Abstract

The proportional-integral-derivative (PID) is still the most common controller and stabilizer used in industry due to its simplicity and ease of implementation. In most of the real applications, the controlled system has parameters which slowly vary or are uncertain. Thus, PID gains must be adapted to cope with such changes. In this paper, adaptive PID (APID) controller is proposed using the recursive least square (RLS) algorithm. RLS algorithm is used to update the PID gains in real time (as system operates) to force the actual system to behave like a desired reference model. Computer simulations are given to demonstrate the effectiveness of the proposed APID controller on SISO stable and unstable systems considering the presence of changes in the systems parameters.

Highlights

  • A challenging problem in designing a PID controller is to find its appropriate gain values [1]

  • In case where some of the system parameters or operating conditions are uncertain, unknown, or varying during operation, a conventional PID controller would not change its gains to cope with the system changes

  • recursive least square (RLS) algorithm is used as adaptation mechanism to tune the PID gains automatically online to force the actual process to behave like the reference model

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Summary

Introduction

A challenging problem in designing a PID controller is to find its appropriate gain values (i.e., proportional gain KP, integral gain KI, and derivative gain KD) [1]. An adaptive PID controller is presented in [10] using least square method which is an offline parameter estimation method. In [11] an online type of controller parameter tuning method is presented by utilizing RLS algorithm. It develops the standard offline fictitious reference iterative tuning FRIT method to be used as a modified estimation error for RLS algorithm. RLS algorithm is used as adaptation mechanism to tune the PID gains automatically online to force the actual process to behave like the reference model.

Problem Formulation
APID Controller Using RLS
Numerical Examples
Conclusions

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