Abstract
We present a study on the suppression of flow-induced vibration using a simple control algorithm with an assumption that the disturbance as well as the system parameters are bounded variables. By introducing three different control signals, we explore three schemes, namely, robust control, sliding mode, and adaptive control. The control schemes are implemented numerically with a few illustrative examples, which includes a bounded chaotic system. It is demonstrated that all three schemes can be effectively used for fluid-structure interaction systems. In addition, with these numerical examples, we also illustrate various advantages and disadvantages of different control schemes. In general, robust control and adaptive control schemes are (globally) ultimately uniformly bounded, whereas sliding mode scheme is (globally) asymptotically stable. Thus, as we further reduce the integration time step, the residual of robust control and adaptive control schemes will approach to a bounded (finite) asymptotic function, and the residual of sliding mode scheme will approach to zero. Furthermore, due to self-tuning, the gain of adaptive control scheme is relatively small, yet, the computation cost is higher because of the excessively small time step requirement for the numerical integration. With respect to sliding mode scheme, the control signal is discontinuous due to the sign function and consequently, the practical implementation has fast switching fluctuations (chattering).
Adaptive Sliding Mode Fixed-Time Tracking Control Based on Fixed-Time Sliding Mode Disturbance Observer with Dead-Zone Input