(537b) Moving Horizon Estimation for Heat Exchanger Processes

Heat exchangers are extensively utilized in chemical engineering practice. The prominent feature of heat exchanger systems is that the underlying models belong to the infinite-dimensional systems and are governed by linear coupled hyperbolic partial differential equations (PDEs), derived from mass, momentum and/or energy conversation laws. As reported, state/output estimation for heat exchanger processes is significant since the spatially distributed state is not always directly observable and/or installing spatially distributed sensors can be quite prohibitive [1-3]. However, the main challenge in addressing state/output estimation of heat exchanger processes is reconstructing the spatiotemporal dynamics using limited measurements at boundary and in presence of plant and measurement disturbances. To address that, this work aims to design a moving horizon estimator (MHE) for heat exchanger processes by extending MHE theories and results well-developed for finite-dimensional systems [4-5].

More specifically, 2x2 linear coupled first-order hyperbolic PDEs are used to model the countercurrent heat exchanger processes in the continuous-time setting. Bounded plant and measurement disturbances are considered along with boundary/point observation and disturbance (corresponding to unbounded linear operators). Considering directly designing MHE for continuous-time infinite-dimensional systems and dealing with unbounded operators can be challenging, the Cayley-Tustin transformation [6] is performed for mode time-discretization without any spatial approximation or model order reduction. Under this transformation, essential model properties remain invariant, such as stability, observability and energy. Most importantly, the Cayley-Tustin transformation is shown to be an input-output convergent transformation [6], allowing that the estimation results for the discrete-time model can be linked back to the continuous-time model.

The moving horizon estimator is designed for the discrete-time heat exchanger model while explicitly handling the disturbance and output constraints. The resulting MHE is shown to be a finite-dimensional quadratic optimization program that is easily solvable by using standard optimization techniques. The effectiveness of the proposed design is validated through simulation. The designed MHE can be applied to a general class 2x2 linear coupled hyperbolic PDE models, including packed gas absorber processes, flow dynamics in pipeline networks, drilling systems and irrigation canals.

References

[1] Harmon, R. W. 1980. Advanced Process Control, McGraw-Hill Inc., USA.

[2] Curtain, R. F., and Zwart, H. 1995. An introduction to infinite-dimensional linear systems theory, Springer.

[3] Xu, C.-Z., and Gauthier, S. 2002. Exponential stability and transfer functions of processes governed by symmetric hyperbolic systems. ESAIM: Control, Optimisation and Calculus of Variations 7: 421-442.

[4] Muske, K. R., Rawlings, J. B., and Lee, J. H. 1993. Receding horizon recursive state estimation. American Control Conference, 900-904.

[5] Rao, C. V., Rawlings, J. B., and Lee, J. H. 2001. Constrained linear state estimation—a moving horizon approach. Automatica, 37(10), 1619-1628.

[6] Havu, V., and Malinen, J. 2007. The Cayley transform as a time discretization scheme, Numerical Functional Analysis and Optimization. 28 (7-8), 825-851.