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1、Symbol1st2ndm(kg)0.91.11(kgm2)0.060.1H(m)0.10.1L(m)0.20.2b(kg m2/s)0.00.0The Robotic SystemTable 1.Parameters of robot.21121221212221222122121 1(2)()2lll cosll cosl sinl sinb The dynamics of the two link robot manipulator:where 222122122122122(ll cos)ll sinb 22211 1211222212212lm hm Ll,lm hlL,lmh(2)
2、(3)(1)Network Structure Use the three layer neural networks with the higher order input terms.The numbers of neurons of the higher order multilayer neural identifier and the higher order multilayer neural controller are 24-35-20-4 and 6-10-7-2.Fourth order Runge Kutta algorithm with sampling time 0.
3、005 is used for solving the differential equations(1)and(2).21121221212221222122121 1(2)()2lll cosll cosl sinl sinb 222122122122122(ll cos)ll sinb(2)(1)Simulation ResultsConventionalmultilayer neural net.Higher order multilayer neural net.Identification9.37 x 10-33.35 x 10-3Computedtorque+PDComputed
4、torque+PD+NNPD+NNControl1.012.28 x 10-23.27 x 10-2Table 2.Rms errors of identification and control.Discussion The computed torque is calculated by inverse dynamics with the parameter values of 10%variation of exact modeling parameters except the length of links.The higher order multilayer neural controller which is an excellent solver of control error obtained from conventional controllers gives very accurate control result even with only PD controller.SummaryHigher order multilayer neural network Feedforward and feedback control structure with learning capabilitySimulation resultsDiscussion