Boundary Optimal Constant Control Versus Periodic Operation (original) (raw)

A numerical method for determining optimal parameter values in forced periodic operation

Chemical engineering science, 1992

A numerical approach for determining values of forcing parameters which maximize performance of a periodically forced system is described. Periodic solutions of the system equations plus a differential form of the time-average performance measure are computed with a shooting algorithm. A nonlinear programming package is used to solve the optimization problem. The algorithm is applied to ethylene oxidation process, using the model of a continous stirred-tank rector (CSTR).

Chemical Engineering Applications of Periodic Optimization

IFAC Proceedings Volumes, 1978

Interest in unsteady-state chemical processing has stimulated a decade of research in periodic optimi zati on. Recent research in cyclic reaction systems suggests several new areas for general investigation. These include multiplicity of stable periodic states, design methods for multiple periodic controls, and optimization of systems with some specified periodic inputs.

On‐Line Feedback Control for Optimal Periodic Control Problems

Canadian Journal of Chemical Engineering, 2008

On présente dans cet article, une méthode pour produire des orbites périodiques pour une catégorie de systèmes non linéaires. Un système Hamiltonien périodique est défi ni comme étant l'équilibre cible pour des systèmes non linéaires sous forme de rétroaction stricte. Une description du système périodique non linéaire dépendant des paramètres est introduite pour un sous-système bidimensionnel et est étendue à des dimensions plus grandes par un processus de rétroitération. La recherche d'extrêmes est utilisée comme loi de mise à jour des paramètres qui garantit la convergence du système vers l'orbite périodique optimale pour une paramétrisation donnée. La procédure aboutit à la mise en oeuvre du contrôle par rétroaction continu qui, typiquement, oriente le système vers une solution sous-optimale qui néanmoins améliore la solution d'optimisation statique. On utilise des exemples typiques de contrôle périodique optimal de la littérature scientifi que pour illustrer l'application de cette méthode.

Solution techniques for periodic control problems: a case study in production planning

Optimal Control Applications and Methods, 1998

Two numerical techniques for solving optimal periodic control problems with a free period are developed. The first method uses shooting techniques for solving an appropriate boundary value problem associated with the necessary conditions of the minimum principle. A convenient form of the transversality condition for the free period is incorporated. The second method is a direct optimization method that applies non-linear programming techniques to a discretized version of the control problem. Both numerical methods are illustrated in detail by a non-convex economic production planning problem. In this model, the-test reveals that the steady-state operation is not optimal. The optimal periodic control is computed such that a complete set of necessary conditions is verified. The solution techniques are extended to obtain the optimal periodic control under various state constraints. A sensitivity analysis of the optimal solution is performed with respect to a specific parameter in the model.

Analytical optimization and sensitivity analysis of forced periodic chemical processes

Chemical Engineering Science, 1980

Intentional periodic mampulatlon of the Inputs to a chemical reactor can In some cases improve the amount of product and its composltlon A vanatlonal method for analyzmg the effects of single and multivariable perlodlc forcmg functions on process performance IS presented in this work and Illustrated in several examples While the method dlscussed here 1s not theoretically Justified for large-amplitude mput vanatlons, comparisons of analytical results obtamed with the method and slmulatlon results for largeamphtude reactor cycling show good quahtatlve agreement The approximate analytlcal method provides a reasonable nntlal estimate of the structure of an advantageous perlodlc control

Optimal periodic output feedback control: a continuous-time approach and a case study

International Journal of …, 2010

This article deals with the problem of optimal static output feedback control of linear periodic systems in continuous time, for which a continuous-time approach, which allows to deal with both stable and unstable open loop systems, is presented. The proposed approach is tested on the problem of designing attitude control laws for a Low-Earth Orbit (LEO) satellite on the basis of feedback from a triaxial magnetometer and a set of highprecision gyros. Simulation results are used to demonstrate the feasibility of the proposed strategy and to evaluate its performance.

Computational Algorithms for Optimization Problems for Periodic Systems

2000

We give a survey of computational algorithms derived in a series of papers for solution of a synthesis problem for optimal stabilization of periodic systems. The proposed algorithms synthesize reliable control, with a given stability tolerance, for periodic systems optimized with respect to the quadratic performance criterion. A reliable controller guarantees the stability and is nearly a linear/quadratic regulator. We also consider the inverse problems for optimal synthesis corresponding to quadratic functionals. The algorithms designed to solve this problem are based on methods of linear matrix inequalities. The efficiency of the proposed algorithms are shown through implementing some examples.

Computation of periodic switching strategies for the optimal control of chemical reactors

In this paper an isoperimetric control problem for the optimization of the performance measure for a nonlinear chemical reaction model with periodic inputs is considered. For this problem, a family of bang-bang controls parametrized by switching times is introduced. The issue of defining these switching times is addressed for periodic boundary conditions by using the Fliess series expansion. Such a technique allows us to obtain analytical relations between the boundary conditions and control parameters for the case of small time periods. These theoretical results are illustrated by numerical simulations for a non-isothermal reaction model with two inputs.

On optimal periodic control and nested optimization problems

Journal of Optimization Theory and Applications, 1986

A minimization problem for a functional on a convex subset C of a normed linear space is considered. Under certain hypotheses, optimality in a certain subset of C implies the validity of first-order necessary optimality conditions for the problem in C. The result is applied to a problem in optimal periodic control of neutral functional differential equations.

The Performance of Discrete Linear Time Varying Control of Linear Periodic Plants

Asian Journal of Control, 2008

ABSTRACTThis paper analyzes the performance of discrete linear time varying (LTV) control of discrete linear periodically time varying (LPTV) plants for l2 disturbance rejection. It extends the results of [11–13] for linear periodic controllers to general LTV control of LPTV plants. It is shown that LPTV control provides strictly better control performance than linear strictly time varying control for LPTV plants. The analysis is carried out in frequency domain. This approach provides not only new results on disturbance rejection of LTV control but also some new insight into properties of general LTV systems.