By M. Moallem
This monograph is anxious with the advance and implementation of nonlinear mathematical ideas for suggestions keep an eye on and form layout of robotic manipulators whose hyperlinks have substantial structural flexibility. numerous nonlinear regulate and commentary thoughts are studied and applied by means of simulations and experiments in a laboratory setup. those options contain fundamental manifolds in singular perturbation thought, nonlinear input-output decoupling, nonlinear observers and sliding control.
The research of dynamic homes and regulate concepts for flexible-link manipulators is usually a framework for designing the mechanical form and fabric of those platforms such that more advantageous homes could be accomplished so as to facilitate the regulate challenge. consequently, structural form optimization is taken into account as a method of bettering the dynamic behaviour of flexible-link manipulators.
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4h). A quantitative measure to evaluate the tracking performance of the controllers can be defined as the ratio of maximum tip deflection error to the maximum arm deflection during the whole trajectory. 5). 13)in the above ratio. Experimental Results In this section, the practical implementation of the control strategy discussed in this chapter is investigated. 6 shows the schematic diagram of our experimental setup. 251kg payload attached to its end point. 216kg that is comparable to its payload.
9: Experimental results for the slow control designed based on the rigid model plus the fast control: a) Strains a t points 1 (-), 2 (--), and 3 (-- -) (rn/nz) b) Torque input (Nm) c) Joint velocity (rad/s) d) Tip trajectory (-) and desired tip trajectory (- - -) (rad) e) Deflection modes dl (-) and J2 (-- -) (m) f) Tip position trajectory error, y, - y (rad). sensor noise, higher frequency unmodeled dynamics, and computational delay of the control law. These factors are among the possible sources that contribute to the difference between the theoretical tracking error estimates and the actual tracking errors.
29), E is the link modulus of elasticity and I is the cross sectional area moment of inertia. 30), d is the damping coefficient of the flexural mode, and u is the input torque. Defining the output y as the tip position and where 9, = +(I j. - m l l 4 , 0. 28) the latter term is given by pA(1 - sb(z)dz). Now, assuming a clamped-free mode shape it can be concluded from +(x) that + e ~ , ' z ~ ( x ) d