Control and analysis of fluid flow networks

The dissertation addresses the problem of nonlinear control for fluid flow networks. It uses lumped-parameter pipe flow dynamic equations in conjunction with Kirchhoff's current and voltage laws as a nonlinear model. It develops control laws that achieve tracking or regulation to desired flow rates.; We start with developing a full-order and a minimal control-oriented model of fluid flow networks consisting of rigid pipes. We then present two control designs for the models. The first design employs actuation in all the branches of the network and achieves a global regulation result. The other employs actuation only in branches not belonging to the tree of the graph of the network and achieves regulation in a (non-infinitesimal) region around the operating point.; In contrast to centralized controllers that require measurements from all the branches of the network, we also solve a decentralized nonlinear control problem where actuator valves and flow rate sensors are collocated in individual branches and do not exchange information. We solve both regulation (constant references) and tracking (time varying reference signals) problems. To eliminate conservativeness in choosing the gains of the controllers, we employ adaptation.; We then use Kirchhoff's laws and pipe flow dynamics equations to describe a fluid flow network in the form of a nonlinear differential equation with a periodic right hand side. We apply the averaging method to find an approximate solution of this equation and analyze its stability properties. The approximate solution consists of three parts: a mean flow part due to the resistive effects of branches, a time-periodic part due to “inductive” effects, and a mean flow average correction due to the interaction of nonlinear and time varying effects. We present an example that may help explain the processes participating in the development of venous diseases.; Finally, we discuss a model of venous flow in the form of a one-dimensional PDE, combined with collapsible tube law. We formulate a control problem for the model and discuss the techniques that need to be developed to solve such a problem.