PDE Modeling and Boundary Control for Flexible Mechanical System by Zhijie Liu & Jinkun Liu

Author:Zhijie Liu & Jinkun Liu
Language: eng
Format: epub
ISBN: 9789811525964
Publisher: Springer Singapore

Fig. 4.3Deformation of flexible satellite with proposed control

Fig. 4.4Boundary displacement w(0, t) of flexible satellite: without control and with control

Fig. 4.5Displacement of center body w(l/2, t) of flexible satellite: without control and with control

Fig. 4.6Boundary displacement w(l, t) of flexible satellite: without control and with control

Fig. 4.7Control input

Simulation results without control (i.e., ) are given in Fig. 4.2. For the results presented here, we can observe that there are large vibrations along the two panels.

The dynamic responses with control are displayed in Figs. 4.3, 4.4, 4.5, 4.6 and 4.7. Figure 4.3 demonstrates the displacement of the flexible satellite with the proposed control. Figure 4.4 shows the left boundary displacement w(0, t) of the flexible satellite. The displacement w(l/2, t) of the centrebody is demonstrated in Fig. 4.5. In Fig. 4.6, the right boundary displacement w(l, t) of the flexible satellite is demonstrated. Control input is shown in Fig. 4.7.

We can see that the proposed controller can suppress the vibrations of the flexible satellite after 25 s, which means a good performance of vibration suppressing can be acquired.

From above analysis, we can draw a conclusion that the control strategy developed in this work can stabilize the system under the condition of input constraint and external disturbance.

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