Model reduction of systems exhibiting two-time scale behavior or parametric uncertainty

Abstract

Model reduction is motivated by the fact that complex process models may pre- vent the application of model-based process control. While extensive research on model reduction has been done in the past few decades, model reduction of systems exhibiting two-time scale behavior as well as parametric uncertainty has received little attention to date. This work addresses these types of problems in detail. Systems with two-time scale behavior can be described by differential-algebraic equations (DAEs). A new technique based on projections and system identification is presented for reducing this type of system. This method reduces the order of the differential equations as well as the number and complexity of the algebraic equations. Additionally, the algebraic equations of the resulting system can be replaced by an explicit expression for the algebraic variables such as a feed-forward neural network or partial least squares. This last property is important insofar as the reduced model does not require a DAE solver for its solution, but system trajectories can instead be computed with regular ordinary differential equation (ODE) solvers. For systems with uncertain parameters, two types of problems are investigated, including parameter reduction and parameter dependent model reduction. The pa- rameter reduction problem is motivated by the fact that a large number of parameters exist in process models while some of them contribute little to a system's input-output behavior. This portion of the work presents three novel methodologies which include (1) parameter reduction where the contribution is measured by Hankel singular val- ues, (2) reduction of the parameter space via singular value decomposition, and (3) a combination of these two techniques. Parameter dependent model reduction investigates how to incorporate the influ- ence of parameters in the procedure of conventional model reductions. An approach augmenting the input vector to include the parameters are developed to solve this problem. Finally, a nonlinear model predictive control scheme is developed in which the reduced models are used for the controller. Examples are investigated to illustrate these techniques. The results show that excellent performance can be obtained for the reduced models.