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为了便于构造两输入非线性前馈系统的镇定控制器,通过变换构造出与原系统等价的复数域低维单输入非线性前馈系统,再利用已有的单输入系统的控制方法对该等价系统设计一个复数域镇定控制器,采用逆变换得到原系统的两个镇定控制器,提出了将原系统转化为等价系统后再进行设计的镇定方法。用Lyapunov稳定性定理证明了闭环控制系统状态的渐进稳定性。结果表明:等价系统比原系统具有更少的输入和更低的维数,基于等价系统的设计方法降低了系统的分析难度,简化了控制器的设计步骤。
In order to facilitate the construction of a stabilization controller with two-input nonlinear feedforward system, a complex low-dimensional single-input nonlinear feedforward system with complex number equivalent to the original system is constructed through transformation, and then the existing single-input system control method Equivalent system A complex number domain stabilization controller is designed. Two stabilization controllers of the original system are obtained by inverse transformation. A stabilization method is proposed after the original system is transformed into an equivalent system. The Lyapunov stability theorem is used to prove the asymptotic stability of closed-loop control system. The results show that the equivalent system has less input and lower dimensionality than the original system. The design method based on equivalent system reduces the difficulty of system analysis and simplifies the design steps of the controller.