PDE Backstepping Boundary Observer Design for Microfluidic Systems

In this brief, we explore the use of conformal mapping theory to reduce the complexity in PDE backstepping boundary observer design. The technique is applied to a genetic analysis microchip that features a collocated sensor-actuator architecture in which the temperature of the reaction chamber is the spatially distributed control variable. The size and structure of the microchip do not allow for sensor placement within the reaction chamber, making temperature estimation mandatory. The PDE backstepping boundary observer design is chosen to provide real-time data from the temperature inside the microchip. The standard PDE backstepping boundary observer design results in a partial differential equation for the kernel function with double the spatial dimension of the original problem, which makes the design intractable for the problems with dimensions higher than one. We show that the spatial domain of the original problem can be reduced with the use of the conformal mapping. The resulting observer is tested and experimentally validated, shown excellent performance with respect to the spacial L² norm of the estimation error.