Nonlinear Controller Designs for Thermal Management in PCR Amplification

We have developed a theoretical model for a cascade two-stage Peltier device based on the electrothermal dynamics of Peltier modules and the heat balance equations of the interfacing materials. Both open-and closed-loop data are used to tune the scaling factors of the nonlinear model. The effectiveness of the model is validated over a large temperature range with the experimental data from a thermal cycling application of the Peltier device used to perform the polymerase chain reaction (PCR), a genetic amplification technique having important medical diagnostic applications. Based on the theoretical model, two novel nonlinear controllers are designed for a PCR cycling temperature profile. The first controller is an extension of conventional input-to-state feedback linearization design to a class of nonlinear systems that is not only affine on the control but also affine on the square of control inputs. The desired performance is achieved by tuning the parameters to control the convergent rates of the tracking errors. The second one is a switching controller design, which switches between a nonlinear pseudo-proportional-integral-differential (PID)/state feedback controller and a linear time-invariant proportional-integral (PI)/state feedback controller. A Lyapunov function method is used to develop the algorithm for the nonlinear controller, whose parameter values at the switching time are used in the linear controller. Such a combination of linear and nonlinear controllers could reduce the calculation burden and minimize the steady-state errors. Both controllers are tested with our simulation model and implemented in a microcontroller. We verified the designs with improved temperature tracking performances compared to our earlier linear switching design on reduced overshoots (<0.5 degrees C) and settling time (8-10 s faster). The modeling methodology and the feedback linearization-based controller design are scalable and both nonlinear designs can avoid future local model identifications when applied to different references, therefore, are easily extended to other thermal applications.