Some Reflections on Sliding Mode Designs in Control Systems: An Example of Adaptive Tracking Control for Simple Mechanical Systems With Friction Without Measurement of Velocity

TL;DR

This paper critically evaluates sliding mode (SM) designs in control, arguing that many SM approaches rely on steps that weaken system structure and introduce chattering, with limited practical guidance. Through analysis of SM examples in mechanical regulation, glucose regulation, and magnetic levitation, the authors illustrate challenges in boundedness assumptions, disturbance handling, and tuning, questioning real-world relevance. They then compare two velocity-free adaptive tracking strategies for a $1$-DoF mechanical system with friction: an Immersion-and-Invariance (I&I) speed observer and a sliding-mode observer, both paired with an adaptive controller. Simulation results show the I&I observer-based controller achieving robust tracking and noise resilience, while the SM observer-based controller suffers from noise sensitivity and poor parameter convergence, highlighting the value of structure-preserving approaches. Overall, the authors advocate retaining physical structure in control design and call for higher standards in SM literature and clearer gain-tuning guidance.

Abstract

The objective of this note is to share some reflections of the authors regarding the use of sliding mode designs in control systems. We believe the abundant, and ever increasing, appearance of this kind of works on our scientific publications deserves some critical evaluation of their actual role, relevance and pertinence. First, we discuss the procedure followed by most of these designs -- illustrated with examples from the literature. Second, we bring to the readers attention several aspects of the control problem, central in classical designs, which are disregarded in the sliding mode literature. Finally, to illustrate with an specific example our previous considerations, we compare the performance of two adaptive tracking controllers for a simple one degree of freedom mechanical systems with unknown parameters and static and Coulomb friction -- that do not rely on the measurement of velocity.

Figures (16)

• Figure 1: Position tracking results
• Figure 2: Observer results
• Figure 3: Control signals
• Figure 4: Parameter estimation errors
• Figure 5: Position tracking results: noisy case