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Proportional-Integral-Derivative (PID) controllers are widely used in various control systems to enhance stability and performance. In a thermostat, it adjusts heating or cooling based on the temperature difference between the actual and desired levels. They are often used in automotive speed systems, effectively managing sudden speed changes while maintaining a constant speed under varying conditions. On the other hand, PI controllers, commonly employed in voltage regulation, enhance stability...
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An optimal PID controller via LQR for standard second order plus time delay systems.

Saurabh Srivastava1, Anuraag Misra1, S K Thakur1

  • 1Variable Energy Cyclotron Center, 1/AF, Bidhan Nagar, Kolkata 700064, India.

ISA Transactions
|December 15, 2015
PubMed
Summary

This study introduces an improved PID controller tuning method for second-order plus time delay systems. The new approach enhances closed-loop time response and reduces control effort compared to existing LQR-based methods.

Keywords:
Closed-loopLinear Quadratic Regulator (LQR)Linear systemPID controllerSystem matrixTime delay

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Area of Science:

  • Control Systems Engineering
  • Process Control
  • Automation

Background:

  • Standard second-order plus time delay (SOPTD) systems present challenges in controller tuning.
  • Existing Linear Quadratic Regulator (LQR) based Proportional-Integral-Derivative (PID) tuning methods have limitations in performance and control effort.

Purpose of the Study:

  • To develop an improved tuning methodology for PID controllers applied to SOPTD systems.
  • To achieve desired performance measures through a novel combination of LQR and pole placement techniques.

Main Methods:

  • A new tuning methodology integrating Linear Quadratic Regulator (LQR) and pole placement is proposed.
  • The time delay component of SOPTD systems is addressed within the controller output equation, not the characteristic equation.
  • Simulations were conducted on various system types: stable open-loop oscillatory, over-damped, critically-damped, and unstable open-loop systems.

Main Results:

  • The proposed methodology demonstrates improved closed-loop time response compared to existing LQR-based PID tuning.
  • Reduced control effort is achieved with the new tuning approach.
  • Effectiveness was validated across diverse SOPTD system configurations.

Conclusions:

  • The developed PID controller tuning method offers superior performance for SOPTD systems.
  • The integration of LQR and pole placement provides an effective way to handle time delays in controller design.
  • The study also discusses the impact of non-dominant poles on controller stability and robustness.