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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.
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Robust adaptive control for uncertain nonlinear systems with odd rational powers, unmodeled dynamics, and

Zhen-Guo Liu1, Wei Sun2, Weidong Zhang3

  • 1School of Automation and Software Engineering, Shanxi University, Taiyuan 030006, China; Department of Automation, Shanghai Jiao Tong University, Shanghai, 200240, China.

ISA Transactions
|November 29, 2021
PubMed
Summary

This study introduces a novel adaptive controller for complex high-order nonlinear systems, addressing challenges like odd rational powers and unmodeled dynamics. The new method simplifies parameter estimation for improved control performance.

Keywords:
Adding a power integrator approachNeural networkNonlinear systemsUnmodeled dynamics

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Area of Science:

  • Control Engineering
  • Nonlinear System Theory
  • Applied Mathematics

Background:

  • Existing control methods are limited to low-order, triangular nonlinear systems.
  • Practical systems often exhibit high-order, non-triangular structures with odd rational powers and unmodeled dynamics.
  • Control of such complex systems remains a significant challenge.

Purpose of the Study:

  • To develop an adaptive control strategy for high-order nonlinear systems with odd rational powers, unmodeled dynamics, and non-triangular structures.
  • To reduce the reliance on parameter estimations in adaptive control for these challenging systems.
  • To demonstrate the effectiveness of the proposed controller through simulation.

Main Methods:

  • Utilized the small-gain theorem as a foundational principle.
  • Employed adaptive control techniques combined with the adding a power integrator method.
  • Integrated neural network methods to enhance control capabilities.
  • Developed a novel adaptive controller with reduced parameter estimation requirements.

Main Results:

  • Successfully designed a new adaptive controller for a challenging class of nonlinear systems.
  • The controller effectively handles high-order dynamics, odd rational powers, unmodeled dynamics, and non-triangular structures.
  • Significantly decreased the number of parameter estimations needed for adaptive control.
  • Validated the controller's performance in regulating complex systems, achieving satisfactory responses.

Conclusions:

  • The proposed adaptive control strategy offers a viable solution for complex nonlinear systems previously difficult to control.
  • The integration of small-gain theorem, adaptive techniques, power integrators, and neural networks provides a robust framework.
  • This approach advances the field of adaptive control for high-order, non-triangular systems with practical uncertainties.