Model description:
The nonliear model for elevator subsystem is as follows:
$$ f(x,u) = \begin{bmatrix} x_2\\ \dfrac{1}{I}(-\tau_g \sin{x_1} +k_{gyro}(u_1x_6\cos{x_1})- B_{\psi} x_2 + a_1 x_3 ^2 + b_1 x_3 )\\ x_4 \\ \dfrac{1}{T_1^2}(u_1 -x_3-2T_1x_4)\\ x_6 \\ \dfrac{1}{I_{\phi}} \left(-B_{\phi}x_6 - \left[K_r \dfrac{T_{or}}{T_{pr}}u_1 + x_9\right] + a_2x_7^2 + b_2x_7\right) \\ x_8 \\ \dfrac{1}{T_2^2}(u_2 - x_7 -2T_2x_8)\\ \dfrac{1}{T_{pr}}\left[K_r \left(1- \dfrac{T_{or}}{T_{pr}}\right)u_1 - x_9\right]\\ \end{bmatrix},$$
where $x_1$ is the elevator angle, $x_5$ is azimuth angle, and $g(x)=\begin{pmatrix}x_1k_{\psi} + y_{\psi \circ} \\ x_2k_{\phi} + y_{\phi \circ }\end{pmatrix}$
| $y_{\psi}$ | Elevator angle read by sensor |
| $k_{\psi}$ | Elevator constant |
| $y_{\psi \circ}$ | Elevator angle offset |
| $y_{\phi}$ | Azimuth angle read by the sensor |
| $k_{\phi}$ | Azimuth constant |
| $y_{\phi \circ}$ | Azimuth angle offset |
| $u_a$ | Control coltage applied to rotors |
| $k$ | Amplifier gain |
Type:
Form:
Time domain:
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Publication details:
| Title | Robust Feedback Linearization Control for a non Linearizable MIMO Nonlinear System in the Presence of Model Uncertainties |
| Publication Type | Conference Paper |
| Year of Publication | 2006 |
| Authors | Karimi, H.R, and Motlagh M.R.J |
| Conference Name | IEEE International Conference on Service Operations and Logistics, and Informatics |
| Date Published | 06/2006 |
| Publisher | IEEE |
| Conference Location | Shanghai |
| ISBN Number | 1-4244-0317-0 |
| Accession Number | 9165735 |
| Keywords | aircraft control, control nonlinearities, control system synthesis, helicopters, linearisation techniques, Lyapunov methods, MIMO systems, nonlinear control systems, robust control, rotors, state feedback, uncertain systems |
| Abstract | During the last decades a considerable progress has been made in the design of stabilizing controllers for nonlinear systems with known and unknown model. Feedback linearization approach via coordinate transformation is considered to be useful to tackle the control problem. Usually however, feedback linearization control does not guarantee exact linearization and robustness in the presence of uncertainties. Meanwhile most of the results developed are applicable to single-input feedback-linearizable systems. In this paper in order to cope the model uncertainties of a non linearizable MIMO nonlinear system, a robust feedback linearization scheme based on Lyapunov function is proposed. To verify the validity and effectiveness of the designed method, the suggested technique is applied to a twin rotor system |
| DOI | 10.1109/SOLI.2006.328881 |