Takagi-Sugeno fuzzy sampled-data observer design for nonlinear permanent magnet synchronous generator-based wind turbine systems using auxiliary function-based integral inequality technique (Q6595318)

The complicated dynamics of the pair wind turbine-synchronous generator (with permanent magnet) is modeled using the Takagi-Sugeno fuzzification approach as \N\[\N\displaylines{\displaystyle{\dot{x}=\sum_1^2\zeta_p(\omega_g(t))\{A_px + B_pu(t)\}}\\ \displaystyle{y(t)=\sum_1^2\zeta_p(\omega_g(t))C_px(t)}}\N\]\Nwith \(\displaystyle{0\leq\zeta_p(\omega_g(t))=\frac{\gamma_p(\omega_g(t))}{\sum_1^2\gamma_r}\;,\; \sum_1^2\gamma_p(\omega_g(t))=1}\)\N\NFor it there is designed a sampled data fuzzy state observer as \N\[\N\displaylines{\displaystyle{\dot{\hat{x}}=\sum_1^2\mu_q(\hat{\omega}_g(t))\{A_q\hat{x} + B_qu(t) + H_q(y(t_k)-\hat{y}(t_k))\}}\\ \N\displaystyle{\hat{y}(t)=\sum_1^2\mu_q(\hat{\omega}_g(t))C_q\hat{x}(t)}} \N\]\Nwith \(\displaystyle{0\leq\mu_q(\hat{\omega}_g(t))=\frac{\hat{\gamma}_p(\hat{\omega}_g(t))} {\sum_1^2\hat{\gamma}_r}\;,\;\sum_1^2\hat{\gamma}_p(\hat{\omega}_g(t))=1}\)\N\NThe control loop is closed by the controller \N\[\N\displaystyle{u(t) = \sum_1^2\delta_r(\hat{\omega}_g(t_k))K_r\hat{x}(t_k)\;,\;t_k\leq t<t_{k+1}} \N\]\NAfterwards the stabilization design of the controller is accomplished using a suitably chosen Lyapunov function.