Many engineering problems related to the control of distributed parameter systems are formulated in spatially variant geometries such as irregular channels or require that the controls and sensors are spatially localized. In that case a reduced order model of the infinite dimensional system is often required.
In this talk, a novel methodology is presented for model reduction of systems described by a general class of spatially variant PDEs using multivariate B-splines defined on triangulations. The multivariate B-spline consists of piecewise defined polynomials of arbitrary degree with user defined smoothness between elements. A novel linear operator for the B-splines is defined that directly reduces distributed parameter systems into systems of ODE’s with boundary and smoothness conditions imposed as side constraints.
The main aim of the new methodology is to simplify the design and implementation of controllers for real-life applications of PDE control such as active flow control, active flexible structures, and chemical processes.
The methodology is applied to two example problems. The first example is intended as a method validation, and concerns the stabilization of the unstable 1-D heat equation using boundary control. A linear systems analysis shows that the dominant eigenmodes of the known analytical solution correspond with those obtained from the B-spline ROM method. A second more challenging example is stabilization of the reaction-convection-diffusion equation on a 2-D non-convex spatial domain using in-domain control.
Finally, an outlook is given on stabilization of the Navier Stokes equations for air foils using localized in-domain flow (plasma) actuators and local pressure sensor feedback with the aim of postponing flow separation and improving drag characteristics.
I am an assistant professor at the department of Control & Simulation at the Faculty of Aerospace Engineering of the Delft University of Technology (TU-Delft). In my current function I strive to make aircraft and spacecraft safer, smarter and more efficient through the application of advanced modelling and control theories. My current research focus is on flight envelope aware fault tolerant control with the goal of preventing Loss of Control related air accidents. Loss of control in flight currently is the main contributor to fatal accidents in civil aviation. Loss of control occurs when the pilot loses the ability to effectively control the aircraft. Loss of control is in most cases caused by the aircraft exiting the safe flight envelope, which is the flight region for which safe operations of the aircraft and its cargo can be guaranteed.