# A Generalized Frequency Domain Embedded State Space Approach for Controller Synthesis

## TL;DR

This paper introduces a generalized frequency domain embedded state space method for synthesizing controllers, capable of designing arbitrary order compensators to meet stability and performance criteria across diverse system types.

## Contribution

It presents a novel control synthesis approach embedding state space systems in the frequency domain, enabling flexible compensator design for various systems with convergence guarantees.

## Key findings

- Successfully designed compensators for linear and nonlinear systems
- Applicable to SISO, MIMO, and delayed systems
- Demonstrated convergence and effectiveness through examples

## Abstract

This paper develops a novel control synthesis approach for a wide class of practical systems. The control action is derived by inserting a compensator device in the forward path of the system that is to be controlled. The compensator design method is based on a state space system that is embedded in the frequency domain of the plant. It uses a nonlinear subspace that is the image of the compensator being used to determine the parameters of the compensator and modify system behavior. The coordinates of the state space system are taken as the compensator parameters. The method is capable of designing a compensator of arbitrary order to make the system comply with given stability performance requirements provided that these requirements can be geometrically interpreted in the frequency domain. The approach is developed and a proof of its ability to converge, if a solution exists, to the compensator tuning parameter set that satisfy the desired performance conditions is provided. A set of design examples are supplied to demonstrate the applicability of the approach to different types of linear, nonlinear, SISO and MIMO systems and system with delays.

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Source: https://tomesphere.com/paper/2302.13038