(582h) Model Predictive Control for Linear Distributed Parameter Systems

Distributed parameter systems (DPS) are ubiquitously present as models of fundamental conservation laws and in process control, manufacturing, transport systems and/or human society. The major drawback of DPS models is that they take form of partial differential equations containing higher order derivatives in space and time. The complexity of a partial differential equation (PDE) in the case of linear PDE models lies in necessity of modellers to account for model spatial characteristics by an approximating underlying model through some spatial approximation arriving to a finite dimensional model representation amenable for subsequent control, observer and/or monitoring device design [1], [2].

This work provides foundation for systematic development of modelling framework for a linear DPS system which uses a finite and low dimensional setting for the controller/observer/estimator design without application of any spatial approximation or order reduction. In particular, we are interested in formulating control design methodology for a general class of linear DPS systems which in this work account for an optimal constrained optimization based setting. Therefore, we propose to develop a linear model predictive controller design for a class of linear distributed parameter system. In this works, we present our results applied to the DPS emerging from the chemical transport-reaction systems varying from the convection dominated models of a plug flow reactor to diffusion dominated models of an axial dispersion reactor. In addition to classical chemical process systems, we also address wave and beam equation system which accounts for a large class of distributed parameter systems. In this work, the discrete model of a distributed parameter system is obtained by using energy preserving Cayley-Tustin discretization [1]. Discrete DPS models are low dimensional, energy preserving and do not dissipate numerically. In particular, discrete setting is amenable to an explicit, economic and/or a classical model predictive control setting realization, with emphasize on the different slight variations in realization of constrained finite dimensional controllers. Having this in mind, the model predictive control [4] is designed by utilizing standard optimal control law with input or/and state/output constraints. The issues of stabilization, optimality and constrained stabilization are addressed for an infinite-dimensional system in this work. Finally, the controller performance is assessed by numerical simulation with application on different distributed parameter systems.

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

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

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

[4] K. R. Muske, J. B. Rawlings, Model predictive control with linear models, AIChE Journal 39 (2) (1993) 262-287.