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Time-Domain Interpretation of PD Control01:07

Time-Domain Interpretation of PD Control

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Proportional-Derivative (PD) control is a widely used control method in various engineering systems to enhance stability and performance. In a system with only proportional control, common issues include high maximum overshoot and oscillation, observed in both the error signal and its rate of change. This behavior can be divided into three distinct phases: initial overshoot, subsequent undershoot, and gradual stabilization.
Consider the example of control of motor torque. Initially, a positive...
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PD Controller: Design01:26

PD Controller: Design

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In automotive engineering, car suspension systems often employ Proportional Derivative (PD) controllers to enhance performance. PD controllers are utilized to adjust the damping force in response to road conditions. A controller, acting as an amplifier with a constant gain, demonstrates proportional control, with output directly mirroring input.
Designing a continuous-data controller requires selecting and linking components like adders and integrators, which are fundamental in Proportional,...
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Frequency-Domain Interpretation of PD Control01:24

Frequency-Domain Interpretation of PD Control

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Proportional-Derivative (PD) controllers are widely used in fan control systems to improve stability and performance. A fan control system can be effectively represented using a Bode plot to illustrate the impact of a PD controller through its transfer function. The Bode plot visually conveys how PD control modifies the fan's response across various frequencies, providing a frequency domain interpretation of the controller's behavior.
The proportional control gain, combined with the...
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PI Controller: Design01:24

PI Controller: Design

656
Proportional Integral (PI) controllers are a fundamental component in modern control systems, widely used to enhance performance and mitigate steady-state errors. They are particularly effective in applications such as automatic brightness adjustment on smartphones, where they excel at mitigating steady-state errors for step-function inputs. Unlike PD controllers, which require time-varying errors to function optimally, PI controllers leverage their integral component to address residual...
656
Time and frequency -Domain Interpretation of PI Control01:27

Time and frequency -Domain Interpretation of PI Control

234
Proportional-Integral (PI) controllers are essential in many control systems to improve stability and performance. They are commonly used in everyday devices like thermostats to enhance system damping and reduce steady-state error. When the zero in the controller's transfer function is optimally placed, the system benefits significantly in terms of stability and accuracy.
Acting as a low-pass filter, the PI controller slows the system's response and extends settling times. This requires...
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PID Controller01:19

PID Controller

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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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Related Experiment Video

Updated: Oct 25, 2025

WheelCon: A Wheel Control-Based Gaming Platform for Studying Human Sensorimotor Control
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PD-Based Optimal ADRC with Improved Linear Extended State Observer.

Zhen Zhang1, Jian Cheng2, Yinan Guo1,3

  • 1School of Information and Control Engineering, China University of Mining and Technology, Xuzhou 221116, China.

Entropy (Basel, Switzerland)
|August 6, 2021
PubMed
Summary
This summary is machine-generated.

This study introduces an improved active disturbance rejection optimal controller (ADRC) that enhances control performance by addressing dead-zone nonlinearity and external disturbances using particle swarm optimization (PSO). The new controller demonstrates superior dynamic and steady-state control.

Keywords:
active disturbance rejection controlimproved extended state observerparticle swarm optimizationproportional-derivative

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Area of Science:

  • Control Systems Engineering
  • Nonlinear Control Theory
  • Optimization Algorithms

Background:

  • Traditional control systems struggle with dead-zone nonlinearities and external disturbances, impacting dynamic and steady-state performance.
  • Existing active disturbance rejection control (ADRC) methods can be complex and may not fully address these challenges.
  • Particle swarm optimization (PSO) offers a robust method for parameter tuning in complex systems.

Purpose of the Study:

  • To develop an efficient and practical active disturbance rejection optimal controller.
  • To improve both dynamic and steady-state control performances in systems with dead-zone nonlinearity and external disturbances.
  • To simplify the control design by integrating proportional-derivative (PD) control law into ADRC.

Main Methods:

  • A 2nd-order system model was established after compensating for dead-zone nonlinearity.
  • A proportional-derivative (PD) control law replaced the traditional state error feedback in ADRC.
  • An improved linear extended state observer was designed to enhance disturbance estimation.
  • Particle swarm optimization (PSO) was employed to optimize controller parameters using a defined objective function.

Main Results:

  • The proposed controller effectively compensates for dead-zone nonlinearity and external disturbances.
  • The improved linear extended state observer demonstrated enhanced disturbance estimation capabilities.
  • PSO-optimized parameters significantly improved the overall control performance.
  • Ten comparative experiments validated the controller's effectiveness and superiority over existing methods.

Conclusions:

  • The novel active disturbance rejection optimal controller offers a practical and efficient solution for systems with dead-zone nonlinearity and external disturbances.
  • The integration of PD control, an improved LESO, and PSO optimization leads to superior dynamic and steady-state control.
  • This approach provides a valuable advancement in control system design for challenging industrial applications.