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