PID Controller
written by Janhvi Thombre, Prasad Tile, Siddhi Umbre, Sakshi Utwale & Varad Vanage
What is PID Controller?
PID is an acronym that stands for proportional-Integral-Derivative which are varied to achieve the greatest possible response. It is the control algorithm used in most of the industry and it has been accepted in industrial control universally. It can keep automated processes like temperature, pressure, or flow, constant for you automatically. PIDs use a control loop feedback device or process variable to monitor where the output should be. This usually comes in the form of sensors and meters.
History:
The PID controller’s history is as follows:
Elmer Sperry created the first PID controller in the year 1911. Following that, in the year 1933, TIC (Taylor Instrumental Company) executed a former pneumatic controller that was completely tunable. Control engineers eliminated the steady-state error observed in proportional controllers after a few years by returning the end to some false value until the error was not zero.
The proportional-Integral controller error was taken into account in this returning. In 1940, the very first pneumatic PID controller was created by using a derivative action in order to reduce overshooting issues.
Engineer Ziegler along with another engineer Nichols, both introduced tuning rules in year 1942 to discover and set appropriate parameters of PID controllers. Finally, by the mid-1950s, automatic PID controllers were widely used in industry.
Control System:
A PID controller works by reading a sensor and then calculating proportional, integral, and derivative responses and summing those three components to compute the desired actuator output. Before defining the parameters of PID controller, First we need to know a closed loop system and some of the terms related with it.
Closed loop System:
The process variable is the system parameter that needs to be controlled in a typical control system, such as temperature (oC), pressure (psi), or flow rate (liters/minute). A sensor measures the process variable and feeds back to the control system. In the case of a temperature control system, the set point is the desired or command value for the process variable, such as 100 degrees Celsius. The control system algorithm (compensator) uses the difference between the process variable and the set point at any given time to determine the desired actuator output to drive the system (plant). For example, if the measured temperature process variable is 100 oC and the desired temperature set point is 120 oC, the control algorithm’s actuator output may be to drive a heater. Driving a actuator to turn on the heater warms the system, resulting in an increase in the temperature process variable. As shown in the figure, we can see the system is with a closed loop control because the process of reading sensors to give const feedback and calculating the intended actuator o/p is repeated continuously as well as at a fixed loop rate.
PID Controller Block Diagram
A feedback control system is included in a closed-loop system such as a PID controller. This system generates an error signal by evaluating the feedback variable with a fixed point. It modifies the system output based on this. This procedure will be repeated until the error reaches zero, at which point the value of the feedback variable will be equivalent to a fixed point.
When compared to the ON/OFF type controller, this controller produces better results. To manage the system, only two conditions are available in the ON/OFF type controller. When the process value falls below the fixed point, the light turns on. Similarly, if the value exceeds a certain threshold, it will turn off. In this type of controller, the output is not stable, and it swings frequently in the fixed point region. However, when compared to the ON/OFF type controller, this controller is more stable and accurate.
Working of PID Controller
With a cheaper and simple ON-OFF controller, there are only two control states are possible: fully ON /fully OFF. It is used in finite control applications where these two control states are sufficient to achieve the control goal. Yet, because of oscillating behavior of this control, it is being replaced by PID controllers.
PID controller maintains the o/p by using closed-loop operations, so that there is no error between the process variable and setpoint/desired output . Three basic control behaviors of PID controller, they are described below.
P- controller
The proportional or P- controller produces an output proportional to the current error e (t). It compares the set point value or desired value to the feedback process value or actual value. The output is gained by multiplying the proportional constant with resulting error. This controller output is zero if the error value is zero.
When used alone, this controller necessitates biasing or manual reset. This is due to the fact that it never reaches a steady-state condition. It provides stable operation but always keeps the steady-state error constant. When the proportional constant Kc increases, so does the response speed.
I-Controller
Because the p-controller has a limitation in that there is always an offset between the process variable and the setpoint, an I-controller is required to provide the necessary action to eliminate the steady-state error. It integrates the error over time until the error value equals zero. It stores the value to the final control device where the error becomes zero.
When a negative error occurs, integral control reduces its output. I-controller slows down the response time as well as degrades the system stability. The response speed of the system is increased by decreasing integral gain, Ki.
In the figure above, as the gain of the I-controller decreases, so does the steady-state error. The PI controller is used in the majority of cases, especially when a fast response is not required.
When we use the PI controller, the output of I-controller is limited to a certain range in order to overcome integral wind up condition, in which integral o/p continues to increase even at the zero error due to the nonlinearities in the plant.
D-Controller:
The I-controller does not have the ability to predict error behavior in the future. As a result, when the setpoint is changed, it reacts normally. D-controller solves this problem by anticipating the error’s future behavior. Its output is determined by the rate of change of error over time multiplied by the derivative constant. It provides a jump start for the output, increasing system response.
In the above figure, the D controller has a higher response than the PI controller, and the output settling time is shorter. It improves system stability by compensating for phase lag caused by the I-controller. Increasing the derivative gain speeds up the response.
Finally, we discovered that by combining these three controllers, we can achieve the desired system response. PID algorithms are designed differently by different manufacturers.
PID Tuning Method
Tuning is the process of determining the corresponding PID parameter values to achieve the most optimal performance. This is obviously a critical component in all closed loop control systems.
A variety of tuning methods have been developed in order to achieve fast and acceptable performance.
These methods involve experimentally determining the dynamic characteristics of the control loop and estimating the controller tuning parameters that produce the desired performance for the determined dynamic characteristics.
Application of PID :
- Driving unmanned vehicle.
- Flying Drones.
- Temperature Control.
Conclusion:
PID controllers are fundamental tools in control systems engineering, offering precise regulation and stability for various processes. Throughout this comprehensive guide, we have explored the inner workings of PID controllers, their components (Proportional, Integral, and Derivative terms), and the principles behind their operation.
Proportional control provides immediate response, while integral control addresses steady-state errors, and derivative control mitigates rapid changes. Understanding their characteristics and tuning methods is essential for achieving optimal performance.
Authors:
Vishwakarma Institute of Technology, Pune.
Janhvi Thombre,
Prasad Tile,
Siddhi Umbre,
Sakshi Utwale,
Varad Vanage.
