In this study, automated generation of linear parameter‐varying (LPV) state‐space models to embed the dynamical behaviour of non‐linear systems is considered, focusing on the trade‐off between scheduling complexity and model accuracy and the minimisation of the conservativeness of the resulting embedding. The LPV state‐space model is synthesised with affine scheduling dependency, while the scheduling variables themselves are non‐linear functions of the state and input variables of the original system. The method allows to generate complete or approximative embedding of the non‐linear system model and also it can be used to minimise the complexity of existing LPV embeddings. The capabilities of the method are demonstrated on simulation examples and also in an empirical case study where the first‐principle motion model of a three degrees of freedom (3DOF) control moment gyroscope is converted by the proposed method to an LPV model with low scheduling complexity. Using the resulting model, a gain‐scheduled controller is designed and applied on the gyroscope, demonstrating the efficiency of the developed approach.

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The filtered split-path nonlinear integrator (F-SPANI) is a generic nonlinear controller designed to improve the transient performance of linear (motion) systems in terms of overshoot. The main idea underlying F-SPANI is that the amplitude and phase of an integrator can be tuned using independent filters, resulting in more efficient use of the buffer of the integrator. In this article, a general description of F-SPANI is presented. In addition, a stability analysis result is presented that provides sufficient conditions in the form of linear matrix inequalities (LMIs) for closed-loop stability analysis on the basis of construction of a common quadratic Lyapunov function (CQLF). The ease of the design, implementation, and the potential of the proposed controller are illustrated both in simulations and in experiments on an industrial pick-and-place machine.

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