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## Robust data-driven control of systems with nonlinear distortions

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The frequency-domain methods that exist for investigating the behaviour of linear systems have become fundamental tools for the control systems engineer. However, due to the increasedperformance demands on today's industrial systems, the effects of certain nonlinearities can no longer be neglected in modern control applications; for such systems, direct application of these frequency-domain tools is not possible. In the current literature, however, frequency-domain methods exist where the underlying linear dynamics of a nonlinear system can be captured in an identification experiment; in this manner, the nonlinear system is replaced by a linear model with a noise source where a best linear approximation of the nonlinear system is obtained with an associated frequency-dependent uncertainty. With the frequency-domain data and uncertainty obtained from an identification experiment, robust control algorithms can then be used to ensure performance for the underlying linear system. This chapter presents a data-driven robust control strategy which implements a convex optimization algorithm to ensure the performance and closed-loop stability of a linear system that is subject to nonlinear distortions (by considering a model-reference objective). The effectiveness of the proposed data-driven method is illustrated by designing a controller for an inertial positioning system that possesses nonlinear torsional dynamics.

Chapter Contents:

• 13.1 Introduction
• 13.2 Preliminaries
• 13.2.1 Class of nonlinearities
• 13.2.2 Class of controllers
• 13.3 Frequency-domain identification
• 13.3.1 Stable plant
• 13.3.2 Unstable plant
• 13.3.3 Uncertainty filters for coprime factorisation
• 13.4 Robust controller design
• 13.4.1 Control performance
• 13.4.2 Convex formulation for robust performance
• 13.4.3 Controller design by convex optimisation
• 13.5 Case study
• 13.5.1 System description
• 13.5.2 Identification experiments
• 13.5.3 Performance specification
• 13.5.4 Experimental results
• 13.6 Conclusion
• References

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