ISSN (Print) : 2320 – 3765
ISSN (Online): 2278 – 8875
International Journal of Advanced Research in Electrical,
Electronics and Instrumentation Engineering
(A High Impact Factor, Monthly, Peer Reviewed Journal)
Website: www.ijareeie.com
Vol. 8, Issue 4, April 2019
PID Controller Tuning using Ziegler-Nichols
Method for Temperature control of Thermal
Cycler
V. Sailaja1, K. Nagabhushan Raju2
Research Scholar, Dept. of Instrumentation, Sri Krishnadevaraya University, Anantapuramu, Andhrapradesh, India1
Professor, Dept. of Instrumentation, Sri Krishnadevaraya University, Anantapuramu, Andhrapradesh, India2
ABSTRACT: The control of constant temperature according to the desired value (set point) in a closed loop used PID
controller system. For this, we are using a microcontroller, a temperature sensor for sensing the temperature of the
closed loops. This paper deals with the controlling of temperature of thermal cycler using a PID controller. This project
is designed in a way as user defined data, the user sets up the required temperature limit in the PID controller as the
controller set point. A heating and cooling element i.e. Thermoelectric Cooler, is used for heating and cooling the metal
block and the thermistor sensor placed in the metal block is responsible for sensing the metal block temperature. Based
on the controller constant values and the temperature of the metal block is maintained. Ziegler Nichols tuning method
is used for the PID controller tuning method. The performance analysis of PI and PID controllers is done for the
thermal cycling system.
KEYWORDS: Thermal Cycler, Polymerase Chain Reaction, PID Controller, Ziegler Nichols method.
I. INTRODUCTION
Process control system is often non-linear and difficult to control accurately for the process. Their dynamic models of
the system are more difficult to derive. The conventional PID controllers, in various combinations have been widely
used for industrial processes due to their simplicity and effectiveness for linear systems, especially for first and second
order systems. It has been well known that Proportional Integral Derivative (PID) controllers can be effectively used
for linear systems, but usually cannot be used for higher order and non-linear systems [1]. One of its main advantages is
that no mathematical modelling is required since the controller rules are especially based on the knowledge of system
behavior and experience of the control engineer [2].
The inaccuracy of mathematical modelling of the plants usually degrades the performance of the controller, especially
for non-linear system and complex control problems. System mainly includes: PID controller module, the control
algorithm module. The PID controller algorithm involves three separate fixed parameters, and is accordingly called
three-term control: the proportional, the integral and derivative values P, I, and D. Simply, these values can be
interpreted in words of time: P depends on the current error, I on the accumulation of past errors, and D is a prediction
of future errors, based on present position of a control valve, a damper, or the power supplied to a heating element.
Thermocyclers, or thermal cyclers, are instruments used to amplify DNA and RNA samples by the Polymerase Chain
Reaction (PCR). The thermocycler raises and lowers the temperature of the samples in a holding block in discrete, pre-
programmed steps, allowing for denaturation and reannealing of samples with various reagents. Amplified genetic
material can be used in many downstream applications such as cloning, sequencing, expression analysis, and
genotyping.
A PCR machine is also called a thermal cycler. It rapidly changes temperatures (heating and cooling) for PCR reactions,
thereby allowing the reaction to cycle between primer annealing (50-60°C), DNA amplification (72°C), and strand
melting cycles (94°C). Each cycle of PCR includes steps for template denaturation, primer annealing and primer
extension. The initial step denatures the target DNA by heating it to 94°C or higher for 15 seconds to 2 minutes. In the
Copyright to IJAREEIE DOI:10.15662/IJAREEIE.2019.0804024 1289
ISSN (Print) : 2320 – 3765
ISSN (Online): 2278 – 8875
International Journal of Advanced Research in Electrical,
Electronics and Instrumentation Engineering
(A High Impact Factor, Monthly, Peer Reviewed Journal)
Website: www.ijareeie.com
Vol. 8, Issue 4, April 2019
denaturation process, the two intertwined strands of DNA separate from one another, producing the necessary single-
stranded DNA template for replication by the thermostable DNA polymerase. In the next step of a cycle, the
temperature is reduced to approximately 40–60°C. At this temperature, the oligonucleotide primers can form stable
associations (anneal) with the denatured target DNA and serve as primers for the DNA polymerase. This step lasts
approximately 15–60 seconds. Finally, the synthesis of new DNA begins as the reaction temperature is raised to the
optimum for the DNA polymerase. For most thermostable DNA polymerases, this temperature is in the range of 70–
74°C. The extension step lasts approximately 1–2 minutes. The next cycle begins with a return to 94°C for denaturation.
II. DESCRIPTION OF THERMAL CYCLER
The Thermal Cycling system consists of several things mainly Sample holder metal block, Temperature sensor, data
acquisition system, controller and heating/cooling module. Here thermistor is used as the temperature sensor, DAQ is
used for inter connection between sensor and controller as well as controller and driver circuit. The thermistor output is
in terms of millivolt range. The working of the system is described as, when the temperature is measured by the
thermistor it is converted into the voltage, which is going to the controller through DAQ. The difference between set
point and actual value is applied to the controller, nothing but error. The PWM signal is produced corresponding to the
output voltage of the sensor to control the temperature of the thermal cycler, it is tuned automatically and correcting the
error in the process its shown figure 1. Where SP: Setpoint and PV= Process Value.
Error
Detection
Metal PV
SP - PID TEC
Block +
Controller Driver
+ Peltier
Thermistor
Fig 1 Block diagram of PID controller for Thermal cycler
Copyright to IJAREEIE DOI:10.15662/IJAREEIE.2019.0804024 1290
ISSN (Print) : 2320 – 3765
ISSN (Online): 2278 – 8875
International Journal of Advanced Research in Electrical,
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(A High Impact Factor, Monthly, Peer Reviewed Journal)
Website: www.ijareeie.com
Vol. 8, Issue 4, April 2019
Fig 2 Block diagram of Thermal Cycler
III. GOVERNING EQUATIONS
A proportional integral derivative controller (PID controller) is a generic control loop feedback mechanism (controller)
widely used in industrial control systems. PID controller is most commonly used for feedback controller. A PID
controller calculates an "error" value as the difference between a measured process variable and a fixed set point. The
controller used to minimize the error by adjusting the process control inputs. A PID controller will be called a P, P or I,
PD controller in the absence of the respective control actions.
The design and use of PID (proportional-integral-derivative) control The basic PID controller has the form
where is the control signal, Kp is Proportional gain, a tuning parameter, Ke is Integral gain, a tuning parameter, Kd
is Derivative gain, a tuning parameter e: Error = SP – PV. t: Time or instantaneous time The control signal is thus a
sum of three terms: a proportional term that is proportional to the error, an integral term that is proportional to the
integral of the error, and a derivative term that is proportional to the derivative of the error.
Integral action guarantees that the process output agrees with the reference in steady state and provides an alternative to
including a feedforward term for tracking a constant reference input. Integral action can be implemented
using automatic reset, where the output of a proportional controller is fed back to its input through a low pass filter:
Copyright to IJAREEIE DOI:10.15662/IJAREEIE.2019.0804024 1291
ISSN (Print) : 2320 – 3765
ISSN (Online): 2278 – 8875
International Journal of Advanced Research in Electrical,
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(A High Impact Factor, Monthly, Peer Reviewed Journal)
Website: www.ijareeie.com
Vol. 8, Issue 4, April 2019
Derivative action provides a method for predictive action. The input-output relation of a controller with proportional
and derivative action is
where is the derivative time constant. The action of a controller with proportional and derivative action can
be interpreted as if the control is made proportional to the predicted process output, where the prediction is made by
extrapolating the error time units into the future using the tangent to the error curve.The effects of increasing each of
the controller parameters Kp, Ki, Kd are summerised as below.
Response Rise Time Overshoot Settling Time S-S Error
Decrease Increase NT Decrease
Decrease Increase Increase Eliminate
NT Decrease Decrease NT
NT: No Definite trend. Minor change
PID gains can be determined using Ziegler-Nichols tuning rules. The step response method characterizes the open loop
response by the parameters and illustrated below (left):
The frequency response method characterizes the process dynamics by the point where the Nyquist curve of the process
transfer function first intersects the negative real axis and the frequency where this occurs (above, right). The
corresponding PID gains are given in the following Table.
Integral windup can occur in a controller with integral action when actuator saturation is present. In this situation, the
system runs open loop when the actuator is saturated and the integral error builds up, requiring the system to overshoot
in order to remove the integrated error. Anti-windup compensation can be used to minimize the effects of integral
windup by feeding back the difference between the commanded input and the actual input. A number of variations of
PID controllers are useful in implementation. These include filtering the derivative, setpoint weighting and other
variations in how the derivative and integral actions are formulated. PID controllers can be implemented using analog
hardware, such as operational amplifiers, or via digital implementations on a computer.
Copyright to IJAREEIE DOI:10.15662/IJAREEIE.2019.0804024 1292
ISSN (Print) : 2320 – 3765
ISSN (Online): 2278 – 8875
International Journal of Advanced Research in Electrical,
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(A High Impact Factor, Monthly, Peer Reviewed Journal)
Website: www.ijareeie.com
Vol. 8, Issue 4, April 2019
The Ziegler-Nichols rule is a heuristic PID tuning rule that attempts to produce good values for the three PID gain
parameters: Kp - the controller path gain, Ti - the controller's integrator time constant, Td - the controller's derivative
time constant. Given two measured feedback loop parameters derived from measurements:
1. The period Pu of the oscillation frequency at the stability limit
2. The gain margin Ku for loop stability.
Closed-loop refers to the operation of a control system with the controlling device in automatic mode, where the flow
of the information from sensing element to transmitter to controller to control element to process and back to sensor
represents a continuous feedback loop. If the total amount of signal amplification provided by the instruments is too
much, the feedback loop will self-oscillate at the system’s natural (resonant) frequency. While oscillation is almost
always considered undesirable in a control system, it may be used as an exploratory test of process dynamics if the
controller acts purely on proportional action providing data useful for calculating effective PID controller settings.
Thus, a closed-loop PID tuning procedure entails disabling any integral or derivative actions in the controller, then
raising the gain value of the controller just far enough that self-sustaining oscillations ensue. The minimum amount of
controller gains necessary to sustain sinusoidal oscillations is called the ultimate sensitivity (Su) or ultimate gain (Ku)
of the process, while the time period between successive oscillation peaks is called the ultimate period (Pu) of the
process. We may then use the measured values of Ku and Pu to calculate reasonable controller tuning parameter values
(Kp, τi, and/or τd). PID Tuning parameters using Ziegler-Nichols Closed-Loop method:
Ziegler Nichols Closed Loop Method
Controller
KP Τi Τd
type
P 0.5*Ku - -
PI 0.45*Ku 0.85*Pu -
PID 0.6*Ku 0.5*Pu 0.13*Pu
Table:1 Ziegler Nichols Closed Loop Method Tuning Parameters
When performing such a test on a process loop, it is important to ensure the oscillation peaks do not reach the limits of
the instrumentation, either measurement or final control element. In other words, in order for the oscillation to
accurately reveal the process characteristics of ultimate sensitivity and ultimate period, the oscillations must be
naturally limited and not artificially limited by either the transmitter or the control valve saturating. Oscillations
characterized by either the transmitter or the final control element reaching their range limits should be avoided in order
to obtain the best closed-loop oscillatory test results.
The main advantage in using the ZN tuning method is that all three tuning constants Kp, Td, and Ti, are pre-calculated
and input to the system at the same time. It does not require any trial and error to achieve initial tuning. The chief
disadvantage in using ZN tuning is that in order to obtain the system’s characteristic data to make the calculations, the
system must be operated either closed loop in an oscillating condition, or open loop.
A. OSCILATION METHOD (CLOSED LOOP METHOD)
Using the oscillation method, we will be determining two machine parameters called the ultimate gain Ku and the
ultimate period Pu. Using these, we will calculate Kp, Ti and Td.
1. Initialize all PID constants to zero. Power-up the machine and the closed loop control system.
2. Increase the proportional gain Kp to the minimum value that will cause the system to oscillate. This must be a
sustained oscillation, i.e., the amplitude of the oscillation must be neither increasing nor decreasing. It may be
necessary to make changes in the setpoint to induce oscillation.
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International Journal of Advanced Research in Electrical,
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(A High Impact Factor, Monthly, Peer Reviewed Journal)
Website: www.ijareeie.com
Vol. 8, Issue 4, April 2019
3. Record the value of Kp as the ultimate gain Ku.
4. Measure the period of the oscillation waveform. The period is the time (in seconds) for it to complete one cycle of
oscillation. This period is the ultimate period Tu.
IV. RESULT AND DISCUSSION
Ziegler Nichols Closed Loop Response for PID Controller for studying the performance of PI & PID Controllers as
shown in figure below for the temperature control system for Thermal Cycling system.
Fig 3 Step Response when Kp =40
Fig 4 Step Response when Kp =100
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ISSN (Online): 2278 – 8875
International Journal of Advanced Research in Electrical,
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(A High Impact Factor, Monthly, Peer Reviewed Journal)
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Vol. 8, Issue 4, April 2019
FiG 5 Oscillations when Kp =180
Fig 6 Step Response when Kp =200
Fig 7 Oscillations when Kp =200
The Values of KP, Ti and Td values of PID Controller is shown in below table are obtained by using the Ziegler
Nichols method. When Ku = 200, Pu = 0.0453 min.
Control
Kp Ti (min) Td (min)
type
P 100 - -
PI 90 0.038533333 -
PID 120 0.022666667 0.005893333
Table 1. The Values of Kp, Ti and Td values of PID Controller
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ISSN (Print) : 2320 – 3765
ISSN (Online): 2278 – 8875
International Journal of Advanced Research in Electrical,
Electronics and Instrumentation Engineering
(A High Impact Factor, Monthly, Peer Reviewed Journal)
Website: www.ijareeie.com
Vol. 8, Issue 4, April 2019
Fig 8 PID output of thermal cycler
V. CONCLUSION
In this paper the temperature process and the control strategy adopted is PID controller. The temperature controller was
identified based the simulation output curve of PI, PID responses respectively with this rise time, settling time, delay
time and maximum peak overshoot values. It is clear that the PID controller has the less settling time, delay time, rise
time and maximum peak overshoot when compared to the other controllers by using the transfer function model,
simulation of Proportional Integral Derivative controller was implemented.
This controller controls the temperature of the metal block and also maintains it while comparing with the other
controllers this PID controller enhances different tuning methods for sensing and controlling the temperature. In future,
we are planning to do the modifications in the control of temperature by controlling the Fan and by using different
controllers. By this we conclude that this method is efficient in maximum temperature tracking capability.
REFERENCES
[1] T.P.Mote, Dr.S.D.Lokhande, “Temperature Control System Using ANFIS”, International Journal of Soft Computing and Engineering (IJSCE)
ISSN: 2231-2307, Volume-2, Issue-1, March 2012.
[2] Melba Mary.P, Marimuthu N.S Albert Singh. N, “Design of Intelligent Self-Tuning Temperature Controller for Water Bath Process”,
International Journal of Imaging Science and Engineering (IJISE), ISSN: 1934-9955, VOL.1, NO.4,October 2007.
[3] "Getting in tune with Ziegler-Nichols," Thomas R. Kurfess, PhD, in the Academic Viewpoint column, Control Engineering magazine, Feb 2007
issue, p. 28, http://www.controleng.com/.
[4] The classic original paper: "Optimum settings for automatic controllers," J. B. Ziegler and N. B. Nichols, ASME Transactions, v64 (1942), pp.
759-768.
[5] A more recent survey that covers the Ziegler-Nichols and Kappa-Tau tuning rules: "Automatic Tuning of PID Controllers," Karl J. Åström &
Tore Hägglund, Chapter 52, The Control Handbook, IEEE/CRC Press, 1995, William S. Levine ed.
Copyright to IJAREEIE DOI:10.15662/IJAREEIE.2019.0804024 1296
