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## Identification for robust control of complex systems: algorithm and motion application

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Increasing performance demands in control applications necessitate accurate modeling of complex systems for control. The aim of this chapter is to develop a new system identification algorithm that delivers models that are suitable for subsequent robust control design and can be reliably applied to complex systems. To achieve this, an identification algorithm is developed that delivers a system model in terms of recently developed coprime factorizations and thereby extends classical iterative procedures to the closed-loop case. These coprime factorizations have important advantages for uncertainty modeling and robust controller synthesis of complex systems. A numerically optimal implementation is presented that relies on orthonormal polynomials with respect to a data-dependent discrete inner product. Experimental results on a nanometer-accurate positioning system confirm that the algorithm is capable of delivering the required coprime factorizations and the implementation is numerically reliable, which is essential for complex systems as common implementations suffer from severe ill-conditioning.

Chapter Contents:

• Abstract
• 5.1 Introduction
• 5.2 Coprime factor identification for refined uncertainty structures in robust control
• 5.2.1 Robust control framework
• 5.2.2 Identification for robust control approach
• 5.2.3 Identifying robust-control-relevant coprime factorizations
• 5.3 Generalized SK-iterations for closed-loop coprime factor identification
• 5.3.1 Model parameterization
• 5.3.2 Frequency domain identification involving ℓ∞-norms via Lawson's algorithm
• 5.3.3 A closed-loop generalization of SK iterations
• 5.4 Orthogonal polynomials w.r.t. a data-dependent discrete inner product
• 5.5 Experimental application
• 5.5.1 Experimental system
• 5.5.2 Coprime factor identification results
• 5.5.3 Numerical conditioning
• 5.5.4 Illustration of robust-control-relevance
• 5.6 Conclusions
• Acknowledgments
• References

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