Abstract
Control of nonlinear systems with input constraints is an interesting topic of control theory that must be solve adequately because of the presence of constraints in almost each real system. There are many authors and several techniques trying to solve this problem (anti-windup structures, positive invariant sets, variable structure systems, global, semi-global and local stabilization of systems with constraints, optimization problems solved by linear matrix inequalities).
This paper shows a different approach that originates in the time optimal control and is improved by decreasing the sensitivity to uncertain model parameters that is balanced by sub-optimality. The design of constrained controller is carried out on the triple integrator system and this is later applied to the nonlinear three-tank hydraulic system after its exact linearization.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Similar content being viewed by others
References
Athans, M., Falb, P.: Optimal Control: An Introduction to the Theory and its Applications. McGraw-Hill, New York (1996)
Bemporad, A., Morari, M., Dua, V., Pistikopoulos, E.N.: The explicit linear quadratic regulator for constrained systems. Automatica 38, 3–20 (2002)
Bisták, P.: The sub-optimal controller for triple integrator applied to three-level hydraulic system. In: Control and Applications: Proceedings of 13th IASTED International Conference, pp. 28–35. ACTA Press, Vancouver (2011)
Blanchini, F.: Set invariance in control a survey. Automatica 35(11), 1747–1767 (1999)
Borelli, F.: Constrained optimal control of linear and hybrid systems. LNCIS, vol. 290. Springer, Heidelberg (2003)
Huba, M.: Constrained pole assignment control. In: Menini, L., Zaccarian, L., Chaouki, T.A. (eds.) Current Trends in Nonlinear Systems and Control, pp. 163–183. Birkhäuser, Boston (2006)
Isidori, A.: Nonlinear Control Systems, 3rd edn. Springer, New York (1995)
Pontryagin, L.S., Boltyanskii, V.G., Gamkrelidze, R.V., Mishchenko, E.F.: The Mathematical Theory of Optimal Processes. Wiley, New York (1962)
Ťapák, P., Bisták, P., Huba, M.: Control for triple integrator with constrained input. In: Proceeding of 14th Mediterranean Conference on Control and Automation. IEEE, Ancona (2006)
Acknowledgments
This work has been partially supported by the grants VEGA 1/0937/14 and APVV-0343-12.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2015 Springer International Publishing Switzerland
About this paper
Cite this paper
Bisták, P. (2015). Time Sub-Optimal Control of Triple Integrator Applied to Real Three-Tank Hydraulic System. In: Moreno-Díaz, R., Pichler, F., Quesada-Arencibia, A. (eds) Computer Aided Systems Theory – EUROCAST 2015. EUROCAST 2015. Lecture Notes in Computer Science(), vol 9520. Springer, Cham. https://doi.org/10.1007/978-3-319-27340-2_4
Download citation
DOI: https://doi.org/10.1007/978-3-319-27340-2_4
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-27339-6
Online ISBN: 978-3-319-27340-2
eBook Packages: Computer ScienceComputer Science (R0)