Approximate Inverse-Dynamics Based Robust Control Using Static And Dynamic Feedback

It is rigorously shown that inverse-dynamics models can be used to stabilize plants of any ord�r provid�d that th� inw:rs�-dynamic mod�l is Ils�d in a miXf:n mod� fashion, in that of a 'Static and Dynamic' State-feedback (SDS) mode, When the r�slllting <":ontrol1�r is lls�d for tra<":king in<":r�asing th� gain of th� dynami<": f��dha<":k decreases lhe tracking error. YeL anoLher al LracLive fealure of Lhe SDS schenle is that th� inv�rs�-dynamin, modd <":all b� tlln�d oll-lin� by IlIlY adaptation mech­ anism without cancelling stability if the conditions of the non-adaptive stability theorem hold at any time instant. Computer simulations of the control of a chaotic bior�ador and a 'r�alisti<":' robotic manipulator J�monstrat� th� rohllstn�ss of th� approach. It is shown that SDS <":ontrol will yi�IJ 7�ro a."lymptotic f:ITor wh�n (:()flLr()lling Lll� bi()re;.u: i,()r Iisi rig an inverse-dynaflli(:s fIl()del whi(:h when Ilsed in a traditional mod� wOllld yidrl i ntolerably large errors. Tn th� <":as� of th� roboti<": ann sirllulalions Lhe eITeds of perLurbaLion and sanlpling frequency are invesLi­ gated and the SDS control is compared \vith the non-adaptive computed torque method . • '\. fully self-organizing associative neural network architecture that can be Ilsf:d to approximat� th� inv�rs�-dynami<":s in th� form of a Position-ann-Dir�<":tion­ to-A<":tion (PDA) map is also d�scrih�d. Similariti�s b�tw��n th� hasal ganglia­ LhalarnocorLical loops and the SDS scheme are discussed and iL is argued lllal. Lhe SDS scheme could he viewed a.o..; a fIlodd or higher order fIlol.or runcLions or Lll�S� area...,.

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