Design of event-based sliding mode controller with logarithmic quantized state measurement and delayed control update

Area of Science:

• Control Systems Engineering
• Robust Control Theory
• Networked Control Systems

Background:

• Perturbed linear time-invariant (LTI) systems require robust stabilization methods.
• Event-based control strategies aim to reduce communication load in control networks.
• Quantization and computational delays are practical challenges in implementing control laws.

Purpose of the Study:

• To develop an event-triggered sliding mode control (SMC) approach for robust stabilization of perturbed LTI SISO systems.
• To analyze the impact of quantization error and computational delay on system stability.
• To reduce communication traffic while ensuring robust stability.

Main Methods:

• Logarithmic quantization of state measurements.
• Event-triggered sliding mode control (SMC) design.
• Analysis of control computation scenarios with and without delay.
• Derivation of minimum inter-event execution time to avoid Zeno behavior.
• Determination of maximum delay bound for Zeno-free behavior and robust stability.

Main Results:

• The proposed event-based SMC ensures robust stability against external disturbances, quantization errors, and computational delays.
• A lower bound for minimum inter-event execution time was derived, guaranteeing Zeno-free behavior.
• A maximum delay bound was obtained to ensure Zeno-free behavior and robust stability of the closed-loop system.
• Simulations on a mechanical system validated the methodology's effectiveness.

Conclusions:

• The event-triggered SMC with quantized measurements offers a robust and efficient solution for stabilizing perturbed LTI systems.
• The approach effectively manages communication load while maintaining stability in the presence of practical implementation challenges like delay and quantization.
• The derived bounds provide crucial parameters for guaranteeing system performance and avoiding undesirable behaviors.