# High Order Disturbance Rejection and Tracking via Delayed Feedback Control Method

## TL;DR

This paper introduces a novel delayed feedback control method that enhances disturbance rejection and tracking capabilities, including ramp signals, by using a robust design and simulated annealing for parameter tuning.

## Contribution

A new delayed feedback control structure is proposed, enabling higher order disturbance rejection and ramp tracking, with a practical implementation approach using simulated annealing.

## Key findings

- Improved disturbance rejection compared to conventional methods.
- Effective tracking of ramp-shaped reference signals.
- Validated through a case study demonstrating practical applicability.

## Abstract

Delayed feedback control is an easy realizable control method which generates control force by comparing the current and the delayed version of the system states. In this paper, a new form of the delayed feedback structure is introduced. Based on the proposed delayed feedback method, a new robust tracking system is designed. This tracking system improves the features of the conventional state feedback with integral action and it is also able to reject higher order disturbances compared to the conventional method. In addition, the proposed tracking system tracks the ramp-shape reference input signal as well, which this is not possible through the conventional state feedback. Due to easy implementable feature of the proposed delayed feedback tracking system, it can be used in practical applications effectively. Moreover, since the proposed method adds delays to the closed loop system dynamics, the ordinary differential equation of the system changes to a delay differential equation with an infinite number of characteristic roots. Thus, conventional pole placement procedures cannot be used to design the delayed feedback controller parameters and place the unstable roots in the left half plane. In this paper, the simulated annealing algorithm is used to determine the proposed control system parameters and move the unstable roots of the delay differential equation to the left half plane. Finally, the efficiency of the proposed reference input tracker is demonstrated on a case study.

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Source: https://tomesphere.com/paper/1812.09958