TY - JOUR
T1 - Non-fragile controller design of uncertain saturated polynomial fuzzy systems subjected to persistent bounded disturbance
AU - Mardani, Mohammad Mehdi
AU - Vafamand, Navid
AU - Khooban, Mohammad Hassan
AU - Dragicevic, Tomislav
AU - Blaabjerg, Frede
PY - 2019/2
Y1 - 2019/2
N2 - This paper investigates the problem of designing a non-fragile polynomial fuzzy controller for a class of polynomial fuzzy models subjected to persistent bounded disturbances and system uncertainty. The proposed controller is considered to satisfy the input saturation constraint. Furthermore, the resilient controller is affected by linear fractional uncertainties. The overall structure of the controller is obtained by the polynomial parallel distributed compensation concept. The sufficient conditions guarantee an L1 performance of the perturbed system and exponential stability of the non-perturbed system is achieved in terms of sum-of-squares decomposition conditions. Subsequently, the sum-of-squares-based conditions lead to minimization of the L1 performance such that the above-mentioned hard constraints on the control input and robustness of the closed-loop system against the system and controller uncertainties will be guaranteed. The controller gain matrices will be achieved by numerically solving the sum-of-squares-based conditions with the third-party MATLAB toolbox ‘SOSTOOLS’. Finally, extensive studies and hardware-in-the-loop simulations on a ball-and-beam system are presented, which illustrate the proposed controller can accurately and smoothly track the set point frequency. Furthermore, the proposed control approach is more robust over prior-art controllers for all the simulation scenarios.
AB - This paper investigates the problem of designing a non-fragile polynomial fuzzy controller for a class of polynomial fuzzy models subjected to persistent bounded disturbances and system uncertainty. The proposed controller is considered to satisfy the input saturation constraint. Furthermore, the resilient controller is affected by linear fractional uncertainties. The overall structure of the controller is obtained by the polynomial parallel distributed compensation concept. The sufficient conditions guarantee an L1 performance of the perturbed system and exponential stability of the non-perturbed system is achieved in terms of sum-of-squares decomposition conditions. Subsequently, the sum-of-squares-based conditions lead to minimization of the L1 performance such that the above-mentioned hard constraints on the control input and robustness of the closed-loop system against the system and controller uncertainties will be guaranteed. The controller gain matrices will be achieved by numerically solving the sum-of-squares-based conditions with the third-party MATLAB toolbox ‘SOSTOOLS’. Finally, extensive studies and hardware-in-the-loop simulations on a ball-and-beam system are presented, which illustrate the proposed controller can accurately and smoothly track the set point frequency. Furthermore, the proposed control approach is more robust over prior-art controllers for all the simulation scenarios.
KW - Sum-of-squares
KW - uncertain polynomial fuzzy models
KW - non-fragile controller
KW - L1 performance
KW - robust controller
KW - input saturation
UR - http://www.scopus.com/inward/record.url?scp=85049009763&partnerID=8YFLogxK
U2 - 10.1177/0142331218774110
DO - 10.1177/0142331218774110
M3 - Journal article
SN - 0142-3312
VL - 41
SP - 842
EP - 858
JO - Transactions of the Institute of Measurement and Control
JF - Transactions of the Institute of Measurement and Control
IS - 3
ER -