Identification And Internal Model Control Of Fractional Order Systems

Fractional systems can be found everywhere in real world, such as viscoelastic systems, diffusion systems and some other systems with a characteristic of memory. In the control field, integer model is mostly used in the system description in the last decades. However, there is always a limit of description accuracy because of the fixed orders. While fractional order model could break through the limit and improve the description accuracy in a large extent. Internal model control is a convenient and efficiency control strategy among the model based control schemes. System disturbance and parameters uncertainty problem can be overcome with this control strategy. And the more precise the model is, the better the controller performance is. Such a convenient and effective control scheme has been applied in many real integer systems, but it has been rarely studied in the fractional systems.On the basis of previous studies, this paper mainly focuses on fractional system identification method and internal model control research as follows:Firstly, according to the characteristics of fractional systems, two novel parameters identification approaches are proposed. One is a kind of identification method using a random search optimal algorithm to estimate the unknown parameters based on time domain information. An improved NLJ (INLJ) optimal algorithm is used in the identification and it is proposed for the first time based on NLJ algorithm in this study. Compared with the traditionai NLJ algorithm, INLJ algorithm could provide a faster speed and a better accuracy. Another one is a kind method using the nonlinear variable damping least square approach based on frequency domain information. According to the fractional system’s frequency characteristic, a fractional frequency identification problem of arbitrary order systems is proposed. After a series of transformation, it will be transformed into a problem of solving nonlinear equations, which can be solved by nonlinear variable damping least square approach. This method is convenient and a high accuracy result could be obtained.After identification, the model obtained can be used in the internal model control design. In this paper, fractional systems are the controlled objects, which always have the problem of model imprecise and system parameters uncertainties. For solving this problem, a novel maximum sensitivity based fractional internal model control is proposed. And the designed controller can be easily tuned to meet different robustness demand. Numerical results verified the convenience and efficiency of this controller design approach.In order to further simplify the control strategy, a novel maximum sensitivity based fractional order IMC-PID control is proposed. For different types of fractional systems, different fractional order IMC-PID structures are designed and unknown parameters could be tuned with maximum sensitivity. Numerical results demonstrate that this proposed controller is effective and convenient.