Convex optimal control of constrained and periodic systems

In the current global economy, chemical plants are being designed aggressively leading to increasingly complex designs. However various economic and ecological restrictions along with the process quality and quantity requirements pose strict constraints on the operating range of the plant. It is not uncommon to see various physical devices in the plant saturating, trying to meet these aggressive objectives. The performance of the plant as a result deteriorates under these unavoidable physical limitations. It is required that an efficient control strategy be developed for such scenarios which not only can guarantee a range of performance objectives but also explicitly accounts for the constraints. The focus of this thesis is to develop control algorithms for systems with input/output constraints and systems with cyclic behavior in a convex optimization framework.;A variety of control studies can be found in literature dealing with input constraints primarily categorised as anti-windup techniques. Most of these control algorithms primarily design a compensation which becomes active in the event of a constraint violation. A very few of these approaches pose the design problem in a convex optimization framework. In first half of this thesis, we present two distinct approaches to the problem of anti-windup compensation design which provide optimal synthesis techniques while establishing the stability criteria for the closed loop constrained systems. The piecewise approach to the anti-windup problem provides less conservative condition to establish stability by quantifying the effect of saturation, as opposed to the traditional techniques which use entire sector bound condition. Using one step design approach, we provide an algorithm in convex optimal framework to design both the linear controller and the anti-windup compensation simultaneously.;The second half of the thesis deals with repetitive/cyclic systems or systems which follow cyclic trajectory. Various approaches, e.g. Repetitive control, Iterative learning control, have been reported in literature. However these techniques do not incorporate input/output constraints which are a typical part of any chemical plant. In addition, lack of ability to handle qualitative/quantitative objectives makes these approaches less attractive. We propose in this thesis a control framework which explicitly identifies the repetitive behavior of these distinct systems while allowing for the incorporation of the frequently occurring input/output constraints. We pose the the stability conditions as convex inequalities to design optimal controller for such systems. Later, we propose to use cyclic control framework for Simulated Moving Bed reactor, a cyclic system and discuss associated challenges ranging from nonlinear process dynamics to modeling details.