Stability Analysis and Controller Design of Local Model Networks

Introduction

This book treats various methods for stability analysis and controller design of local model networks (LMNs). LMNs have proved to be a powerful tool in nonlinear dynamic system identification. Their system architecture is more suitable for controller design compared to alternative approximation methods.

Advantages of LMNs

The main advantage is that linear controller design methods can be, at least locally, applied and combined with nonlinear optimization to calibrate stable state feedback as well as PID controller. The calibration of stable state-feedback controllers is based on the closed loop stability analysis methods.

Stability Analysis Methods

Here, global LMIs (Linear Matrix Inequalities) can be derived and numerically solved. For LMN based nonlinear PID controllers deriving global LMIs is not possible. Thus, two approaches are treated in this book.

Approaches

The first approach works iteratively to get LMIs in each iteration step. The second approach uses a genetic algorithm to determine the PID controller parameters where for each individual the stability is checked. It allows simultaneous enhancement of competing optimization criteria.