PID Control Explained
Introduction to PID Control
Foreword:
Every electrical/electronic control system uses some form of feedback to govern the behavior of its output to the real-world processes it was meant to control. One of the main control systems used today is the PID Controller. The Proportional-Integral-Derivative (PID) controller is used virtually all over the world in industry, business, and even in the home.
Unfortunately, while explaining PID Control to non-technical audiences, the instructor or technical publication tends to move into mathematical formulas and technical jargon which does not help in the audiences’ understanding of PID Control.
This article was written in order to present basic PID theory to the non-technical reader while helping to refresh basic control theory used by engineers and technicians within their respective fields.
What is PID Control?
PID Control is a math based electronic control system which uses a closed-loop control system to modify and change its output to conditions of the system it was meant to control. The PID Controller uses sensors to feedback signals to itself so it may govern the applicable controlled system to a steady-state. The system being controlled may be a furnace, oven, motor, or any number of electrical/electronic devices. The widespread use of the PID Controller is due to its efficiency and relatively low costs. PID Control can be found in virtually every industry. The PID theory is applicable to every device made for heating, cooling, and even for material/liquid feed systems. PID Control was invented in the early 20th century to automate and mimic human control. In modern industry, PID Control is found in Programmable Logic Controllers (PLC), Supervisory Control and Data Acquisition systems (SCADA), OEM software control systems, heating/cooling stand-alone temperature controllers, and a host of other electronic/electrical control systems.
Typical Closed Loop Diagram
In the above example, an oven (G) is outputting a voltage that corresponds to the temperature within the oven.
An electronic device (H) converts/conditions the feedback signal for it to be received by an external control device. The difference between the Feedback Path signal and the Input signal is the error signal sent back to an oven’s internal temperature controller. PID control utilizes the same principles used in the above example.
Typical Miniature Control Systems utilizing PID control
(Courtesy Watlow Corporation)
Practical PID Theory Example:
In any process, there is a set-point (SP), a final numerical number that is what one hopes to achieve in a process. You set your thermostat to 68 F degrees in the summer and that is what you hope to achieve temperature-wise in your house during a hot summer day.
In any process, there is the process value (PV), that is what your thermostat is currently reading in your home as it tries to cool down to 68 F degrees during a hot summer day.
In any process there is the error (e), that is the difference between the process value and the set-point value (PV-SP). The error (e) value is what is of interest to the PID Controller.
Error (e) = Process value (PV) – Set-Point value (SP)
The PID controller will use mathematical functions to create a steady-state control of the temperature in your house. Most readers will notice that their cooling/heating system at home over-shoots in temperature or does not come on at your exact desired temperature. This is acceptable at home since it is only one or two degrees, but in scientific process and industry this is not acceptable in many cases. A steady-state control of temperature is desired.
Your home’s heating and cooling is what is called a simple “on-off” control system. The heating and cooling comes on when the error (e) is greater than 1 or 2 degrees. It will turn off when the error (e) is less than 1 or 2 degrees. But what if your heating/cooling system cannot react quickly enough and it overshoots/undershoots your desired temperature by 20 degrees. This is the problem with “on-off” control systems in some cases. In other cases this would cause big swings in temperature in your house known as “oscillations” in the controls system world.
Imagine too if your home’s cooling system could reach 68 F degrees quickly after coming home from work to a hot home. In many cases, you must wait hours for the home to cool. This would be unacceptable in industry, where time is money, and processes need the correct set-point value to operate.
What if you could never achieve your desired house temperature due your thermostat not acting on an error value less than say 10 degrees? This too would be unacceptable in industry.
PID Controller Theory with a Practical Example:
The PID controller uses a mathematical function called an algorithm and basic math to create the desired steady-state control system without oscillations or a high error (e) value. Below is the most common PID algorithm in use:
Let us refer back to cooling a home in the summer and the above PID algorithm:
Output represents the output voltage/signal of a PID control device, in this case, an output to the cooling fan’s motor-speed electronics box.
K (p) represents the error (e) value between the desired set-point temperature (SP) and actual temperature (PV) of the home. This is the “P” in PID.
K (I) represents how much time and how long the temperature error has persisted and how weak or strong of a controlling action is needed. This is the “I” in PID.
K (D) accounts for rate-of-change of the temperature in the house with the PID Controller in use. This is the “D” in PID.
So, as we can see with regards to the K (p) value, the greater the error (e) between the SP and PV, the greater the controlling action (Output). In this case, the greater/slower the speed of the cooling fan’s motor.
K (I) samples the error (e) every few seconds and adds or decreases to the Output value.
K (D) adds acceleration or deceleration to the Output value every second depending on how fast the temperature is changing in the house.
Examples of PID Controllers in Industry:
PID controllers are often used in industrial heating applications for furnaces along with process gas heating:
Here a PID controller would be installed with its output sending a control signal to a high power relay, which in-turn sends high voltage to the heater coils of a furnace or to a heat trace for heating process gas. The controller, once installed, would need to be programmed and tested in what is called “tuning” a PID based control system. This step is needed to create a steady-state control system, namely to prevent a control system that is too slow, too fast, or a control system that overshoots/undershoots the desired set-point (SP) value.
Furnace Programmable Logic Controller (PLC) and Human Machine Interface (HMI) Touch-Screen with PID Control
(Courtesy Thermcraft Corp.)
PID controllers are often used for pressure control:
Here a PID controller would use feedback signals from a pressure transducer to optimize pressure in a tank or pressure vessel. Quick reaction time and a stable set-point can be achieved using a PID controller. In addition, the system can be controlled automatically, reducing labor costs in having to hire someone to manipulate manual pressure control valves.
Compact Pressure PID Controller
(Courtesy Dwyer/Love Controls)
PID Controller Issues and Tuning issues:
PID controllers have come down in cost to where their value far outweighs the costs associated with their installation. Software PID control systems are commonly installed free-of-charge with most control systems software. Still, PID control systems do often cost more than simple on-off control systems.
The tuning of a PID controller can be difficult and time consuming. High thermal mass loads take a long time to heat and tend to overshoot in temperature during tuning. Multiple heating and cooling zone interactions on the same piece of equipment being commissioned, along with constantly changing ambient temperatures can also cause problems with tuning. Auto-tuning is common with PID controller manufacturers (OEMs), where tuning is done with a simple push-button procedure, in which the PID values are calculated and stored within the PID controller’s Read-Only Memory (ROM) automatically.
Unfortunately, auto-tuning is ineffective in many instances since it needs an oscillating or unstable system to calculate the correct PID values. High thermal mass loads do not cooperate well with auto-tuning in many cases.
Advanced PID control system schemes like cascading PID control loops take even more time to setup and can be difficult to optimize. Cascading loops use two PID Controllers, where one PID Controller actually controls the other PID Controller.
A control system is often unstable when commissioning new equipment using PID controllers. Start-up issues can often be minimized by following manual tuning techniques from the PID controller manufacturer. Using a simpler Proportional-Integral (PI) controller is often a solution and quite suitable in most cases. Here, the technician setting up the PID controller can set the derivative (D) value to zero to create PI-only control.
PID Control System Conclusions:
The PID Controller has found its way into virtually all industries around the world due to its simple and cost-saving features. Using PID control systems saves companies money in optimizing electrical usage in heating/cooling systems within many diverse industries. PID Control also optimizes processes, saving companies millions of dollars in production and labor costs by automating these processes. As with many things in the control design world, cost savings and industrial efficiency is the mother of invention. The PID controller has fulfilled its role in these two capacities many times over.