Modeling and controller design of a nonlinear time-varying thermal device in a microfluidic platform Jingbo Jiang Govind V. Kaigala Christopher J. Backhouse Horacio J. Marquez Abstract— A switching controller is designed and imple- mented in a custom-made temperature control system to perform sensitive bio-chemical reactions for medical diagnostics within a microfluidic platform. Nonlinear and time-varying characteristics of the plant are considered, and the system is approximated by multi-linear models. Both simulation and experimental results demonstrate that the switching controller exhibits superior performance compared with other controllers considered. The efficacy of this design is exhibited by the application to a clinically important diagnostic test - polymerase chain reaction (PCR). I. I NTRODUCTION Microfluidic devices fabricated with photolithographic techniques are projected to be the driving force towards miniaturization leading to rapid, low volume and inexpensive implementation of conventional life-science procedures. We have ported numerous conventional molecular biology pro- cedures to the microfluidic platform e.g. Polymerase Chain Reaction (PCR) [1], DNA sequencing [2] and diagnostics of hereditary diseases etc. [3]. Controlled localized heating is considered a critical requirement for bio-analytical systems and a key component for miniaturized platforms. Therefore both hardware design considerations such as cost, size, power consumption and heat efficiency and software design such as accurate temperature control are important in the microfluidic implementation. Integration of different analytical function- alities is being performed on the system with the aim of building a total molecular analysis instrument for human cancer diagnosis [4]. Custom-made instrumentation was built by the cascade arrangement of thermoelectric modules (TEMs) together with the temperature control system and reusable pumping and valving infrastructure. Unlike commercially available conventional thermal cycling devices, that are primarily op- timized for large volume reactions in tubes (typically 25μL), the system built is in the μL and sub-μL regimes. This total analysis system could functionally be divided into three sub- systems: microchips for fluid confinement, heating system with a digital controller, servo-motors for on-chip pumping and valving [5]. The heating subsystem composed of five blocks: (a) the cascaded TEMs (9500/127/085B, Ferrotec, USA) as the plant, (b) a digital controller resident in a PIC microcontroller (18F458, Microchip technologies Inc., USA) We gratefully acknowledge the support by the Natural Sciences and Engineering Research Council of Canada (NSERC). J. Jiang, G.V. Kaigala, C.J. Backhouse and H.J. Marquez are with Depart- ment of Electrical & Computer Engineering, University of Alberta, Edmon- ton, AB, T6G 2V4, Canada jbjiang@, govind@, chrisb@, marquez@ece.ualberta.ca with A/D converter (TLC2543, Texas instruments, USA) and D/A converter (LTC1590, Texas instruments,USA) and other circuit elements on the control board, (c) temperature sensors (LM50, National semiconductors, USA), (d) actuator with power supply and (e) Graphical User Interface (GUI) on a PC. Fig. 1 is a schematic diagram of the heating subsystem. In this paper, we focus on the controller design of the heating sub-system necessary for PCR. TEMs are solid- sate devices that function as heat pumps and the major physical laws behind them are Seebeck effect, Peltier effect and Thomson effect, and all these effects depend on the temperatures on two sides of the TEM and the P-N junctions inside it and therefore the performance of TEM has nonlinear relation with input current and temperatures of both sides [6]. Theoretical modeling based on heat balance and heat transfer equations will lead to complex nonlinear functions and implicit input/output relations. This is the motivation to apply system identification to obtain black-box models. Through open-loop experiments, we observed nonlinearities of system in different temperature regions and time-varying phenomena in system responses, additional transformations and methods employed are introduced and linear system identification techniques are used to obtain the system models. Switching controller was designed and simulated and finally implemented, as it most closely satisfied the requirements of both rapid set-point transitions and minimum steady-state deviation. Rest of the paper is organized as follows. In section II, the heating sub-system model and system identification results are presented. In section III, the design of the switch- ing controller is explained, followed by the closed-loop simulation results and the experiment results together with implementation considerations in section IV. Conclusions of the temperature control design are presented in section V. Fig. 1. Block diagram depicting the functional components of the thermal system. Proceedings of the 2006 American Control Conference Minneapolis, Minnesota, USA, June 14-16, 2006 FrB13.3 1-4244-0210-7/06/$20.00 ©2006 IEEE 5330