Extended Basis Function Iterative Learning Control Of Flexible Manipulator

In this paper,we proposed a new basis function iterative learning control scheme to deal with non-minimum phase,underactuated flexible manipulator system,which is unpractical to use model-based control theory as the complicated,distributed parameter dynamics and modeling uncertainty in flexible structure stystem.In order to deal with the nonminimum phase characteristics,a non-causal type learning control approach is adopted.Among the existent iterative leanring control algorithm designed for non-minimum phase system control,there are two main types of them "black box" approach(algorithm without model information),which is unable to compensate the non-minimum phase lag perfectly without the aid of model information and "white box"(algorithm with model information) approach,which suffers from model uncetainties with a dependence on an exact system model.Therefore a "grey box" approach based on stable inversion and basis function iterative learning control,is proposed.In order to simulate and conduct a simulation test for the model,we introduce a new Scilab and Scicos based modeling and simulation toolbox.Simulation on the model verifies the effectiveness of this approach.This paper is organized as follows:(1) We first conduct a survey of the modeling theory of flexible manipulator and software tools for modeling and simulation,with analysis of both advantages and disadvantages in current modeling methods.Besides,A survey of th existent control schemes for flexible manipulators tip tracking is also given in this chapter,with an emphasis on the non-causal inversion approach,together with the description of "black box" and "white box" iterative leanring control approaches in non-minimum phase system(2) Introduction to a new flexbile manipulator modeling and simulation toolbox based on open-source Scilab/Scicos is given.This toolbox provides a convenient solution tor control system engineers to build and simulate the flexible manipulator in a block diagram platform compared to general purpose multip-body modeling and simulation commercial computing software. Moreover,using Scicos and Modelica interface,the implicit nonlinear equation which cannot be dealt with conveniently in Simulink can be solved in a systematic and convenient way.Simulation results is given to show the function of the toolbox.(3) A new extended Laguerre basis function iterative learning control algorithm is proposed to solve linear invariant non-minimum phase system.With extension of the tradition Laguerre function,the linear stable inversion defined in the frequency domain can be approximated by the extended Laguerre function with objective trajectory and its n-order series of derivatives.With the help of basis function iterative learning control,the static tracking error can be eliminated.An analysis of the approximation truncation error is also given. Simulations on a linear flexible manipulator model are conducted,which proves the effectiveness of the method.(4) A general extended basis function iterative learninig control in time domain is given for linear invariant and variant non-minimum phase system tracking. Based on the optimal control of stable inversion,a pseudo-inverse iterative learning control is proposed for the time invariant linear system.Simlations results verifies that the method can also lead to an approximation of the stablc inversion of the plant.