Experimental study of robustness in adaptive control for large flexible structures

Abstract

An experimental study is performed to investigate the robustness of model reference adaptive control for the large flexible structures control application. The main nonidealities of concern are unmodeled dynamics, input saturation, and time-delay effects (here, actuator and sensor dynamics are lumped into the last item for convenience). This study focuses on the robustness with respect to input saturation and time-delay effects, since robustness to unmodeled dynamics is inherent to the basic algorithm and has been demonstrated experimentally elsewhere. N experimental study is performed to investigate the robustness of model reference adaptive control for the large flexible structures control application. Although adaptive control methods are robust to parametric uncertainty by design, other types of nonidealities are known to lead to degradation and even instability of the closed-loop adaptive system. The main nonidealities of concern in the flexible structures control application are unmodeled dynamics, input saturation, and time-delay effects (here, actuator and sensor dynamics are lumped into the last item for convenience). Because of the use of the command generator tracker (CGT) approach, the adaptive algorithm considered here achieves tracking objectives that are in theory robust to unmodeled dynamics.1'2 This theoretical robustness to unmodeled dynamics has also been verified experimentally in Refs. 3 and 4 and will not be an issue in the present study. In contrast, there are presently no assurances as to the stability of the adaptive system to input saturation and time-delay effects. These latter issues will be the focus of the present study. It is shown experimentally in this paper that the basic adaptive algorithm is robust to input saturation, whereas timedelay effects can cause significant degradation and even instability. It is also shown experimentally that stability in the presence of time delay can be recovered by using a technique advocated by Bar-Kana5 of placing a small feedforward on the plant (or equivalently for the regulation problem, of placing a small feedback on the compensator). This stabilizes the closedloop system and recovers a certain degree of performance in the process. As a side benefit, the input torque requirements are also reduced. Certain theoretical results are included in this paper to support the experimental effort. In particular, it is shown that for structures with collocated actuators and sensors, there always exists a bounded feedforward gain that guarantees L2 stability of the closed-loop adaptive system in the presence of a pure time delay.