Studies On Hybrid Different-layered Time-varying Linear System And Its Application

Linear systems are widely used in the science and engineering calculation.Scholars have been interesting in solving many kinds of linear systems effectively.In practical application,there are many difficulties to meet the requirements of industrial real-time calculation for the traditional static linear system.Although the problem of weak real-time performance can be solved through time-varying linear system,but its structure is relatively simple,and complex real-time problems cannot be described suitably by it,such as the tracking control problem of manipulator with multi-constraints,strong real-time and high dynamic characteristics.First of all,a hybrid different-layered time-varying linear system is constructed.The systems have a two-layer hybrid structure,which have the solution layer and derivative layer of the mixed structure with strong description for the complex practical problems such as the tracking control of the manipulator.The traditional methods for solving hybrid different-layered time-varying linear system have some shortcomings,and thus this paper uses the zeroing neural network method and time discretization formula to solve the problem.Secondly,the continuous zeroing neural network model and the discrete zeroing neural network model are proposed.In order to solve the hybrid different-layered time-varying linear system,it is necessary to construct the error function and use the linear design formula of zeroing neural network to transform the solution layer into the derivative layer.The known derivative layer system is integrated,and the continuous zeroing neural network model is obtained.Then,a time discretization formula with0-stability is proposed and combined with the continuous zeroing neural network model to obtain a hybrid discrete-time zeroing neural network model.At the same time,in order to verify that the model can effectively solve the hybrid different-layered time-varying linear system,a large number of comparative numerical experiments are carried out by using the matrix with all elements changing with time and different time sampling intervals.Finally,the control algorithm of manipulator is proposed.With the rapid development of robot industry,the tracking control of robot manipulator is widely used in practice,which includes tracking main task and joint limit,fault tolerance and other subtasks.Effective control algorithm can ensure the accuracy of the manipulator tracking control.In this paper,the tracking control problem of a robot manipulator is descripted as a hybrid different-layered time-varying linear system.The main tracking task is described by the derivative layer,and other subtasks are described by the solution layer.Following the solving process of the hybrid different-layered time-varying linear system,the solution layer of the problem is transformed derivative layer equivalently,and the discrete-time manipulator control algorithm is obtained.The algorithm is applied to six-link planar manipulator,and a large number of experiments are carried out to verify the effectiveness of the algorithm.