PI Contoller

Introduction

The PI controller (Proportional-Integral Controller) is one of the most widely used feedback control systems in industrial settings.

Theory

 PID Controller 구조

  PID Controller의 수학적 표현은 다음과 같다.

PID Controller Equation

   u(t): Output

   e(t): Error Signal

   Kp: Proportional Gain

   Ki: Integral Gain

   Kd: Derivative Gain

 

  PID Controller의 Block diagram은 다음과 같다.

PID Controller Block diagram

 

 The PI Controller is a form of the PID Controller without the D (Derivative) term.

 The differential term is a control that adjusts the input for the rate of change.

If the input contains a lot of noise components, the rate of change becomes distorted, which makes the design of the controller using the differential term difficult.

PI Controller 장점

1) Steady-state error elimination: The integral term compensates for the accumulation of error over time, thereby eliminating steady-state error.

2)  Fast response: Provides faster response time than proportional control.

3)  Stability: Provides more stable control than PI controller.

4)  Simple implementation: Relatively simple to implement and tune compared to PID controller.

Example

 

Simulation Circuit

Step input & Output

 

Dampling ration(zeta) 에 따른 response가 다른 것을 알 수 있다. 

 

RLC Circuit을 response를 Python Spyder를 사용하여 plot했다.

RLC Circuit

Python Spyder Code

Python plot

Reference

[Modern Control Systems], Ricard C. Dorf, Robert H. Bishop