自動化專業畢業設計外文翻譯--輸入力矩受限的機器人魯棒自適應控制-其他專業(編輯修改稿)

　

【文章內容簡介】 ? ? ? ? ? ?21 sck T u k?? = ? ?? ? ? ? ? ?22M q k L f k s k? (9) ? ?? ? ? ? ? ?? ? ? ? ? ? ? ?22 1 2? ?? scM q k L I f k f k q k k T u k? ? ? ? ? Which ? ? ? ? ? ?? ? ? ? ? ?? ? ? ?1 2 1 2k k M q k L I f k f k q k? ? ? ? ? ?? ? ? ? ? ?? ? ? ?2 1 2? ??M q k L I f k f k q k? ? ? Assuming , ? ? ? ?? ??M k M q k? , ? ? ? ? ? ?? ? ? ?11??M k f k M q k f k? and ? ? ? ? ? ?? ? ? ?22??M k f k M q k f k? ,if ??cuk is selected as ? ? ? ?? ? ? ? ? ?? ? ? ?2 2 1 2? ??csu k T M q k L I f k f k q k?? ? ? then Δ(k) = 0 , and then (9) can be written as ? ? ? ? ? ?221s k L f k s k? ? ? ? ? ? ? ? ?221s k L f k s k? ? ? (10) Since in Property 2 ? ?2f k I?? ? ?2f k I?? as Ts → 0 in a pact set of? ?,qq ? ?,qq , a small sample time Ts can be selected such that the inequality ? ?22 1L f k ? can be satisfied. Therefore, the tracking filtered error s(k) asymptotically converges to zero in this case. The convergence of s(k) to zero in turn guarantees the convergence of q(k) to zero. Because of the dynamics of the estimator and the timevarying coefficients of the characteristic model, it is almost impossible to satisfy the above assumptions. Therefore, we can design a suitable pensation control law ??cukto avoid possibly the case that the control performance is deteriorated or that the close loop system is even unstable due to the estimation errors. Hence ??cuk is designed as ? ? ? ? ? ?111s k q k L q k? ? ? ? ? ? ? ? ? ? ? ?? ? ? ? ? ?? ?? ? ? ? ? ?2 2 1 2? ? ?csi i iu k T M k L I f k f k q k kk T y k k???? ? ? ??? ? ? ? ? ? ? ? ?? ? ? ? ? ?? ?22 1 2? ? ?csu k T M k L I f k f k q k k?? ? ? ? (11) where ???k is the estimate of Δ(k) . Assuming Δ(k) is smooth enough and bounded, it then can be approximated by the linearly parameterized NN to any required degree of accuracy [6,14]. Then the element Δi(k) of Δ(k) can be expressed as ? ? ? ? ? ?i i ik Ty k k???? (12) where i= 1,…n, Tni R??? is the column i of the optimal NN weight matrix,1 Tn?? ? ???? ??… ,.Activation functions ? ? ? ? ? ?, Tny k y k y k???? ??… represent the basis function vector, which can be selected as any one of Gaussian radial basis, Bspine basis, Wavelet basis, and etc. [14], and δi (k) denotes the element I of the NN reconstruction error vectork δ(k), namely ? ? ? ? ? ?1 , Tnk k k? ? ?? ????… , . Using pensation control law ??cuk, (9) can be written as ? ?? ? ? ? ? ?? ? ? ? ? ?221M q k s k M q k L f k s k? ? ? ? ? ? ?11? ?, Tnn y k k??? ? ? ? ???? ? ? ???… (13) Where ???i k? is the estimate of i? , and ? ?m a x s u pi k k? ? ?? ? ? An estimate ???i k? is now obtained by minimizing the cost function ? ? ? ?? ? ? ?1 112 TJ s k M q k s k? ? ? (14) After substituting (13) into (14), the gradient of the cost function in (14) is derived as ? ? ? ?1? TJ y k s k?? ? ? ?? (15) According to the gradient descent method the NN weight adaptation law can be designed as ? ? ? ? ? ? ? ?? ?11Tk k y k s k? ? ?? ? ? ? (16) with α 0 . Then the pensation control law ??cuk in (11) can be written as ? ? ? ? ? ? ? ?? ? ? ? ? ? ? ?2 1 222? ? Tc ssu k M k L I f k f k q k k y kTT ?? ? ? ? (17) In view of the case ? ? ? ?12? ? 0I f k f k? ? ? the term ??cuk can be simplified as ? ? ? ? ? ?21 ? Tc su k k y kT ?? 4. SIMULATION RESULTS Consider a planar, twolink, articulated manipulator as in [3] (as presented in Fig. 1), whose dynamics can be written explicitly as ? ?1 1 1 2 1 1 12 1 22 1 2 2 2 2 21 0M M q q uh q h q qM M q q uhq? ? ???? ? ? ? ? ? ? ?????? ? ? ? ? ? ? ?? ? ? ? ? ? ? ??? Where 12 21 2 3 2 4 2c os si nM M a a q a q? ? ? ? 11 1 3 2 3 22 c os 2 sinM a a q a q? ? ? 22 2Ma? 3 2 4 2s in c o sh a q a q?? With 2 2 21 1 1 1 1c e e c e ea I m l I m l m l? ? ? ? ?, 22 e e cea I m l?? 31cose ce ea m l l ?? , 41sine ce ea m l l ?? , 111 , 1 , 2 , 30 ,eem l m ?? ? ? ? , , ,ceI I I? ? ?and ? . In the simulation, the sample time Ts = 2ms, the initial values and the parameters of the estimator and the controller are selected as P(0) =1 310 I,λ(0) = , μ0 = , the antisingularity factors (k) can be designed as ε(k) =5610? exp(?kTs). According to the Property 2, the initial estimate values of the characteristic model coefficient matrixes are chosen as ? ? ? ?12? ?0 2 , 0f I f I? ? ? A basis set of activation function y(k) can be selected as in the Random Vector Function Link [16], namely, ? ? ? ?? ?Ty k V