Research On Fractional Order System Identification Method Based On Particle Swarm Optimization

The identification of fractional order systems as one of branches of the theory of fractional order control,has become one of the hotspot in control field.Studies have shown that real objects in general are fractional order systems,and that fractional order models are more adequate for the description of dynamical systems than integer order models.It is well known that adequate model of system are in favor of controllers design to achieve better control performance.Therefore,researches about identification of fractional order systems identification have theoretical value and applied value.On the basis of previous studies,this paper in the following aspects of the identification method for fractional order systems:Firstly,the classical least square identification of integer order systems was extended to identification of commensurate rate fractional order systems in time domain.The model structure of commensurate rate fractional order systems is similar to integer order systems.Fractional common factor was selected in a range,then,using the G-L definition of fractional calculus to calculate the corresponding fractional derivative.According to the least square method,identification results were obtained.Further,compare the errors of identification results and the minimum of errors is the optimal result.Digital simulations demonstrate the validity of this method.Secondly,for the non-commensurate rate fractional order systems,based on an improved particle swarm optimization algorithm,a method of fractional order system identification was proposed.In order to increased the population of particles and improved the algorithm searching time,the basic particle swarm optimization algorithm was improved by using the inertia weight adaptive law.The fitness function was the sum of deviations of output of the actual system and the identification system.The scheme of fractional order system identification based on the improved particle swarm optimization was realized.This method can identify both the model parameter and the fractional order,and be applicable to the commensurate rate and non-commensurate rate fractional order systems,even the integer systems.Simulation results show that this method has high precision with the noise interference,is easy programming.Finally,an identification method in frequency domain for the commensurate rate fractional order systems with time delay is proposed.Using the Euler formula,the time delay parameter was translated to polynomial coefficient,and the transfer function of the fractional order system was simplified in a form with imaginary part and real part.Through separated the operational data in imaginary part and real part,the complexity of the identification process was reduced.Based on the least square to get multiple sets of data,as the initial data of the weight adaptive particle swarm optimization algorithm,the identification problem of fractional order system be changed to a parameter optimization problem.Further,the fractional common factor and delay parameter can be identified.A number of numerical simulations show the effectiveness of this method.