# L1 Adaptive Controller -- Performance Analysis of the Inverse DC Gain Method

## TL;DR

This paper analyzes a modified L1 adaptive control law that uses the inverse DC gain, showing it can control non-minimum phase systems without pole-zero cancellation, with slight performance trade-offs.

## Contribution

It introduces a modified L1 adaptive control law leveraging the DC gain, removing the need for stability of transmission zeros, and compares its performance to the original law.

## Key findings

- Modified law can control non-minimum phase systems without pole-zero cancellation
- Slight performance degradation compared to original law
- Stability of transmission zeros no longer required

## Abstract

This paper presents an analysis of the modified L1 adaptive control law. The performance of this control law is compared to the original control law. The modified L1 control law uses the DC gain of the transfer function of the closed loop plant dynamics. There is slight worsening of the controller performance. Furthermore, this analysis shows that provided that there is room for slight performance reduction, L1 adaptive control law can be used to control non-minimum phase systems without the use of a pole-zero cancellation technique. L1 adaptive control requires five assumptions before it can be applied. The stability of matched transmission zeros is no longer a condition that a system needs to meet as a result of this modification to the adaptive control law.

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Source: https://tomesphere.com/paper/1903.09453