PID controller theory
WHAT IS PID CONTROLLER?
It uses a control loop feedback mechanism to control process variables and is the most accurate and controlled.
PID control is a well-known method for guiding a system to a desired location or level. It's almost ubiquitous as a temperature controller, with applications in a wide range of chemical and scientific operations, as well as automation. PID control employs closed-loop control feedback to maintain a process's real output as close as feasible to the target or setpoint output.
Digital PID controller
A digital PID controller receives the sensor data, which is typically from a thermocouple or RTD, and converts it to engineering units like degrees Fahrenheit or degrees Celsius, which are then presented in a digital format.
Block diagram of PID controller
Working of PID Controller
Typically, PID controllers work by adjusting or tuning proportional, integral, or derivative terms. Input signals are evaluated, and part of the difference is fed back to the device as a feedback control signal. This value is called the correction factor.
In the generalized form, the PID controller maintains the output such that there is zero error between the process variable and setpoint/ desired output by closed-loop operations.
P- Controller
The output of a proportional or P-controller is proportional to the current error
e(t). Using the feedback process, it compares the desired or set point to the actual value. The output is obtained by multiplying the error by a proportional constant. If the error value is zero, then this controller output is zero.
It requires biasing or manual reset when used alone. This is because it never reaches a steady state. However, it maintains steady-state errors. When the proportional constant Kc increases, the response speed increases.
Due to the limitation of the p-controller where there always exists an offset between the process variable and setpoint, I-controller is needed, which provides necessary action to eliminate the steady-state error. It integrates the error over a period of time until the error value reaches zero. It shows the value of the final control device at which the error is zero.
I-controller doesn’t have the capability to predict the future behavior of error. So it reacts normally once the setpoint is changed. D-controller overcomes this problem by anticipating the future behavior of the error. Its output depends on the rate of change of error with respect to time, multiplied by the derivative constant. It gives the kick start for the output thereby increasing system response.
It requires biasing or manual reset when used alone. This is because it never reaches a steady state. However, it maintains steady-state errors. When the proportional constant Kc increases, the response speed increases.
I-Controller
Due to the limitation of the p-controller where there always exists an offset between the process variable and setpoint, I-controller is needed, which provides necessary action to eliminate the steady-state error. It integrates the error over a period of time until the error value reaches zero. It shows the value of the final control device at which the error is zero.
D-Controller
I-controller doesn’t have the capability to predict the future behavior of error. So it reacts normally once the setpoint is changed. D-controller overcomes this problem by anticipating the future behavior of the error. Its output depends on the rate of change of error with respect to time, multiplied by the derivative constant. It gives the kick start for the output thereby increasing system response.
by summing of all the controllers, we can get one generalized equation
where,
 | = | PID control variable |
 | = | proportional gain |
 | = | error value |
 | = | integral gain |
 | = | change in error value |
 | = | change in time |
From this equation, we can find out the process variable and solve the error.
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