In some of the complicated control problems we have to use the controllersthat apply nonlocal operators to the error signal to generate the control.Currently, the most famous controller with nonlocal operators is thefractional-order PID (FOPID). Commonly, after tuning the parameters of FOPIDcontroller, its transfer function is discretized (for realization purposes)using the so-called generating function. This discretization is the origin ofsome errors and unexpected results in feedback systems. It may even happen thatthe controller obtained by discretizing a FOPID controller works worse than adirectly-tuned discrete-time classical PID controller. Moreover, FOPIDcontrollers cannot directly be applied to the processes modeled by, e.g., theARMA or ARMAX model. The aim of this paper is to propose a discrete-timeversion of the FOPID controller and discuss on its properties and applications.Similar to the FOPID controller, the proposed structure applies nonlocaloperators (with adjustable memory length) to the error signal. Two methods fortuning the parameters of the proposed controller are developed and it is shownthat the proposed controller has the capacity of solving complicated controlproblems with a high performance.
展开▼
