Design of PID Controller used Ziegler-Nichols technique (Robust Control)

Abstract

This paper studies the design of a proportional-differential-integral (PID) control for position control system using the Ziegler-Nichols (Z-N) Method.

The study begins with a complete presentation of the mathematical model of the PID control, and a presentation of the scientific steps followed in the design theory of the Ziegler-Nichols Method, then the practical application of the theory using the mathematical model of a laser manipulator that uses a DC motor Laser Manipulator Control System Where the laser can be used to drill the hip socket to insert the artificial hip joint appropriately, and the use of laser in surgery requires high accuracy in response to location and speed, and this is what the proportional-differential-integral controller works on.

The design steps using the Ziegler-Nichols Method are summarized in calculating the forward path gain Kp using the Routh method and equating the forward path gain coefficient Kp with the coefficient Kcr and substituting the coefficient Kcr in the characteristic equation to obtain Pcr. Through the table, by estimating the Ziegler-Nichols Theory, we calculate the three proportional-differential-integral controller factors Tp, Ti and Td, which determine the response of the system that was designed.

The practical part of the paper uses MATLAB to program and simulate the control system design, and to extract and analyze the results.

Study Objectives

1- Study and design of a proportional-differential-integral (PID) control to control the position control system using the Ziegler-Nichols Method.

2- Practical application of the theory on the mathematical model of a laser manipulator using a DC motor Laser Manipulator Control

3- Calculate the PID controller factors (Tp, Ti and Td), which determine the response of the designed system.

4- Use MATLAB to program and simulate the design of the control system