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Linear Parameter Varying Representation of a class of MIMO Nonlinear Systems

机译：一类MIMO非线性系统的线性参数变化表示

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Linear parameter-varying (LPV) models form a powerful model class to analyze and control a (nonlinear) system of interest. Identifying an LPV model of a nonlinear system can be challenging due to the difficulty of selecting the scheduling variable(s) a priori, especially if a first principles based understanding of the system is unavailable. Converting a nonlinear model to an LPV form is also non-trivial and requires systematic methods to automate the process. Inspired by these challenges, a systematic LPV embedding approach starting from multiple-input multiple-output (MIMO) linear fractional representations with a nonlinear feedback block (NLFR) is proposed. This NLFR model class is embedded into the LPV model class by an automated factorization of the (possibly MIMO) static nonlinear block present in the model. As a result of the factorization, an LPV-LFR or an LPV state-space model with affine dependency on the scheduling is obtained. This approach facilitates the selection of the scheduling variable and the connected mapping of system variables. Such a conversion method enables to use nonlinear identification tools to estimate LPV models. The potential of the proposed approach is illustrated on a 2-DOF nonlinear mass-spring-damper example.
机译：线性参数变化（LPV）模型形成强大的模型类，用于分析和控制其感兴趣的（非线性）系统。识别非线性系统的LPV模型可能是具有挑战性的，因为难以选择调度变量，特别是如果基于系统的第一个原则不可用。将非线性模型转换为LPV形式也是非琐碎的，并且需要系统的方法来自动化该过程。通过这些挑战的启发，提出了一种从具有非线性反馈块（NLFR）的多输入多输出（MIMO）线性分数表示开始的系统LPV嵌入方法。该NLFR模型类是通过模型中存在的（可能的MIMO）静态非线性块的自动分解来嵌入到LPV模型类中。作为分解的结果，获得了具有仿射依赖性的LPV-LFR或LPV状态空间模型。这种方法有助于选择调度变量和系统变量的连接映射。这种转换方法使得能够使用非线性识别工具来估计LPV模型。所提出的方法的潜力在2-DOF非线性质量弹簧阻尼器示例中示出。

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