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to Basics in process control
Closing the loop in PID Control Systems
Carl Ljungholm, Control Engineer, National Instruments
Despite recent advances in control theory into adaptive, predictive and optimal
control, the most widely controller remains the PID controller. Its success can
be explained by characteristics such as simplicity and good results in many
applications. What are the basic principles behind the use of PID controller?
How does a PID controller work? Some considerations for implementing a PID
controller by Control Engineer Carl Ljungholm of National Instruments.
Take the example of the flow rate of a fluid running through a pipe. The fluid
in the pipe represents the plant or system we want to control and the process
variable is the flow rate we want to control. The plant is controlled by a
compensator consisting of a PID controller and an actuator, in this case a
valve. The PID controller outputs a signal that opens or closes the valve. The
opening and closing of the valve affects the flow rate through the pipe. The
valve position is the compensator output. Finally, we need a sensor to measure
the flow rate in the pipe so the measurement is fed back and compared to the
desired flow rate or set point (figure 1)
Open- and Closed Loop
Feedback distinguishes a closed loop system from an open-loop system. An
open-loop control system is similar to trying to walk across a room
blind-folded. With out the blind-fold we get feedback from our surroundings
creating a closed loop system. Also present in the system are disturbances in
the form of leaks or variations in the supply pressure. We want the process
variable, the flow rate, to depend only on the set point while ensuring the
disturbances have no affect on results. Closed-loop systems can reject
disturbances by measuring the output. The comparison of the set point with the
current value of the process variable gives the error. The goal of the control
system is to make the error zero. (Figure 2)
In a PID controller this is done through the combination of its three terms:
proportional, integral and derivative. The first term is the proportional term,
which produces a signal that is proportional to the error. The valve is opened
if the flow rate is too small and is closed if the flow rate is too high.
Increasing the proportional gain generally increases the performance of the
control system. As the proportional gain increases, the response to change in
the input becomes faster while the affect of a disturbance decreases. However, a
gain that is too high will make the system unstable.
The integral term sums the error over time. The output from the controller is
only constant if the error is zero. Therefore, the integral term continues to
adjust the actuator until there is zero error. The integral is useful for
rejecting disturbances. Decreasing integral time (Ti) increases the rate at
which the system reacts to a disturbance. Too small of an integral time will
give overshoot, which occurs when the controller over adjusts the output after a
change in the set point. The process variable temporarily exceeds the set point
before settling in. A small amount of overshoot is often desirable as it will
give a faster response to a change in the set point.
The last term is the derivative. If the output of the system is approaching the
set point quickly, then the derivative term reduces the signal to the actuator.
Increasing the derivative time (Td) tends to make a system more stable and
reduce overshoot. However, in practice, the range for the derivative term is
limited due to the amplified noise in the measurement of the output variable. A
filter can remove the high frequencies noise from the measured signal.
Implementing a PID controller
Determining the parameters of the PID is only a small part of implementing a
control system. We must also measure the process variable, output a control
signal, and evaluate the PID calculation. Even a poorly implemented PID
controller can increase quality and yield in a production process, but to get
the full advantage, we must consider the way it is implemented. The performance
of the PID controller is affected by the chosen loop rate in addition to the
accuracy of the measurement, calculation and controller output.
The first step in implementing the PID controller is determining an appropriate
loop rate. Most control systems are discrete, meaning they measure the process
variable and update their outputs at a fixed rate. The output remains constant
in between updates. Although a faster loop rate has better performance, it also
requires more expensive hardware. The necessary loop rate depends on how quick
the system responds to changes. For example, a large tank that takes several
minutes to undergo a temperature change requires a slow loop rate compared to
the loop rate speed necessary to control an unstable airplane. A rule of thumb
is that the rate of the controller should be ten to fifteen times faster than
the time constant of the system. Increasing the loop rate beyond this will not
significantly increase the performance of the system. For many industrial
processes the required loop rate is less than 100 Hz.
Accuracy in the process measurement variable, PID calculation, and output of the
compensator is also an important consideration. A sensor will measure the
process variable and output a voltage, current or pulse-width modulated signal
that can be measured by the controller. Both the accuracy of the sensor as well
as the accuracy of the measurement is important, since control systems cannot
adjust for errors in the measurement of the process variable. The precision of
the measurement is, in part, measured in bits. An 8 bit measurement will only
allow the controller to distinguish between 256 different levels of the process
variables, where as a 16 bit measurement will give over 65,000 levels. The same
applies to the output of the controller. A small resolution on the output will
limit the compensators ability to precisely control the plant. Finally the
accuracy of the measurement must be maintained in the PID calculations. A
floating point processor is ideal for doing the calculations needed for PID
control. A fixed point processor can be used, but care must be taken to preserve
the accuracy.
PC based control systems
PC based control systems allow for a more capable control system. Higher
loop rates are now possible, multiple PID loops can run on the same controller,
and precision of measurements have increased. The cost of both analog input and
output has dropped as much as 70%. Higher precision measurements, while once too
costly to ascertain, are now affordable. As a result, 8 bit measurements are no
longer considered adequate, and 12 and 16 bit measurements are becoming
increasingly common. Control systems are also performing tasks beyond strict
control. For example, a control system can now do data logging which can later
verify that the process is operating within the limits. Additionally, it can
tune the PID loop or to predict maintenance. Having the same hardware performing
both control and data logging reduces the cost of the overall system.
However, in industrial environments the PC may not be adequately rugged. PLCs
have the required ruggedness, but do not have the flexibility and functionality
of a PC. The new Programmable Automation Controllers (PACs) emerged to combine
the benefits of a PC with the benefits of a PLC. PACs integrate the ruggedness
and durability of a PLC, with the analysis and measurement capabilities of a PC
making PACs ideal for industrial control applications.
A closed loop control system can increase quality and yield from a production
line, by maintaining operation conditions at a desired set point. The PID
controller is the most common controller, because it is simple and produces good
results in most situations. The output of the PID controller is defined by three
terms: proportional, integral and derivative. When implementing a PID control
system, chosen hardware must maintain the necessary loop rate, and produce
adequate precision measurements and calculations. <<
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