By Astrom K.J., Wittenmark B.
Appropriate for complex undergraduates and graduate scholars, this review introduces theoretical and useful facets of adaptive keep an eye on. It provides a great viewpoint on recommendations and an energetic wisdom of key techniques, supplying a well-developed feel of while to exploit adaptive suggestions and while different tools are extra applicable. 1995 version.
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Extra info for Adaptive control
115) The stability and bifurcation of such a periodic motion of the kth generalized coordinates can be classified by the eigenvalues of Dfs0 s1 …sk+1 (z∗s0 s1 …sk+1 ) with (n1 , n2 , n3 |n4 , n5 , n6 ). 116) i. If all eigenvalues of the equilibrium possess negative real parts, the approximate quasi-periodic solution is stable. ii. If at least one of the eigenvalues of the equilibrium possesses positive real part, the approximate quasi-periodic solution is unstable. iii. The boundaries between stable and unstable equilibriums with higher order singularity give bifurcation and stability conditions with higher order singularity.
5(vii), the harmonic amplitude A5∕4 ∼ 10−2 for period-4 motion is presented and A5∕4 = 0 for period-2 and period-1 motions. 0 (continued) period-1 motion. 5(ix), the harmonic amplitude A7∕4 ∼ 10−1 for period-4 motion is presented and A7∕4 = 0 for period-2 and period-1 motions. 5). 5(xi), the harmonic amplitude (A9∕4 ∼ 10−1 ) for period-4 motion is presented and A9∕4 = 0 for period-2 and period-1 motions. 5(xii), the harmonic amplitude A5∕2 ∼ 100 for period-2 and period-4 motions are presented and A5∕2 = 0 for period-1 motion.
5(xxiii), the harmonic amplitude (A39∕4 ∼ 10−3 ) for period-4 motion is presented and A39∕4 = 0 for period-2 and period-1 motions. 5). The harmonic phases for right and left asymmetry have a relation like ????Lk∕m = mod(????Rk∕m + (k + 1)????, 2????), which is not presented herein. 3 Numerical Simulations In this section, the initial conditions for numerical simulations are computed from approximate analytical solutions of periodic solutions. In all plots, circular symbols gives approximate solutions, and solid curves give numerical simulation results.