Convergence Analysis of Feedback Control with Integral Action and Discontinuous Relay Perturbation

Core Concepts

Analysis of convergence behavior in feedback control systems with integral action and relay perturbation.

Abstract

The content discusses the convergence analysis of third-order dynamic systems with integral feedback action and discontinuous relay disturbance. It focuses on motion systems with Coulomb-type friction, exploring stick-slip cycles and global stability. The system is proven to be globally asymptotically stable but not exponentially stable. Specific conditions for slowly converging stick-slip cycles are analyzed. The study provides numerical examples to illustrate the developed analysis.

Stats

Third-order dynamic systems considered.
Conditions for slowly converging stick-slip cycles analyzed.
Global asymptotic stability proven.
Exponential stability not achieved.
Specific parameters for system stability discussed.

Quotes

"We consider third-order dynamic systems which have integral feedback action and discontinuous relay disturbance."
"Global asymptotic stability (GAS) of a proportional-integral-derivative controlled system with relay-type Coulomb friction is given."
"The appearance of persistent stick-slip cycles can depend on whether the conjugate complex roots dominate over the real one."

Key Insights Distilled From

On convergence analysis of feedback control with integral action and discontinuous relay perturbation

by Michael Rude... at arxiv.org 03-18-2024

https://arxiv.org/pdf/2311.03724.pdf

Deeper Inquiries

How does the presence of Coulomb friction impact the convergence behavior in feedback-controlled systems?

Coulomb friction has a significant impact on the convergence behavior in feedback-controlled systems, particularly in motion control applications. The discontinuous nature of Coulomb friction introduces challenges such as stiction, where the system remains idle until a certain threshold is reached to overcome static friction and initiate motion. This leads to stick-slip cycles, where the system alternates between sticking (stiction) and slipping phases. These cycles can result in non-exponential convergence and oscillatory behavior in the system's response.

What are the implications of slowly converging stick-slip cycles on practical applications of motion control systems?

Slowly converging stick-slip cycles have several implications for practical applications of motion control systems:

Performance Degradation: Stick-slip cycles can lead to performance degradation by causing oscillations or delays in achieving desired positions or velocities.
Wear and Tear: The repetitive nature of stick-slip cycles can increase wear and tear on mechanical components due to frequent transitions between sticking and slipping states.
Energy Efficiency: Stick-slip behavior may result in energy inefficiencies as additional energy is required to overcome static friction during each sticking phase.
Control Complexity: Designing control strategies that effectively manage stick-slip phenomena adds complexity to controller development.

How can the findings in this study be applied to improve control strategies in mechatronic systems beyond motion control?

The findings from this study offer insights that can be applied to enhance control strategies in various mechatronic systems beyond just motion control:

Friction Compensation: Understanding how Coulomb friction impacts convergence behavior enables better compensation techniques like adaptive or robust controllers tailored for specific types of frictions.
System Stability Analysis: By analyzing stability properties under relay perturbations, similar methodologies could be extended to analyze other nonlinearities present in mechatronic systems for improved stability analysis.
Sliding Mode Control Enhancement: Insights into sliding mode principles used for handling discontinuities due to relays can be leveraged for developing more robust sliding mode controllers applicable across different mechatronic domains.
Optimal Control Strategies: Utilizing knowledge about slow-converging behaviors, optimal control strategies could be devised considering trade-offs between performance metrics like settling time, overshoot, and energy consumption.

These applications demonstrate how research on convergence analysis with integral action under relay disturbances extends beyond pure motion controls into broader areas within mechatronics requiring effective feedback mechanisms amidst nonlinear dynamics like Coulomb friction effects."