# Classic Sliding Mode Control From First Principles

## TL;DR

This paper provides an intuitive, first-principles derivation of classic sliding mode control, clarifying its assumptions, limitations, and pedagogical value in control system design.

## Contribution

It offers a foundational derivation of sliding mode control, explaining its assumptions and applicability from first principles, enhancing understanding for control engineers.

## Key findings

- Derives a sliding mode controller without assuming control input sign
- Explains why sliding mode control handles only matched disturbances
- Clarifies the linearity requirement in the control signal

## Abstract

This is an intuitive introduction to classic sliding mode control that shows how the associated assumptions and condition for its use arise in the context of a derivation of the method. It derives a controller that obviates the need for the assumption of any sign for the control input vector, answers why it is said that it deals only with matched disturbances and why a system that it may apply to 'must' be linear in the control signal. Additionally, it may be viewed as an example of how a control design method might be developed, adding to its pedagogical usefulness.