458097 Output Regulation for Boundary Controlled Linear Coupled Hyperbolic Pides: Application to a Parallel-Flow Heat Exchanger System

Wednesday, November 16, 2016: 3:51 PM
Monterey II (Hotel Nikko San Francisco)
Xiaodong Xu and Stevan Dubljevic, Chemical and Materials Engineering, University of Alberta, Edmonton, AB, Canada

Transport equations described as first order hyperbolic linear partial differential equations
(PDEs) are utilized to demonstrate different complex physical processes. To mention repre-
sentative engineering applications, we consider heat exchanger [1], production systems [2], oil
well [3] and road traffic [4]. Due to the wide area of applications, the control problems of
such systems has been active research topics. We refer [5], [6], [7] for significant contributions
related hyperbolic PDE systems.

The backstepping method known from nonlinear control theory [8], has been extended to
PDEs solving stabilization problems. Many efforts and results have been established that can
help to simplify the formulation of control problems, e.g. output regulation.

In this work, the output regulation is addressed for boundary controlled hyperbolic partial
integro-differential equations (PIDE) systems. Thereby, the outputs to be measured do not
belong to the set of outputs to be controlled. The change of variables is applied such that
the completely separated first order hyperbolic PIDE systems can be obtained. Consequently,
the backstepping approach is applied in such a way that the state feedback regulator problem
is solved and regulator equations with a simple structure are obtained. In output feedback
regulator design, in order to find observer gains, triangularization is performed and the observer
error systems are transformed into cascade systems with a simple structure. Moreover, it is
shown that for the resulting output feedback regulator, the separation principle holds implying
output regulation for the exponentially stable closed-loop systems.

Finally, the output regulation results are demonstrated by means of a parallel-flow heat
exchanged system with in-domain pointwise controlled outputs.

[1] Xu, X., and Dubljevic, S. (2016). The state feedback servo-regulator for countercurrent heat-
exchanger system modelled by system of hyperbolic PDEs. European Journal of Control.

[2] Marca, M. L., Armbruster, D., Herty, M., and Ringhofer, C. (2010). Control of continuum
models of production systems. IEEE Transactions on Automatic Control, , 55(11), 2511-2526.

[3] Landet, I. S., Pavlov, A., and Aamo, O. M. (2013). Modeling and control of heave-induced
pressure fluctuations in managed pressure drilling, IEEE Transactions on Control Systems
and Technoloy, 21(4), 1340–1351.

[4] Amin, S., Hante, F. M., and Bayen (2008). A. M., On stability of switched linear hyperbolic
conservation laws with reflecting boundaries, in Hybrid Systems: Computation and Control.
Springer-Verlag, 602–605.

[5] Coron, J.-M., d’Andrea Novel, B., and Bastin, G. (2007). A strict lyapunov function for
boundary control of hyperbolic systems of conservation laws, IEEE Transactions on Automatic
Control, 52(1), 2–11.

[6] Di Meglio, F., Vazquez, R., and Krstic, M. (2013). Stabilization of a system of n + 1 cou-
pled first-order hyperbolic linear PDEs with a single boundary input, IEEE Transactions on
Automatic Control, 58(12), 3097–3111.

[7] Aamo, O. M. (2016). Leak detection, size estimation and localization in pipe flows, IEEE
Transactions on Automatic Control, 61(1), 246–251.

[8] P. V. Kokotovic (1992). The joy of feedback: nonlinear and adaptive, Control Systems, IEEE,
12(3), 7–17.

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