The document discusses various types of controllers used in industrial control applications. It describes PI, PD, and PID controllers, which use proportional, integral, and derivative terms to adjust the control signal. Ziegler-Nichols and Cohen-Coon tuning methods are presented for optimizing controller parameters. Both analog and digital implementations of PID controllers are discussed.

1. Chapter:4
Controller tuning
Suvendu Mondal
AP,EED, SurTech
20-04-2023 SurTech, JIS, DumDum 1

2. PI controller
• A PI controller, also known as a proportional-integral controller, is a type of feedback control system
commonly used in industrial control applications. It is a type of controller that uses two terms to
adjust the control signal: the proportional term and the integral term.
• The proportional term in a PI controller produces an output that is proportional to the error
between the desired set point and the actual process variable. The integral term in a PI controller
produces an output that is proportional to the integral of the error over time. The sum of these two
terms forms the output of the controller, which is used to adjust the control signal to the process.
• The proportional term in the PI controller helps to reduce the steady-state error, while the integral
term helps to reduce the transient error. The PI controller is widely used in various industrial
applications such as temperature control, pressure control, and speed control.
• The PI controller can be tuned to achieve optimal performance by adjusting the values of the
proportional gain (Kp) and the integral gain (Ki). The values of Kp and Ki can be adjusted to achieve
the desired response of the control system, such as minimizing overshoot, reducing settling time,
and improving stability.
• In summary, the PI controller is a widely used feedback control system that uses two terms, the
proportional term and the integral term, to adjust the control signal. It is commonly used in
industrial control applications and can be tuned to achieve optimal performance by adjusting the
values of the proportional gain and integral gain.
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3. PD controller
• A PD controller, also known as a proportional-derivative controller, is a type of feedback control system that
uses two terms to adjust the control signal: the proportional term and the derivative term.
• The proportional term in a PD controller produces an output that is proportional to the error between the
desired set point and the actual process variable, similar to the PI controller. The derivative term in a PD
controller produces an output that is proportional to the rate of change of the error over time. The sum of
these two terms forms the output of the controller, which is used to adjust the control signal to the process.
• The derivative term in a PD controller helps to predict and anticipate the future error, which can be used to
adjust the control signal before the error occurs. This can help to reduce the overshoot and settling time in the
control system, resulting in faster and more accurate control.
• PD controllers are commonly used in industrial control applications, particularly in systems where fast response
and precise control are required, such as in robotics, motors, and servo systems.
• The PD controller can be tuned to achieve optimal performance by adjusting the values of the proportional gain
(Kp) and the derivative gain (Kd). The values of Kp and Kd can be adjusted to achieve the desired response of
the control system, such as minimizing overshoot, reducing settling time, and improving stability.
• In summary, the PD controller is a feedback control system that uses two terms, the proportional term and the
derivative term, to adjust the control signal. It is commonly used in industrial control applications where fast
response and precise control are required, and can be tuned to achieve optimal performance by adjusting the
values of the proportional gain and derivative gain
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4. PID controller
• A PID controller, also known as a proportional-integral-derivative controller, is a type of feedback control system
that uses three terms to adjust the control signal: the proportional term, the integral term, and the derivative
term.
• The proportional term in a PID controller produces an output that is proportional to the error between the
desired setpoint and the actual process variable, similar to the PI controller. The integral term produces an
output that is proportional to the integral of the error over time, and the derivative term produces an output
that is proportional to the rate of change of the error over time.
• The sum of these three terms forms the output of the controller, which is used to adjust the control signal to
the process. The proportional term provides a rapid response to changes in the error, while the integral term
helps to reduce the steady-state error, and the derivative term helps to reduce the overshoot and settling time
in the control system.
• PID controllers are commonly used in various industrial control applications, such as temperature control,
pressure control, and speed control, as well as in robotics and automation systems.
• The PID controller can be tuned to achieve optimal performance by adjusting the values of the proportional
gain (Kp), the integral gain (Ki), and the derivative gain (Kd). The values of Kp, Ki, and Kd can be adjusted to
achieve the desired response of the control system, such as minimizing overshoot, reducing settling time, and
improving stability.
• In summary, the PID controller is a feedback control system that uses three terms, the proportional term, the
integral term, and the derivative term, to adjust the control signal. It is commonly used in industrial control
applications and can be tuned to achieve optimal performance by adjusting the values of the proportional gain,
integral gain, and derivative gain
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5. Ziegler-Nichols tuning method
• The Ziegler-Nichols tuning method is a popular and widely used technique for tuning PID controllers.
It was proposed by John G. Ziegler and Nathaniel B. Nichols in the 1940s and is also known as the
ultimate gain method.
• The Ziegler-Nichols tuning method involves a step response test in which a step change is made to
the setpoint of the control system and the resulting response of the system is observed. Based on
the response, the ultimate gain and ultimate period of the system are determined.
• The ultimate gain (Ku) is the gain at which the system starts to oscillate continuously, and the
ultimate period (Tu) is the period of oscillation at that gain. From these values, the controller gains
(Kp, Ki, and Kd) can be calculated using the following rules:
• Proportional gain (Kp) = 0.6*Ku
• Integral gain (Ki) = 1.2*Ku/Tu
• Derivative gain (Kd) = 0.075KuTu
• Once the gains are calculated, the controller can be tested again to verify its performance and
adjusted if necessary.
• The Ziegler-Nichols tuning method is a simple and effective method for tuning PID controllers, but it
has some limitations. It is primarily suited for systems with a single dominant time constant and can
result in overshoot and instability in some systems. Therefore, it is important to verify the
performance of the controller after tuning and make adjustments as necessary.
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6. Cohen coon tuning method
• The Cohen-Coon tuning method is another popular technique for tuning PID controllers. It was
proposed by G.C. Cohen and D.W. Coon in 1953 and is based on the process reaction curve of the
system.
• The Cohen-Coon tuning method involves a step response test in which a step change is made to the set
point of the control system and the resulting response of the system is observed. Based on the
response, the process parameters of the system are determined, including the process gain (Kp) and
the process time constant (Tp).
• The controller gains (Kp, Ki, and Kd) can then be calculated using the following equations:
• Proportional gain (Kp) = (1.35*Tp)/Kp
• Integral time (Ti) = 2.5*Tp
• Derivative time (Td) = 0.37*Tp
• Once the gains are calculated, the controller can be tested again to verify its performance and adjusted
if necessary.
• The Cohen-Coon tuning method is a relatively simple and effective method for tuning PID controllers,
but it can result in overshoot and instability in some systems. Therefore, it is important to verify the
performance of the controller after tuning and make adjustments as necessary. It is also important to
note that this method assumes that the system has a first-order plus dead-time (FOPDT) response,
and may not be suitable for more complex systems.
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7. Implementation of PID controllers (digital and
analog)
• PID controllers can be implemented using both digital and analog circuits,
depending on the application and system requirements.
• Analog PID Controller: Analog PID controllers use operational amplifiers
and other analog components to implement the PID algorithm. Analog PID
controllers are widely used in process control systems, where high-speed
and high-precision control is required.
The analog PID controller circuit consists of three amplifiers, each connected
to the proportional, integral, and derivative signals. The input signal is first
amplified and then split into three branches, each with its gain controlled by
the proportional, integral, and derivative gain coefficients. The outputs from
the three branches are then added together and fed into the plant. The
output from the plant is then fed back to the controller as feedback, which is
used to adjust the control signal.
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8. Implementation of PID controllers (digital and
analog)
• Digital PID Controller: Digital PID controllers use microcontrollers or digital
signal processors (DSPs) to implement the PID algorithm. Digital PID controllers
are widely used in control systems that require flexible and programmable
control algorithms.
• The digital PID controller circuit consists of a microcontroller or DSP, which runs
the PID algorithm using the feedback signal and set point. The microcontroller
or DSP uses digital computation to calculate the control signal based on the
proportional, integral, and derivative terms. The control signal is then output to
a digital-to-analog converter (DAC), which converts the digital signal to an
analog signal that can be used to control the plant.
• The advantage of a digital PID controller over an analog controller is the ability
to easily change the PID algorithm by modifying the software. Additionally,
digital PID controllers can handle complex control algorithms and advanced
control strategies, which may not be possible with analog controllers.
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9. Implementation of PID controllers (digital and
analog)
• In summary, PID controllers can be implemented using both analog
and digital circuits, depending on the application and system
requirements. Analog PID controllers use operational amplifiers and
other analog components, while digital PID controllers use
microcontrollers or DSPs. The choice of implementation depends on
factors such as accuracy, speed, complexity, and flexibility of the
control system.
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