| Chemical and biological systems typically exhibit multi-scale dynamics, owing to the interaction of physical phenomena characterized by a wide range of time and length scales. These systems give rise to stiff mathematical models due to the presence of parameters of disparate orders of magnitude, leading to computationally intensive numerical schemes when a solution is sought. Controllers designed without explicitly accounting for this scale multiplicity are sensitive to modeling and measurement errors, and may cause closed-loop instability. This motivates the need for reduced order models capturing the dynamics in the desired scale (such models are appropriate as a basis for control), and for methods to derive such non-stiff models. The thesis addresses the development of such methods for broad classes of mathematical models.; For spatially homogeneous multi-time scale chemical processes modeled by Ordinary Differential Equations (ODEs), the slow dynamics have been shown to be modeled by Differential Algebraic Equations (DAEs). When the algebraic equations involve the manipulated inputs, the underlying state-space depends on the control law. The thesis addresses the derivation of an output feedback precompensator to obtain a new DAE system with control independent state-space suitable for controller synthesis, and its application to the output feedback control of integrated process networks.; For spatially inhomogeneous systems, reaction-convention processes are considered in the possible presence of fast convection or fast heat transfer in addition to fast and slow reactions. The resulting first order stiff hyperbolic partial differential equation models are recast in the method of characteristics, which enables deriving reduced models of the slow dynamics using reduction methods for ODEs. The performance and robustness of controllers designed on the basis of the reduced models are evaluated through simulations.; For chemical reaction networks with fast and slow reactions modeled by stiff Chemical Langevin Equations (CLEs), a coordinate change is proposed to identify fast and slow variables. After completion of this step, the fast variables are eliminated by application of the method of adiabatic elimination to the Fokker-Planck equation associated with the CLE, leading to an approximation of the density probability. |
