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Englewood Cliffs, 1991, ISBN: 0-13-040890-5. Tayebi A. (2007). Analysis of two particular iterative learning control schemes in frequency and time domains, Automatica, Vol. 43, 2007, pp. 1565-1572, ISSN 0005-1098. ; Dawson, D. & McIntyre, M. (2004). A discontinuous output feedback controller and velocity observer for nonlinear mechanical systems, Automatica, Vol. 40, No. 4, 2004, pp. 695–700, ISSN 0005-1098. Yu, W. & Li, X. (2006). PD Control of robot with velocity estimation and uncertainties compensation, Int.

G1  m 2 l 2 g cos(q1  q 2 )  (m1  m 2 )l1 g cos(q1 ) , G 2  m 2 l 2 g cos(q1  q 2 ) . The desired trajectories are chosen as: q d 1(t )  2 cos ( 4  t / 3 )  sin ( 2  t / 3 ) (rad), with 0  t  5. qd 2 (t )  1 2 cos ( 4  t / 3 )  sin ( 2  t / 3 ) (rad), with 0  t  5. 5[m] . 2 Therefore, we find that V m  10[rad / s ] , M m  1[kgm ] . The simulation results of the proposed scheme on two-link robot manipulator along a trajectory are shown below. Figure 1 show the observer result, where we can see the convergence of the observed velocity to real velocity, of each joint, in a minimum time.

The on-line identified kˆ and ˆ are used in Eq. (9) and Eq. (14) respectively as the adaptive rules. 4 Fuzzy Logic Control Although PI control and adaptive control provide stable and zero static error solutions for MRR control, they are only feasible for applications with slow feed speed, such as end milling and grinding. Their response is limited by the open loop gain to maintain a stable performance. For deburring applications, where the cycle time is critical, faster feed speed up to 200 mm/s is usually required.

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An Idealist View of Life (The Hibbert Lectures for 1929) by Radhakrishnan


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