Mechanical System Stabilization via Differential Observer

Uniform global position feedback tracking control of mechanical systems without friction

“…Remark 1 We stress that the controller (13) corresponds to that from [12] where semiglobal asymptotic stability is established. The controller is also reminiscent of that published in [4] whose author relies on singular perturbation theory to establish that the domain of attraction may be extended to R 3n provided that a → ∞.…”

“…For instance, the classic paper [4] presented a proof of uniform asymptotic stability using Kelly's controller [8] originally proposed for set-point control. The author in [4] invokes Tychonov's theorem on singularly perturbed systems to show uniform global asymptotic stability provided that the unique pole of the dirty-derivatives filter used in [8] is placed at −∞ that is, the result actually establishes semi-global asymptotic stability. The same property is achieved via Lyapunov's direct method in [12].…”

“…Those based on Lyapunov's direct method and those which intended to exploit structural properties. In the first case, stability is global only with respect to part of the states -as in [27] or is semiglobal -as in [4], [12] etc. In the second case, the structural assumptions needed to perform convenient changes of coordinates do not hold for EL systems -cf.…”

Global tracking for robot manipulators using a simple causal PD controller plus feedforward

“…Initial conditions as high as q(0) =q(0) = [10 5 10 5 ] T were taken and the error state x e still converged to zero using Euler's numerical integration method with step size h = 5 × 10 −7 .…”

“…Theorem 3: Consider system (47) with control law given by (5) and (52). If the control gains K d and K p are sufficiently large and the lead filter parameter μ is chosen sufficiently small, then the error system given by (26) and (53), with state x e defined in (27), is uniformly globally asymptotically stable.…”