116 IEEE TRANSACTIONS ON EDUCATION, VOL. 52, NO. 1, FEBRUARY 2009 Design of a PID Controller for a PCR Micro Reactor Mihai P. Dinca, Marin Gheorghe, and Paul Galvin Abstract—Proportional-integral-derivative (PID) controllers are widely used in process control, and consequently they are described in most of the textbooks on automatic control. However, rather than presenting the overall design process, the examples given in such textbooks are intended to illuminate specific focused aspects of selection, tuning and implementation of the controller. This paper describes in detail the design of a PID controller for temperature control of a polymerase chain reaction (PCR) microreactor showing how different aspects, which necessarily are taught separately, interact in a real-world design. After setting the design targets by taking the hardware limitations into considera- tion, a continuous time controller, having two degrees of freedom, is designed by placing its dominant pair of poles using the root locus technique. Then, the integrator wind-up is addressed, the controller is translated into a discrete time version and, after implementation, the experimental performances are measured. Index Terms—Control system design, proportional-inte- gral-derivative (PID) controllers, root locus diagram. I. INTRODUCTION F OR more than 50 years, proportional-integral-derivative (PID) controllers have had remarkable success in various industries. They have been applied to control an extremely broad variety of processes from aerospace to motion control, incor- porating slow to fast systems. The main reason for their ver- satility is their relatively simple structure, which can be easily understood and implemented in practice. However, in spite of the enormous amount of research work reported in the liter- ature, many PID controllers are poorly tuned in practice [1]. This shortcoming is perhaps due to the extreme diversity of con- trolled processes and specific user needs. Since there is no magic tuning formula among the myriad proposed ones, more detailed application examples from the real world are still required as instructional material in process control courses. Temperature control is a very important problem in many technological processes in industry. Theoretical work has been conducted for many years and accompanied by many practical implementations using existent technology [2], [3]. The devel- opment of new microanalytical systems requires a much higher level of performance from specifically designed and tuned con- trollers. Among them, the microsystems used for polymerase chain reaction (PCR) are extremely demanding [4], since they require fast and damped tracking response, precise control of plateaus and fast settling of load perturbation response. PCR amplification is an enzyme-mediated process where, in response Manuscript received August 13, 2007; revised January 21, 2008. Current ver- sion published February 4, 2009. This work was supported by the EU 6th IST Framework Programme under project 027333 (Micro2DNA). The authors are with the Tyndall National Institute—LSI “Lee Maltings,” Prospect Row, Cork, Ireland (e-mail: mihai.dinca@tyndall.ie). Digital Object Identifier 10.1109/TE.2008.919811 to temperature cycling, a single DNA molecule can be rapidly amplified into many billions of molecules [5]. Different kinds of controllers have been considered in the thermocyclers reported in the PCR microreactors literature. While the classical PID con- troller is broadly used [6]–[8], approaches based on more elabo- rated strategy as PD-PID, fuzzy-PID, and a predictive controller in conjunction with a neural network have also been described [4], [9], [10]. This paper describes the design of a PID controller that was implemented for fast and accurate temperature control of a PCR microreactor realized in a lab-on-a-chip research project. Although simple to implement, the controller provided a better performance than those reported in the mentioned references. The control system uses a personal computer running Labview and GPIB controlled instrumentation. Hardware limitations such as sampling time, maximum heating power and process response time are taken into consideration from the start in setting appropriate design targets. Using information obtained from the open loop step response, a continuous time PID controller with two degrees of freedom is first designed. This design is achieved through placement of the dominant poles pair. The controller is then translated into a discrete time form. Other difficulties like the integrator wind-up and supplementary lag introduced by the sampling are addressed after conversion to the digital form. After implementation and experimental evaluation, it was found that the control system meets the design targets and provides better performance than those reported in literature for PCR microreactors. The present paper can be useful as a reference or application example, either in an introductory course on process control or in a second control course. As the design is applied to a real system, this paper can be also of interest for an advanced course on industrial control and for control practitioners. The detailed description of the PID controller presents a didactic contribu- tion, by starting from the various hardware constraints of a very specific application, and illuminating in a realistic situation the danger of canceling a process slow pole by a controller zero for a lag dominated process. The latter clearly emphasizes the ne- cessity to address disturbance rejection and set-point tracking in separate design steps. All this shows how different aspects, which are often taught separately, interact in a real-world design. Matlab, which has become an essential tool for both undergrad- uate and post graduate courses in the field of systems and con- trol area, was used during the controller design and performance evaluation, and this also can provide a didactic contribution. The paper is organized as follows. Process information and target design setting are presented in Section I, and the design of the continuous time controller is addressed in Section II. In Section III, the digital implementation is carried out and finally the experimental results are given in Section IV. 0018-9359/$25.00 © 2008 IEEE