Robust Control Methods for a Recycle Bioreactor

The paper presents a robust control design strategy for bioprocesses, which are characterized by strongly nonlinear dynamics. More precisely, we present the H2 methodology in order to compute the controller for a recycle Continuous Stirred Tank Bioreactor (CSTB). We consider a general method of formulating control problem, which makes use of linear fractional transformation as introduced by Doyle (1978). The formulation makes use of the general two-port configuration of the generalized plant with a generalized controller. The H2 norm is the quadratic criterion used in optimal control as LQG. The overall control objective is to minimize the H2 norm of the transfer matrix function from the weighted exogenous inputs to the weighted controlled outputs. The advantage of H2 control technique, which uses the linearized model of the CSTB, is that it is completely automated and very flexible. Finally, we prove that the closed loop control structure has very good inner robustness

Robust Multivariable Microgrid Control Synthesis and Analysis

AbstractIn this paper, an islanded microgrid is modelled as a linear multivariable dynamic system. Then, the multivariable analysis tools are employed. The generalized Nyquist diagram and the relative gain array are used respectively for the stability assessment and solving the paring problem among the inputs and outputs. Droop control dependency on the X/R ratio of the microgrid DERs is recognized and its type is proposed using the relative gain array concept. Robust stability, nominal performance and robust performance requirements are evaluated in order to a better understanding of the system dynamics. Finally, three different controllers including H∞, H2 and sequential proportional-integral-derivative controls are designed and compared

Mixed generalized Dynkin game and stochastic control in a Markovian framework

We introduce a mixed {\em generalized} Dynkin game/stochastic control with ${\cal E}^f$-expectation in a Markovian framework. We study both the case when the terminal reward function is supposed to be Borelian only and when it is continuous. We first establish a weak dynamic programming principle by using some refined results recently provided in \cite{DQS} and some properties of doubly reflected BSDEs with jumps (DRBSDEs). We then show a stronger dynamic programming principle in the continuous case, which cannot be derived from the weak one. In particular, we have to prove that the value function of the problem is continuous with respect to time $t$, which requires some technical tools of stochastic analysis and some new results on DRBSDEs. We finally study the links between our mixed problem and generalized Hamilton Jacobi Bellman variational inequalities in both cases

Strong local optimality for generalized L1 optimal control problems

In this paper, we analyse control affine optimal control problems with a cost functional involving the absolute value of the control. The Pontryagin extremals associated with such systems are given by (possible) concatenations of bang arcs with singular arcs and with inactivated arcs, that is, arcs where the control is identically zero. Here we consider Pontryagin extremals given by a bang-inactive-bang concatenation. We establish sufficient optimality conditions for such extremals, in terms of some regularity conditions and of the coercivity of a suitable finite-dimensional second variation.Comment: Journal of Optimization Theory and Applications, Springer Verlag, In pres

Evolution Semigroups in Supersonic Flow-Plate Interactions

We consider the well-posedness of a model for a flow-structure interaction. This model describes the dynamics of an elastic flexible plate with clamped boundary conditions immersed in a supersonic flow. A perturbed wave equation describes the flow potential. The plate's out-of-plane displacement can be modeled by various nonlinear plate equations (including von Karman and Berger). We show that the linearized model is well-posed on the state space (as given by finite energy considerations) and generates a strongly continuous semigroup. We make use of these results to conclude global-in-time well-posedness for the fully nonlinear model. The proof of generation has two novel features, namely: (1) we introduce a new flow potential velocity-type variable which makes it possible to cover both subsonic and supersonic cases, and to split the dynamics generating operator into a skew-adjoint component and a perturbation acting outside of the state space. Performing semigroup analysis also requires a nontrivial approximation of the domain of the generator. And (2) we make critical use of hidden regularity for the flow component of the model (in the abstract setup for the semigroup problem) which allows us run a fixed point argument and eventually conclude well-posedness. This well-posedness result for supersonic flows (in the absence of rotational inertia) has been hereto open. The use of semigroup methods to obtain well-posedness opens this model to long-time behavior considerations.Comment: 31 page