Predictor based Self tuning Control of Pressure Plants

Transcription

Predictor based Self tuning Control of Pressure Plants
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http://dx.doi.org/10.5755/j01.itc.43.4.8742
Abstract. A digital predictor-based self-tuning control with constraints for the pressure plants, which is able to
cope with minimum-phase and nonminimum-phase plant models is presented in this paper. We determined that
applying polynomial factorization for such models the characteristic polynomials of closed-loops are changed.
Therefore, the on-OLQHLGHQWLILFDWLRQRIWKHPRGHOV¶SDUDPHWHUVLVSHUIRUPHGLQDZD\WKDWHQVXUHVVWDEOHFORVHG-loops.
A choice of the sampling period in digital control typically impacts a control quality of the plant, thus we propose a
method for optimization of a sampling period in the digital predictor-based self-tuning control system. The impact of
the selection of the sampling period and input signalV¶constraints ± amplitude boundaries and the change rate - on the
control quality of the pressure plant is experimentally analysed.
Keywords: predictor-based self-tuning control, minimum-phase and nonminimum-phase model, factorization, online identification, closed-loop stability, sampling period optimization, pressure plant.
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Figure 4. Search process of the optimal sampling period T0 in the digital predictor-based self-tuning control system
with various input signal constraints for the pressure plant
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for the pressure plant
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Figure 6. Control performance of predictor-based self-tuning control with input signal constraints (34)
for the pressure plant
T0*
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[9]
[10]
[11]
[12]
[13]
[14]
[15]
5HIHUHQFHV
[1]
[2]
K. J. Åström, B. Wittenmark. Self-tuning controller
based on pole-zero placement. In: IEE Proceedings D,
1980, Vol. 127, pp. 120-130.
K. J. Åström, B. Wittenmark. Computer-Controlled
Systems: Theory and Design. New Jersey: Prentice
Hall, Third Edition, 1997.
[16]
V. Bobál, J. Böhm, J. Fessl, J. 0DFKiþHN Digital
Self-tuning Controllers. London: Springer-Verlag,
2005.
C. Caro, N. Quijano. Low Cost Experiment for Control System. IEEE IX Latin American and IEEE Colombian Conference on Automatic Control and Industry Applications (LARC), Robotics Symposium, 2011,
pp. 1-6.
S. L.Coelho, W. M. Pessôa. Nonlinear Model Identification of an Experimental Ball-and-Tube System
using a Genetic Programming Approach. Mechanical
Systems and Signal Processing, 2009, Vol. 23, No. 5,
1434-1446.
R. Isermann. Digital Control Systems: Volume 2:
Stochastic Control, Multivariable Control, Adaptive
Control, Applications. London: Springer-Verlag, 2nd
edition, 1991.
V. Kaminskas. Dynamic System Identification via
Discrete-time Observation: Part 1. Statistical Method
Foundation. Estimation in Linear Systems. Vilnius:
Mokslas Publishers, 1982 (in Russian).
V. Kaminskas. Predictor-based Self-tuning Control
Systems. Preprints of 33rd International Scientific
Colloquium, Ilmenau, 1988, 153-156.
V. Kaminskas. Predictor-Based Self Tuning Control
with Constraints. Book Chapter in Book Series
Springer Optimization and Its Applications, Vol. 4,
Model and Algorithms for Global Optimization, eds.
Aimo Törm, Julius Zilinskas, New York, N.Y.:
Springer, 2007, 333-341.
W. S. Levine (Ed.). The Control Handbook, Second
Edition Control System Fundamentals. London: CRC
Press, 2nd edition, 2011
G. Liaucius, V. Kaminskas, R. Liutkevicius. Digital
Self-Tuning PID Control of Pressure Plant with
Closed-Loop Optimization. Information Technology
and Control, 2011, Vol. 40, No. 3, 202-209.
G. Liaucius, V. Kaminskas. Adaptive digital PID
control of pressure process. Power Engineering, 2012,
Vol. 58, No. 3, 158-165.
G. Liaucius, V. Kaminskas. Closed-Loop Optimization Algorithms in Digital Self-Tuning PID Control of
Pressure Process. In: Proceedings of the 7th
International Conference on Electrical and Control
Technologies (ECT2012), 2012, pp. 25-29.
J. S. Perreira, J. B. Bowles. Comparing Controllers
with the Ball in a Tube Experiment. IEEE International Conference on Fuzzy Systems, 1996, Vol. 1, pp.
504-510.
N. Quijano, A. E. Gil, K. M. Passino. Experiments
for Dynamic Resource Allocation, Scheduling, and
Control: New Challenges from Information
Technology-enabled Feedback Control. IEEE Control
Systems, 2005, Vol. 25, No. 1, 63-79.
O. Ziwei, S. Michael, K. Wei. 7KH([SHULPHQW³%DOOin-WXEH´ZLWK)X]]\-PID Controller Based on Dspace.
IEEE International Conference on Systems, Man and
Cybernetics, 2007, pp. 877-881.
Received November 2014.

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