Performance Recovery of Feedback-Linearization-Based Designs
Performance Recovery of Feedback-Linearization-Based Designs
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DOI：
10.1109/tac.2008.2006821
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发表时间：
2008-11
影响因子：
6.8
通讯作者：
L. Freidovich;H. Khalil
中科院分区：
文献类型：
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作者：
L. Freidovich;H. Khalil
考虑一类具有稳定零动态的部分反馈线性化非线性系统的跟踪问题。系统是不确定的，只有输出被测量。我们使用n+1维的扩展高增益观测器，其中n是相对次数。观测器估计跟踪误差的n个导数，其中前(n-1)个导数是对象的正规型状态，n个导数估计模型不确定性和扰动引起的摄动。控制器取消摄动估计，并实施反馈控制律，该反馈控制律是针对标称线性模型设计的，如果所有非线性已知且信号可用，则反馈线性化将获得标称线性模型。我们证明了当观测器增益足够高时，闭环系统在基于观测器的控制器下恢复了标称线性模型的性能。此外，我们还证明了该控制器具有积分作用性质，因为它保证了在存在恒定非零扰动的情况下，跟踪误差能被调节到零。
We consider a tracking problem for a partially feedback linearizable nonlinear system with stable zero dynamics. The system is uncertain and only the output is measured. We use an extended high-gain observer of dimension n+1, where n is the relative degree. The observer estimates n derivatives of the tracking error, of which the first (n-1) derivatives are states of the plant in the normal form and the nth derivative estimates the perturbation due to model uncertainty and disturbance. The controller cancels the perturbation estimate and implements a feedback control law, designed for the nominal linear model that would have been obtained by feedback linearization had all the nonlinearities been known and the signals been available. We prove that the closed-loop system under the observer-based controller recovers the performance of the nominal linear model as the observer gain becomes sufficiently high. Moreover, we prove that the controller has an integral action property in that it ensures regulation of the tracking error to zero in the presence of constant nonvanishing perturbation.