System Order Identification and Control

Abstract

For unknown systems, ‘system identification’ has become the standard tool of the control engineer and scientists. Identifying a given system from data becomes more difficult, however when fractional orders are allowed. Here identification process is demonstrated using assumption that system order distribution is a continuous one. Frequency domain system identification can thus be performed using numerical methods demonstrated in this chapter. Here one concept of r-Laplace transforms is discussed (Laplace transform in log domain), to discuss the system order distribution. Also mentioned is variable order identification as further development where the system order also varies with ambient and time is highlighted. Here in this chapter, an identification method based on continuous order distribution, is discussed. This technique is suitable for both the standard integer order and fractional order systems. This is topic for further advance research as to qualify the procedure of system order identification and to have technique of tackling variable order. Extending this continuous order distribution discussion, the advance research of having a continuum order feedback and generalized PID control is elucidated. Also in this chapter some peculiarities of the pole property of fractional order system as ultra-damping, hyper-damping and fractional resonance is explained. Elaborate research in this direction is ongoing process; to crisply define the system identification, crisply define the variable order structure, along with generalized controller for future applications. The system identification in presence of disorder is what is challenging and some unification of disordered time-response that is relaxation is too discussed. This is general process of returning to equilibrium for say any stable system or properties of condense matter physics. The introduction to complex order calculus in system identification is too touched upon, in this chapter, along with identification of main parameters of ‘irregular’ stochastically behaving systems.