Control of Limit Cycle Oscillations of a Two-Dimensional Aeroelastic System

Table 1

System variables.

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$d=m_T{I}_{\alpha }-m_W^2{x}_{\alpha }^2{b}^2$

$k_1=(I_{\alpha }\rho b{c}_{l_{\alpha }}+m_W{x}_{\alpha }\rho b^3{c}_{m_{\alpha }})/d$

$k_2=-(m_W{x}_{\alpha }\rho b^2{c}_{l_{\alpha }}+m_T\rho b^2{c}_{m_{\alpha }})/d$

$c_1=[I_{\alpha }(c_h+\rho Ub{c}_{l_{\alpha }})+m_W{x}_{\alpha }\rho U{b}^3{c}_{m_{\alpha }}]/d$

$c_2=[I_{\alpha }\rho U{b}^2{c}_{l_{\alpha }}(1/2-a)-m_W{x}_{\alpha }b{c}_{l_{\alpha }}+m_W{x}_{\alpha }\rho U{b}^4{c}_{m_{\alpha }}(1/2-a)]/d$

$c_3=[-m_W{x}_{\alpha }b(c_h+\rho Ub{c}_{l_{\alpha }})-m_T{x}_{\alpha }\rho U{b}^2{c}_{m_{\alpha }}]/d$

$c_4=[m_T(c_{\alpha }-\rho U{b}^3{c}_{m_{\alpha }}(1/2-a))-m_W{x}_{\alpha }\rho U{b}^3{c}_{l_{\alpha }}(1/2-a)]/d$

$p_{\alpha }(\mathbf{Y})=-m_W{x}_{\alpha }b{k}_{\alpha }(\mathbf{Y})/d$

$q_{\alpha }(\mathbf{Y})=m_T{k}_{\alpha }(\mathbf{Y})/d$

$p_h(\mathbf{Y})=I_{\alpha }{k}_h(\mathbf{Y})/d$

$q_h(\mathbf{Y})=-m_W{x}_{\alpha }b{k}_h(\mathbf{Y})/d$

$g_{NL1}(\mathbf{Y})=(c_s\rho U^{2}b)(c_{l_{\alpha }}{I}_{\alpha }+m_W{x}_{\alpha }{b}^2{c}_{m_{\alpha }}){\alpha }_{\text{eff}}^3(\mathbf{Y})/d$

$g_{NL2}(\mathbf{Y})=-(c_s\rho U^2{b}^2)(c_{l_{\alpha }}{m}_W{x}_{\alpha }+m_T{c}_{m_{\alpha }}){\alpha }_{\text{eff}}^3(\mathbf{Y})/d$

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