A Theory for Sparse Event-Based Closed Loop Control.

Area of Science:

• Control Engineering
• Dynamical Systems Theory
• Signal Processing

Background:

• Discrete time controllers are essential for dynamic systems, but selecting the optimal sampling time presents a trade-off between accuracy and computational load.
• Traditional time-based control can be energetically inefficient as it updates the control law even after the setpoint is reached.
• Event-based control, like send-on-delta, offers potential energy savings but requires careful tuning to balance accuracy and update frequency.

Purpose of the Study:

• To propose a novel non-linear event-based discretization method for digital control systems.
• To demonstrate the method's ability to achieve arbitrary accuracy independently of setpoint amplitude.
• To show the method's effectiveness in reducing computational load and improving energy efficiency.

Main Methods:

• Development of a non-linear event-based discretization technique based on inter-event durations.
• Analysis of the method's performance in terms of accuracy, computational requirements, and energy efficiency.
• Comparison with traditional time-based and existing event-based control strategies.

Main Results:

• The proposed method achieves arbitrary accuracy for controlled outputs, irrespective of the setpoint amplitude.
• It significantly reduces the number of samples required to estimate system states and the actuator update rate.
• Energy efficiency is improved by minimizing unnecessary control updates without increasing network bandwidth.

Conclusions:

• The novel inter-event duration-based non-linear event-based discretization offers a more energy-efficient approach to digital control.
• This method provides a robust solution for achieving high accuracy in dynamic systems with reduced computational and energy costs.
• The findings suggest a promising direction for designing efficient and accurate digital control systems.