【正文】 ion of (1) bees ? ?? ? ? ? ? ? ? ? ? ? ? ? ? ?? ? ? ?1221 1S M q k q k f k q k f k q k G k u kT ?? ? ? ? ? ? (2a) Premultiplying (2a) by ? ?? ?21sT mM q k?results in ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ?1211q k f k q k f k q k G k k u k??? ? ? ? ? ? where ? ? ? ?? ? ? ? ? ?? ?11 2,sf k I T M q k C q k q k??? , ? ? ? ?? ? ? ? ? ?? ?12 ,sf k I T M q k C q k q k?? ? ? ? ? ? ?? ? ? ?? ?? ? ? ?? ?2121ssG k T M q k G q kk T M q k???? ?? and I denotes the unitary diagonal matrix with an appropriate dimension. If the designed ? ?,u t qq ? ?,u t qqis continuous in t ,q and q , then the solution (q, q ) of (1) will be continuously differentiable. Let ? ? ? ? ? ?1,W q q M q C q q?? and ? ?,ijw qq be ijth element of matrix ? ?,ijW qq 。 parametric uncertainties。 robot manipulator。 and is subject to the physical conditions, the output of the drive torque is limited, so the controller may lead to the control failure or deterioration of the quality the controller design must take into account the limited joint drive dynamic capability. For example, the operation of the industry to help the robot, some parameters are uncertain or unknown, adaptive control is based on the estimated parameters to deal with such issues one of the main control strategy, using the robot dynamic equations of linear parametric nature, through an integral operator estimates the robot parameters. As integral part of the role in the continued interference conditions, stability control system is not easy, so appropriate to limit or adjust the integral part of the role of the adaptive system to achieve an effective means of stabilization. Son ah estimated parameters can limit the extent required, thereby increasing the robustness of adaptive control system. However, this algorithm has six switch ponent, a little plicated, but really is the parameter is not specified range, it cannot give the system control quality and robustness of information. This paper presents a simple robust adaptive control algorithm, when the estimated parameters field contains the parameters of the true value, the closedloop system to achieve asymptotically stable tracking。 L1 and L2 are goldensection coefficients, that is, 2 51 ???1 35 ???, 2 51 ???, which satisfy the relationship L1+L2=1 and 212LL? Substituting (7) into (2), we can get ? ?? ? ? ? ? ? ? ?? ? ? ? ? ?22 1 1 2 111 scM q k q k L f q k L f q k k T u k? ? ? ? ? ? (8) ? ? ? ?? ? ? ?? ? ? ? ? ?? ? ? ? ? ?? ? ? ? ? ?? ?? ?? ? ? ? ? ?? ? ? ? ? ? ? ?? ? ? ? ? ?? ? ? ?? ? ? ? ? ?? ? ? ? ? ?1 1 1 2 12 2 2 1 221 2 2?? ?11dsck M q k M k q k M q k f M k f k L q k L q kM q k s k M q k L f k s k M q k L I f k f k q kk T u k M q k L f k s k? ? ? ? ? ?? ? ? ? ? ?? ? ? ?? ?? ? ? ? ? ?? ? ? ? ? ?? ? ? ?? ? ? ? ? ? ? ?? ?? ?2 2 1 2? ?? ?11dM q k f M k f k L q k L q k M q k G k M k G q k? ? ? ? ? ? ? and ? ? ? ? ? ?? ? 12 ??sM k T k k I?? ???.Defining the tracking filtered error s(k +1) as and using the relationships L1+L2=1 and 212LL? , 212LL? (8) can be expressed as ? ?? ? ? ? ? ?? ? ? ? ? ? ? ?? ? ? ? ? ?? ? ? ?2 2 2 1 21M q k s k M q k L f k s k M q k L I f k f k q k? ? ? ? ? ? ? ? ? ?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