Effects of Proportional Integral Controller with Equation
A proportional-integral controller is a feedback control system component with an equation Co(t) = Kp . e(t) + Ki . ∫ e(t) dt , combining proportional band integral action. The proportional component responds to the current error, while the integral component accumulates past errors to eliminate steady-state errors. Properly tuning the Kp and Ki gains is crucial to achieve stable control with fast response and minimal error in various engineering applications. The PI controller diagram illustrates its functioning with error input, proportional, integral actions and the output controlling a process.
The system equation with the PI controller is
M(s)/E(s) = Kp. {1 + (1/s.Ti)} from equation no(2). so,
M(s)= Kp. {1 + (1/s.Ti)} . E(s)
Here M(s) is equal of the system , and E(s) is the error signal.
The error signal E(s) is difference between the reference input (R(s)) and the system output (Y(s)):
E(s) – R(s) – Y(S)
Now, let’s substitute the expression for E(s) into the equation for M(s)
M(s) = Kp{1 + (1/s.Ti)} (R(s) – Y(s))
The output (Y(s)) of the system can be expressed as the product of the plant transfer function (G(s)) and the controller output C(s) :
Y(s) = G(s).C(s)
Now, let’s substitute this expression for Y(s) into the equation
M(s) = Kp{1 + (1.s.Ti)}(R(s) – G(s).C(s))
Proportional Integral Controller – Control System
The proportional controller commonly known as PI controller is an essential part of the Industrial Automation and Control system. It is a closed-loop feedback control mechanism that aims to adjust the process variable by manipulating the variable based on the error between the setpoint and the process variable. It strikes a balance between quick response to deviations and long-term error elimination. Tuning the controller allows adjustment to meet the desired value.
Table of Content
- Definition
- Equation and Diagram
- Block Diagram
- Effects
- Tuning
- Applications
- Advantages and Disadvantages
- Comparison with Other Types of Controllers