Adaptive Control of Robot Manipulators: A Unified by An-chyau Huang

By An-chyau Huang

This booklet introduces an unified functionality approximation method of the keep watch over of doubtful robotic manipulators containing basic uncertainties. it really works at no cost area monitoring regulate in addition to compliant movement keep an eye on. it's appropriate to the inflexible robotic and the versatile joint robotic. in spite of actuator dynamics, the unified procedure remains to be possible. a majority of these gains make the booklet stick out from different latest guides.

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Example text

Once e gets close to zero, the estimated parameters converges to some values. We cannot predict the exact values these parameters will converge to from the above derivation. , when t → ∞ . c. gain of the reference model (2). Equation (12) further implies kaɶ + bɶ = 0 (13) which is exactly a straight line in the parameter error space. Therefore, for a constant reference input r, both the estimated parameters do not necessarily converge to zero. To investigate the problem of parameter convergence, we need the concept of persistent excitation.

The PE condition says that there exist T, k>0, such that ∫ t +T t Ω(τ )ΩT (τ )dτ ≥ kI > 0 ∀t ≥ t 0 .

Under this condition, (36) can be further = ε for all t ≥ Tε . This completes the proof of z → 0 as t → ∞ , if the claim is justified. Since all properties hold for all x and z, and are uniform respect to the initial time, the equilibrium point (x, z ) = 0 is globally uniformly stable. Since the system is linear, it is also globally exponentially stable. , to prove that ∀ε > 0 , we cannot find t1>0 such that z (t ) > ε for all t ≥ t1 . Suppose there exists a t1 > 0 such that z (t ) > ε for all t ≥ t1 .

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