# STATE OBSERVER FOR NONLINEAR SYSTEMS: APPLICATION TO GRINDING PROCESS CONTROL

### Seraphin C. Abou, Thien-My Dao

#### Abstract

Due to the measurement problems encountered in mineral processes, observers are appropriate ingredients of advanced model based control algorithm. The measurement problem can be solved by designing nonlinear observer. This paper discusses the way in which a state observer may be designed to control a special class of nonlinear systems. Focus is put on the pertinent applicability of the scope of these techniques, to control the dynamics of mills in mineral processes. The approach uses a small number of parameters to control the mill power draw affected by sudden changes within the system. It provides with principles and ability of the system to adapt to changing circumstances due to intermittent disturbances (like for instance changes in hardness of the raw material). Performance and stability analysis was developed. Using a generalised similarity transformation for the error dynamics, it is shown that under boundedness condition the proposed observer guarantees the global exponential convergence of the estimation error. This way, the nominal performance of the process is improved but the robust stability is not guaranteed to fully avoid the mill plugging.

#### References

- /h4
- t 3
- in2
- ir 1
- Abou S.C., 1998. Contribution to ball mill modelling 7878. Doctorate thesis, Laval University, Ca,
- Abou S.C., 1997. Grinding process modelling for automatic control: application to mineral and cement industries''. Engineering Foundation Conferences, Delft, the Netherlands
- Austin L. G., 1990. A mill power equation for SAG mills. Minerals and Metallurgical Processing, pp.57-62.
- Busawon K. ,Ratza M.& Hammouri H, 1998. Observer design for a class of nonlinear systems. Int. J. Control 71, pp.405-418.
- Davis, E.W., 1919. Fine crushing in ball mills. AIME Transaction, vol. 61, pp.250-296.
- Iwasaki M., Shibata, & Matsui., 1999. Disturbanceobserver-based nonlinear friction compensation in table drive system. IEEE/ASME Trans. Mechatronic, vol.4. pp.3-8.
- Misawa E.A. & Hedrick J.K., 1989. Nonlinear observer. A state of the art survey,. Trans. of the ASME, 111, pp.344-352.
- Morell S., 1993. The prediction of powder draw in wet tumbling mills. Doctorate thesis, University of Queensland.
- Nijmeijer, H., & Van Der Schaft A.J., 1990. Nonlinear dynamical control systems”. Springer Berlin.
- Plummer A.R. & Vaughan N.D., 1996. Robust adaptive control for Hydraulic Servo-systems, ASME J. of dynamic systems, Measurement, and control. No 11., pp.237-244
- Van Heerden, W.L., 1987. General relations between static and dynamic moduli of rocks, (pp. 381-385). Int. J. Rock Mech. Min. Sci. Geomech. no. 24.
- Weller K. R, 1980. Automation in mining, mineral and metal processing, Proc. 3rd IFAC symposium Pergamon Press. pp. 295-302

#### Paper Citation

#### in Harvard Style

C. Abou S. and Dao T. (2004). **STATE OBSERVER FOR NONLINEAR SYSTEMS: APPLICATION TO GRINDING PROCESS CONTROL** . In *Proceedings of the First International Conference on Informatics in Control, Automation and Robotics - Volume 3: ICINCO,* ISBN 972-8865-12-0, pages 312-319. DOI: 10.5220/0001131803120319

#### in Bibtex Style

@conference{icinco04,

author={Seraphin C. Abou and Thien-My Dao},

title={STATE OBSERVER FOR NONLINEAR SYSTEMS: APPLICATION TO GRINDING PROCESS CONTROL},

booktitle={Proceedings of the First International Conference on Informatics in Control, Automation and Robotics - Volume 3: ICINCO,},

year={2004},

pages={312-319},

publisher={SciTePress},

organization={INSTICC},

doi={10.5220/0001131803120319},

isbn={972-8865-12-0},

}

#### in EndNote Style

TY - CONF

JO - Proceedings of the First International Conference on Informatics in Control, Automation and Robotics - Volume 3: ICINCO,

TI - STATE OBSERVER FOR NONLINEAR SYSTEMS: APPLICATION TO GRINDING PROCESS CONTROL

SN - 972-8865-12-0

AU - C. Abou S.

AU - Dao T.

PY - 2004

SP - 312

EP - 319

DO - 10.5220/0001131803120319