考虑到模糊隶属度函数(FMFs)是T-S模糊模型的主要特征,建立了包含状态变量和依赖隶属度函数的李雅普诺夫泛函,对带有量化和不确定性的模糊系统的稳定性和镇定问题进行了研究。同时,为更充分地容纳关于实际抽样的信息,抽样间隔两侧的状态也被加入到泛函当中。当对泛函进行求导的时候,出现了由隶属度函数的导数和泛函系数组成的乘积项。然后,通过讨论隶属度函数的导数正负确保其负数定义。进一步求解,得到了以线性矩阵不等式形式表达的稳定性定理。在得到最优参数之后,通过LMI工具箱进行求解,可得到控制器的增益参数和最大抽样间隔上界的数值。数值仿真实例证明对T-S模糊倒立摆系统控制的最大抽样间隔提升到0.040s。
Abstract
The stability and stabilization problems of the T-S fuzzy system with uncertainty and state quantization were studied. Considering that fuzzy membership functions (FMFs) are the main characteristic of T-S fuzzy model, if the information about FMFs is not added, it will be conservative. So, a novel Lyapunov-Krasovskii functional (LKF) which contained not only the information of state variables but also FMFs was constructed. Besides, the states on both sides of the sampling interval were incorporated into LKF. When deriving LKF, the product terms which consisted of derivative of FMFs and LKF coefficient were involved. And the product terms were discussed to ensure their negative definition. Later, enough stability conditions were expressed in the form of linear matrix inequalities (LMIs). The maximum sampling intervals and controller parameters were solved by MATLAB toolbox with the optimal parameters. Finally, a numerical example was simulated, and the maximum sampling interval for the T-S fuzzy inverted pendulum system was increased to 0.040s.
关键词
计量学 /
T-S模糊系统 /
抽样控制 /
状态量化 /
隶属度函数 /
倒立摆
Key words
metrology /
T-S fuzzy system /
sampled-data control /
state quantization /
membership function /
inverted pendulum
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基金
河北省自然科学基金(E2019105123); 河北省高等学校科学技术研究项目(ZD2019311); 唐山市人才投资项目(A2021110015)
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