Design of model predictive control for linear fractional-order systems

The Design of a Coprime‐Factorized Predictive Functional Controller for Unstable Fractional Order Systems

“…The coprime factorization method seems useful. In order to extend this model structure for fractional order systems, here, at first, the fractional model is approximated by an integer one via the well‐known Oustaloup method . Next, the resulting high order model is reduced to make it more applicable for prediction.…”

“…In [12][13][14] a model predictive approach was applied to control a stable fractional order system based on an approximation method. In [43][44][45] a fractional order generalized predictive control method based on fractional order cost function was proposed to control stable integer order systems.…”

“…Heat conduction, physical drug diffusion, electrochemistry, electromagnetic waves, and some biological systems are among the dynamical systems described using fractional order equations. In the field of control systems, controllers such as PID controllers , adaptive controllers , sliding mode controller , and MPC controller have been proposed for fractional order systems to improve the performance of the closed loop control systems.…”

“…Therefore, the main contributions of this paper compared to the most related works could be summarized as follows. First, unlike previous works on MPC design for FO systems , which deal with high order approximated models, in this paper, LMI‐BT order reduction method has been employed to reduce the order of the approximated model of the fractional‐order system to reduce controller complexity. Second, the coprime‐factorized representation, presented previously for integer systems in , has been extended for unstable fractional order systems for the reduced approximated model of unstable FO system.…”

“…Third, unlike the previous PFC design for stable fractional order systems , in this paper, predictive functional control was designed for the coprime‐factorized unstable plant. Fourth, unlike previous related works , the robust stability of the closed‐loop system (including unstable fractional systems and PFC controller) was investigated via small gain theorem.…”