scholar 

  • Bose, N. K., Buchberger, B., & Guiver, J. P. (2003). Multidimensional systems theory and applications. Berlin: Springer.

    MATH  Google Scholar 

  • Bristow, D. A., Tharayil, M., & Alleyne, A. G. (2006). A survey of iterative learning control: A learning based method for high performance tracking control. IEEE Control Systems Magazine, 26(3), 96–114.

    Article  Google Scholar 

  • Cantrell, R. S., & Cosner, C. (2003). Spatial ecology via reaction-diffusion equations. London: Wiley.

    MATH  Google Scholar 

  • Cichy, B., Galkowski, K., & Rogers, E. (2014). \(2\)D systems based robust iterative learning control using noncausal finite-time interval data. Systems and Control Letters, 64, 36–42.

    Article  MATH  MathSciNet  Google Scholar 

  • Crank, J. (1975). The mathematics of diffusion. Oxford: Oxford Science Publications, Oxford University Press.

    Google Scholar 

  • Crossbow Inc., TelosB Mote Research Platform Datasheet [Online]. http://www.xbow.com/.

  • Dabkowski, P., Galkowski, K., Bachelier, O., & Rogers, E. (2012). Control of discrete linear repetitive processes using strong practical stability and \(H_{\infty }\) disturbance attenuation. Systems and Control Letters, 61(12), 1138–1144.

    Article  MATH  MathSciNet  Google Scholar 

  • Dabkowski, P., Galkowski, K., Rogers, E., & Kummert, A. (2009). Strong practical stability and stabilization of discrete linear repetitive processes. Multidimensional Systems and Signal Processing, 20, 311–331.

    Article  MATH  MathSciNet  Google Scholar 

  • D’Andrea, R., & Dullerud, G. (2003). Distributed control design for spatially interconnected systems. IEEE Tranactions on Automatic Control, 48, 1478–1495.

  • Dewasurendra, D. A., Liang, Y., & Bauer, P. H. (2006). Distributed multidimensional evidence filtering. In Proceedings of the International Conference for Young Researchers (ICYR’06), Zielona Gora, Poland, CD Rom Proceedings.

  • Dewasurendra, D. A., Bauer, P. H., & Premaratne, K. (2006). Distributed evidence filtering in networked embedded systems. In P. J. Antsaklis & P. Tabuada (Eds.), Network embedded sensing and control (pp. 183–198). Berlin: Springer.

    Chapter  Google Scholar 

  • Du, C., & Xie, L. (2002). \(H_{\infty }\) control and filtering of two-dimenional systems (Vol. 278). Berlin: Springer LNCIS.

  • Edwards, J. B. (1974). Stability problems in the control of multipass processes. IEE Proceedings on Control Theory and Applications, 124(11), 1425–143.

    Google Scholar 

  • Edwards, J. B., & Greenberg, J. M. (1974). Longitudinal interaction in multipass processes. IEE Proceedings on Control Theory and Applications, 124(4), 385–392.

    Google Scholar 

  • Einicke, G., Ralston, J., Hargrave, C., Reid, D., & Hainsworth, D. (2008). Longwall mining automation: An application of minimum-variance smoothing. IEEE Control Systems Magazine, 28(6), 28–37.

    Article  MathSciNet  Google Scholar 

  • Emelianova, J., Pakshin, P., Galkowski, K., & Rogers, E. (2014). Stability of nonlinear \(2\)D systems described by the continuous-time Roesser model. Automation and Remote Control, 75(5), 845–858.

    Article  MATH  MathSciNet  Google Scholar 

  • Emelianova, J., Pakshin, P., Galkowski, K., & Rogers, E. (2015). Stability of nonlinear discrete repetitive processes with Markovian switching. Systems and Control Letters, 75, 108–116.

    Article  MATH  MathSciNet  Google Scholar 

  • Fagin, R., & Halpem, J. (1990). A new approach to updating beliefs. In Proceedinsg of the Sixth Annual Conference on Uncertainty in Artificial Intelligence (pp. 347–374).

  • Fornasini, E., & Marchesini, G. (1978). Doubly-indexed dynamical systems: State-space models and structural properties. Mathematical Systems Theory, 12(1), 59–72.

    Article  MATH  MathSciNet  Google Scholar 

  • Freeman, C. T., Lewin, P. L., & Rogers, E. (2007). Further results on the experimental evaluation of iterative learning control algorithms for non-minimum phase plants. International Journal of Control, 80(4), 569–582.

    Article  MATH  MathSciNet  Google Scholar 

  • Freeman, C. T., Rogers, E., Hughes, A. M., Burridge, J. H., & Meadmore, K. L. (2012). Iterative learning control in healthcare electrical stimulation and robotic-assisted upper limb stroke rehabilitation. IEEE Control Systems Magazine, 32(1), 18–43.

    Article  MathSciNet  Google Scholar 

  • Hladowski, L., Galkowski, K., Cai, Z., Rogers, E., Freeman, C. T., & Lewin, P. L. (2010). Experimentally supported \(2\)D systems based iterative learning control law design for error convergence and performance. Control Engineering Practice, 18(4), 339–348.

    Article  Google Scholar 

  • Hladowski, L., Galkowski, K., Cai, Z., Rogers, E., Freeman, C. T., & Lewin, P. L. (2012). Output information based iterative learning control law design with experimental verification. Journal of Dynamic Systems, Measurement and Control, 134(2), 021012/1–021012/10.

    Article  Google Scholar 

  • Kar, H., & Singh, V. (2001). Stability analysis of \(1\)D and \(2\)D fixed point state-space filters using any combination of overflow and quantization nonlinearities. IEEE Transactions on Signal Procesing, 49(5), 1095–1105.

    Google Scholar 

  • Kurek, J. E. (1995). Stability of nonlinear parameter-varying digital \(2\)-D systems. IEEE Transactions on Automatic Control, 40(8), 1428–1432.

    Article  MATH  MathSciNet  Google Scholar 

  • Kurek, J. E., & Zaremba, M. B. (1993). Iterative learning control synthesis based on \(2\)D system theory. IEEE Transactions on Automatic Control, 38(1), 121–125.

    Article  MATH  MathSciNet  Google Scholar 

  • Longman, R. W. (2000). Iterative learning control and repetitive control for engineering practice. International Journal of Control, 73(10), 930–954.

    Article  MATH  MathSciNet  Google Scholar 

  • Meadmore, K. L., Hughes, A. M., Freeman, C. T., Cai, Z., Tong, D., Burridge, J. H., et al. (2012). Functional electrical stimulation mediated by iterative learning control and \(3\)D robotics reduces motor impairment in chronic stroke. Journal of Neuroengineering and Rehabilitation, 9(32), 1–11.

    Google Scholar 

  • Mooney, M. A., & Adam, D. (2007). Vibratory roller integrated measurement of earthwork compaction: an overview. In Proceedings of the 7th International ASCE Symposium. Field Measurements in Geomechanics, CD Rom Proceedings.

  • Moore, K. L., & Chen, Y-Q. (2006). Iterative learning control approach to a diffusion control problem in an irrigation application. In Proceedings of the International Conference on Mechatronics and Automation, Luoyang, P. R. China.

  • Norrlof, M. & Gunnarsson, S. (1999). A frequency domain analysis of a second order iterative learning control algorithm. In Proceedings of the 38th Conference on Decision and Control (pp. 1587–1592).

  • Paszke, W., Rogers, E., Galkowski, K., & Cai, Z. (2013). Robust finite frequency range iterative learning control design and experimental verification. Control Engineering Practice, 21(10), 1310–1320.

    Article  Google Scholar 

  • Qin Liu, Q., Gonzalez M. A., & Werner, H. (2014). Distributed control of spatially-interconnected parameter-invariant and LPV models for actuated beams. In Proceedingss of 2014 American Control Conference (pp. 3381–3386).

  • Rabenstein, R., & Trautmann, L. (2000). Models for continuous and discrete multidimensional systems. In Proceedings of the 2nd International Workshop on Multidimensional (nD) Systems (pp. 47–54).

  • Ratcliffe, J. D. (2005). Iterative learning control implemented on a multi-axis system. PhD Thesis, University of Southampton, UK

  • Ratcliffe, J. D., Lewin, P. L., Rogers, E., Hatonen, J. J., & Owens, D. H. (2006). Norm-optimal iterative learning control applied to gantry robots for automation applications. IEEE Transactions on Robotics, 22(6), 1303–1307.

    Article  Google Scholar 

  • Recht, B., & D’Andrea, R. (2004). Distributed control of systems over discrete groups. IEEE Transactions on Automatic Contol, 49(9), 14461452.

    MathSciNet  Google Scholar 

  • Rocha, P., & Wood, J. (2001). Trajectory control and interconnection of \(1\)D and \(n\)D systems. SIAM Journal on Control and Optimization, 40(1), 107–134.

    Article  MATH  MathSciNet  Google Scholar 

  • Roesser, R. P. (1975). A discrete state-space model for linear image processing. IEEE Transactions on Automatic Control, AC–20, 1–10.

    Article  MathSciNet  Google Scholar 

  • Rogers, E., Galkowski, K., Gramacki, A., Gramacki, J., & Owens, D. H. (2002). Stability and controllability of a class of \(2\)D linear systems with dynamic boundary conditions. IEEE Transactions on Circuits and Systems I: Fundamental Theory and Applications, 49(2), 181–195.

    Article  MathSciNet  Google Scholar 

  • Rogers, E., Galkowski, K., & Owens, D. H. (2007). Control systems theory and applications for linear repetitive processes (Vol. 349). Berlin: Springer LNCIS.

    MATH  Google Scholar 

  • Rogers, E., & Owens, D. H. (1992). Stability analysis for linear repetitive processes (Vol. 175). Berlin: Springer LNCIS.

    Book  MATH  Google Scholar 

  • Sammons, P. M., Bristow, D. A., & Landers, R. G. (2013). Height dependent laser metal deposition process modeling. ASME Journal for Manufacturing Science and Engineering, 135(5), 054501-(1-7).

    Article  Google Scholar 

  • Shafer, G. (1976). A mathematical theory of evidence. Princeton: Princeton University Press.

    MATH  Google Scholar 

  • Soltanian, L. (2014). Distributed distant-downstream controller design for large-scale irrigation channels. PhD thesis, University of Melbourne, Australia.

  • Szewczyk, R., Osterweil, E., Polastre, J., Hamilton, A., Mainwaring, A., & Estrin, D. (2004). Habitat monitoring with sensor networks. Communications of the ACM, 47(6), 34–40.

    Article  Google Scholar 

  • Wallen, J., Norrlof, M., & Gunnarsson, S. (2008). Arm-side evaluation of ILC applied to a six-degrees-of-freedom industrial robot. In Proceedings of 17th IFAC World Congress (pp. 13450-13455).

  • Wallen, J., Gunnarsson, S., & Norrloff, M. (2013). Analysis of boundary effects in iterative learning control. International Journal of Control, 86(3), 410–415.

    Article  MATH  MathSciNet  Google Scholar 

  • Yeganefar, N., Yeganefar, N., Ghamgui, M., & Moulay, M. (2013). Lyapunov theory for \(2\)-D nonlinear Roesser models: Application to asymptotic and exponential stability. IEEE Transactions on Automatic Control, 58(5), 1299–1304.

    Article  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Electronics and Computer Science, University of Southampton, Southampton, SO17 1BJ, UK

    E. Rogers

  2. Institute of Control and Computation Engineering, University of Zielona Gora, 65–246, Zielona Gora, Poland

    K. Galkowski, W. Paszke & L. Hladowski

  3. College of Engineering and Computational Sciences, Colorado School of Mines, Golden, CO, 80401, USA

    K. L. Moore

  4. Department of Electrical Engineering, University of Notre Dame, Notre Dame, IN, 46556-5637, USA

    P. H. Bauer

  5. Institute of Physics, Faculty of Physics, Astronomy and Informatics, Nicolaus Copernicus University, ul. Grudziadzka 5, 87–100, Toruń, Poland

    P. Dabkowski

Authors
  1. E. Rogers
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. K. Galkowski
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. W. Paszke
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. K. L. Moore
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. P. H. Bauer
    View author publications

    You can also search for this author in PubMed Google Scholar

  6. L. Hladowski
    View author publications

    You can also search for this author in PubMed Google Scholar

  7. P. Dabkowski
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to E. Rogers.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Rogers, E., Galkowski, K., Paszke, W. et al. Multidimensional control systems: case studies in design and evaluation. Multidim Syst Sign Process 26, 895–939 (2015). https://doi.org/10.1007/s11045-015-0341-8

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11045-015-0341-8

Keywords

Search

Navigation