Power-Based Setpoint Control: Experimental Results on a Planar Manipulator

Authors

D. A. Dirksz, J. M. A. Scherpen

Abstract

In the last years the power-based modeling framework, developed in the sixties to model nonlinear electrical RLC networks, has been extended for modeling and control of a larger class of physical systems. In this brief we apply power-based integral control to a planar manipulator experimental setup. An integrator is known to compensate for steady-state errors, which usually occur in real applications. Recent developments in power-based control have shown the possibility of applying integral control to globally asymptotically stabilize a nonlinear system, without losing the original structure. In contrast, the more common PI or PID controllers do not provide such global properties. Both simulation and experimental results show an improvement in transient performance compared to PID control.

Citation

• Journal: IEEE Transactions on Control Systems Technology
• Year: 2012
• Volume: 20
• Issue: 5
• Pages: 1384–1391
• Publisher: Institute of Electrical and Electronics Engineers (IEEE)
• DOI: 10.1109/tcst.2011.2163514

BibTeX

@article{Dirksz_2012,
  title={{Power-Based Setpoint Control: Experimental Results on a Planar Manipulator}},
  volume={20},
  ISSN={1558-0865},
  DOI={10.1109/tcst.2011.2163514},
  number={5},
  journal={IEEE Transactions on Control Systems Technology},
  publisher={Institute of Electrical and Electronics Engineers (IEEE)},
  author={Dirksz, D. A. and Scherpen, J. M. A.},
  year={2012},
  pages={1384--1391}
}

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References

• Jeltsema, D. & Scherpen, J. M. A. A power-based description of standard mechanical systems. Systems & Control Letters vol. 56 349–356 (2007) – 10.1016/j.sysconle.2006.10.015
• Multidomain modeling of nonlinear networks and systems. IEEE Control Systems vol. 29 28–59 (2009) – 10.1109/mcs.2009.932927
• Kelly, R. Global positioning of robot manipulators via PD control plus a class of nonlinear integral actions. IEEE Transactions on Automatic Control vol. 43 934–938 (1998) – 10.1109/9.701091
• Ortega, R., Loría, A., Nicklasson, P. J. & Sira-Ramírez, H. Passivity-Based Control of Euler-Lagrange Systems. Communications and Control Engineering (Springer London, 1998). doi:10.1007/978-1-4471-3603-3 – 10.1007/978-1-4471-3603-3
• Putting energy back in control. IEEE Control Systems vol. 21 18–33 (2001) – 10.1109/37.915398
• Ortega, R., van der Schaft, A., Maschke, B. & Escobar, G. Interconnection and damping assignment passivity-based control of port-controlled Hamiltonian systems. Automatica vol. 38 585–596 (2002) – 10.1016/s0005-1098(01)00278-3
• Ortega, R., Jeltsema, D. & Scherpen, J. M. A. Power shaping: A new paradigm for stabilization of nonlinear RLC circuits. IEEE Transactions on Automatic Control vol. 48 1762–1767 (2003) – 10.1109/tac.2003.817918
• van der Schaft, A. L2 - Gain and Passivity Techniques in Nonlinear Control. Communications and Control Engineering (Springer London, 2000). doi:10.1007/978-1-4471-0507-7 – 10.1007/978-1-4471-0507-7
• Donaire, A. & Junco, S. On the addition of integral action to port-controlled Hamiltonian systems. Automatica vol. 45 1910–1916 (2009) – 10.1016/j.automatica.2009.04.006
• dirksz, Power-based control: Canonical coordinate transformations, integral and adaptive control. Automatica (0)
• García-Canseco, E., Jeltsema, D., Ortega, R. & Scherpen, J. M. A. Power-based control of physical systems. Automatica vol. 46 127–132 (2010) – 10.1016/j.automatica.2009.10.012
• Favache, A. & Dochain, D. Analysis and control of the exothermic continuous stirred tank reactor: the power-shaping approach. Proceedings of the 48h IEEE Conference on Decision and Control (CDC) held jointly with 2009 28th Chinese Control Conference 1866–1871 (2009) doi:10.1109/cdc.2009.5400318 – 10.1109/cdc.2009.5400318
• Fujimoto, K., Sakurama, K. & Sugie, T. Trajectory tracking control of port-controlled Hamiltonian systems via generalized canonical transformations. Automatica vol. 39 2059–2069 (2003) – 10.1016/j.automatica.2003.07.005
• Modeling and measuring friction effects. IEEE Control Systems vol. 28 82–91 (2008) – 10.1109/mcs.2008.929546
• Dirksz, D. A. & Scherpen, J. M. A. Power-based adaptive and integral control of standard mechanical systems. 49th IEEE Conference on Decision and Control (CDC) 4612–4617 (2010) doi:10.1109/cdc.2010.5717079 – 10.1109/cdc.2010.5717079
• Brayton, R. K. & Moser, J. K. A theory of nonlinear networks. I. Quarterly of Applied Mathematics vol. 22 1–33 (1964) – 10.1090/qam/169746
• Jeltsema, D., Ortega, R. & Scherpen, J. M. A. On passivity and power-balance inequalities of nonlinear rlc circuits. IEEE Transactions on Circuits and Systems I: Fundamental Theory and Applications vol. 50 1174–1179 (2003) – 10.1109/tcsi.2003.816332