Fractional Order System Identification And Controller Design

Fractional order calculus has gained much attention in lots of research areas during recent years. It has also been applied to control area, where fractional order systems attract many research interests. In fact, some actual complicated systems are hard to be modeled as traditional integer order models. While, FOC (Fractional Order Calculus) is a good mathematical tool, which can describe these systems precisely. Therefore, modeling of fractional order systems becomes an open question, and many works associated with this problem have been done. At the same time, researches have demonstrated that fractional order controllers have better performance and design of fractional order controllers becomes a hotspot.This dissertation focuses on the fractional order system identification and fractional order controller design. In the part of fractional modeling, several system identification methods are studied. Based on commensurate fractional order transfer function, a fractional order maximum likelihood algorithm is presented in frequency domain. A frequency domain subspace method is studied based on fractional state space model, and it is convenient for the identification of MIMO fractional order systems. Then, this subspace method is extended to the fractional order systems with time delay. With the aid of orthogonal basis theory, fractional order orthogonal basis is applied to fractional order system identification. In the part of fractional controller design, systems with high uncertainties and disturbances are considered, and a fractional order controller design method combined with QFT (Quantitative Feedback Theory) is presented.Maximum likelihood method is popular for its excellent statistic characteristics, and the maximum likelihood identification of fractional order systems is studied in Chapter 3. The identification algorithm is deduced in frequency domain based on SISO commensurate fractional order transfer function. Detailed optimization computing is also presented. Numerical simulations validate the proposed algorithm with existence of noise, impact of which is analyzed at the same time.Many actual systems are MIMO systems, and it is necessary to research the identification of MIMO fractional order systems. Usually, identification methods for SISO systems can not be applied to MIMO systems directly, and it is hard to extend those algorithms based on optimization to MIMO cases. Subspace method is a good choice for MIMO system identification. Therefore, a frequency domain subspace method for fractional MIMO system identification is presented in Chapter 4. The problem, that fractional subspace identification result is not unique, is proposed, and an efficient solution is drawn. Determination of system order and commensurate order is discussed. When noise is considered, the choice of weighting matrix is also discussed in this chapter. Considering the common existence of input time delay, the presented fractional subspace method is extended to fractional order systems with time delay. Numerical simulations are performed for both non-delay system and delay system, and the results validate the algorithm.Orthogonal basis theory has been applied to system modeling and control lately. Traditional reasonable orthogonal basis is extended to fractional cases. In Chapter 5, the application of fractional orthogonal basis in fractional system identification is discussed. A method of using fractional generating functions is presented, and complex orthogonization computation is avoided. After parameter decoupling, an optimization method combined PSO and LS is presented. Simulation results validate the presented algorithm.For the systems with high uncertainties and disturbance, QFT is a robust theory proposed from the engineering point of view. In Chapter 6, a fractional QFT controller design is studied. Based on several typical fixed structure fractional controllers, an automatic loop shaping method on Nichols chart is presented. The fractional feedback controller is designed automatically during the process of loop shaping, during which, robustness to gain variation is considered, and the controller is designed with iso-damping characteristic. In the design of pre-filter, two design methods of fractional pre-filters are proposed:one is FOB (Fractional-order Orthogonal Basis) method and the other is FCT (Fractional. Complex Term) method. A classical example is performed, and the effectiveness of the new design method is proved.