Table 1 Nomenclature.
Expression | Description | Expression | Description |
|---|---|---|---|
\(\theta\) | Pitch (elevation) angle | \(\phi\) | Yaw (azimuth) angle |
\(\tau _1\) | Momentum of main rotor | \(\tau _2\) | Momentum of tail rotor |
\(I_1\) | Main rotor inertia | \(I_2\) | Tail rotor inertia |
\(x \in R\) | (real number) of states | \(u \in R\) | input signal |
\(\rho\) | Euclidean error norm | D | Diagonal matrix |
Y | Control vector | P | Projection matrix |
\(a_1\) | Constant | \(b_1\) | Constant |
\(a_2\) | Constant | \(b_2\) | Constant |
\(M_g\) | Gravitational momentum | \({B_{1\theta }}\) | Frictional parameter |
\({B_{2\theta }}\) | Frictional parameter | \({B_{1\varphi }}\) | Frictional parameter |
\({B_{2\varphi }}\) | Frictional parameter | \(k_{gy}\) | Gyroscopic parameter |
\(k_1\) | Gain of main motor | \(k_2\) | Gain of tail motor |
\(T_{11}\) | Denominator constant of main motor | \(T_{10}\) | Denominator constant of tail motor |
\(T_{21}\) | Denominator constant of main motor | \(T_{20}\) | Denominator constant of tail motor |
\(u_{h}\) | Horizontal axis control input | \(u_{v}\) | Vertical axis control input |
\(I_v\) | Inertial momentum of main rotor | \(I_h\) | Inertial momentum of tail rotor |
\(e_z (t)\) | Tracking of pitch and yaw angles | 2DOF | Two degree of freedom |
\(k_{H_h }, k_{H_v}\) | Velocity gains | \(k_{f_h }, k_{f_v }\) | Frictional momentum |
\(R_V\) | Returned torque of rotors | \(G_d\) | Disturbance of plant |
\(G_u\) | Transfer matrix of control signal | \(K_y\) | Feedback matrix functions |
\(K_r\) | Transfer function matrix of pre-filter | r, d | Reference input, input disturbance |
\(\Delta _F\) | Fictitious perturbation | \(S_o\) | Output sensitivity matrix |
