ポポフの超安定理論を使った片持梁振動の能動的制御

概要

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The active control of cantilevered-beam vibrations has been investigated both from simulation and experiment points of view, by positively utilizing the adaptive model-following control techniques based on the hyperstability theorem by Popov. The followings have been obtained. The choice of the elements (diag[q_i]_<i=1,2>) of the matrix Q in the Lyapunov eq. (A_M'P+PA_M=-Q, where the A_M is a reference model matrix) affects the decaying speed of the tracking error e(t) on a sliding mode (v=0), and the more prominent the relation q_1≫q_2,the more greatly is improved the steady tracking error e(∞). By taking the continuous function cont (v)=v/(||v||+δ) in place of the discontinuous input function sgn (v) for the robust compensation, the chattering during the sliding mode is not only removed, but the e(∞) can be also minimized when there is employed an optimal value of δ. Under the condition of Q=diag[10^3,1] and δ=0.2,the maximum controlled logarithmic decrement(δ_1) is δ_<1max>=0.3248 including the free vibration damping δ_<1f>=0.0117 in the open loop system. Furthermore, it is found that the adaptive control scheme adopted here guarantees a fairly large robustness even in the presence of the imprecise modeling and parameter variations.
1993-09-15