Article

# Robust $H_{\infty}$ Fuzzy Control for a Class of Uncertain Discrete Fuzzy Bilinear Systems

Nat. Cheng Kung Univ., Tainan
(Impact Factor: 6.22). 05/2008; 38(2):510 - 527. DOI: 10.1109/TSMCB.2007.914706
Source: IEEE Xplore

ABSTRACT

The main theme of this paper is to present robust fuzzy controllers for a class of discrete fuzzy bilinear systems. First, the parallel distributed compensation method is utilized to design a fuzzy controller, which ensures the robust asymptotic stability of the closed-loop system and guarantees an Hinfin norm-bound constraint on disturbance attenuation for all admissible uncertainties. Second, based on the Schur complement and some variable transformations, the stability conditions of the overall fuzzy control system are formulated by linear matrix inequalities. Finally, the validity and applicability of the proposed schemes are demonstrated by a numerical simulation and the Van de Vusse example.

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• "The robust stabilization for continuous-time fuzzy bilinear uncertain system with disturbance was studied in [15], and then the result was extended to the robust stabilization for continuous-time fuzzy bilinear systems with time-delay only in the state [16] [17]. For the discrete case, the robust H1 fuzzy control for a class of uncertain discrete fuzzy bilinear systems has been studied in [18], and then the result was extended to the discrete fuzzy bilinear system with time-delay only in the state [19], fuzzy observer design for time-delay T–S uncertain discrete fuzzy bilinear systems with disturbance in [20]. All the results are obtained based on either state feedback controller or observer-based controller. "
##### Article: Robust fuzzy output feedback controller for affine nonlinear systems via T–S fuzzy bilinear model: CSTR benchmark
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ABSTRACT: In this paper, a robust H∞ fuzzy output feedback controller is designed for a class of affine nonlinear systems with disturbance via Takagi-Sugeno (T-S) fuzzy bilinear model. The parallel distributed compensation (PDC) technique is utilized to design a fuzzy controller. The stability conditions of the overall closed loop T-S fuzzy bilinear model are formulated in terms of Lyapunov function via linear matrix inequality (LMI). The control law is robustified by H∞ sense to attenuate external disturbance. Moreover, the desired controller gains can be obtained by solving a set of LMI. A continuous stirred tank reactor (CSTR), which is a benchmark problem in nonlinear process control, is discussed in detail to verify the effectiveness of the proposed approach with a comparative study. Copyright © 2014 ISA. Published by Elsevier Ltd. All rights reserved.
ISA Transactions 07/2015; 57:85-92. DOI:10.1016/j.isatra.2014.11.012 · 2.98 Impact Factor
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• "The robust stabilization for continuoustime fuzzy bilinear uncertain system with disturbance was studied in [19], and then the result was extended to the robust stabilization for continuous-time fuzzy bilinear systems with time-delay only in the state [20] [21]. For the discrete case, the robust H∞ fuzzy control for a class of uncertain discrete fuzzy bilinear systems has been studied in [22], and then the result was extended to the discrete fuzzy bilinear system with time-delay only in the state [23], fuzzy observer design for time-delay T–S uncertain discrete fuzzy bilinear systems with disturbance in [24]. All the results are obtained based on either state feedback controller or observer-based controller. "
##### Conference Paper: Fuzzy PDC Controller for a Class of T-S Fuzzy Bilinear System via Output Feedback
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ABSTRACT: In this paper, fuzzy output feedback controller has been designed for a class of continuous time Takagi-Sugeno T-S fuzzy bilinear system. The parallel distributed compensation (PDC) technique is utilized to design a fuzzy controller. The stability conditions of the overall closed loop T-S fuzzy bilinear system are formulated in terms of Lyapunov via linear matrix inequality (LMI) and the desired controller gains can be obtained by solving a set of LMI. Some LMI conditions to set up the fuzzy controller to stabilize the T-S fuzzy bilinear system have been proposed. Finally, a numerical example and a practical application of dynamics of an isothermal continuous stirred tank reactor for the Van de Vusse are used to illustrate the applicability of the proposed method.
The 2nd International Conference on Engineering and Technology (ICET 2014), Cairo, Egypt; 04/2014
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• "Loop shaping is a design procedure to formulate frequencydomain specifications as H 1 constraints problems [18] [19] [20] [21]. To get a feeling for the loop-shaping methodology, consider the general pattern loop of Fig. 1. "
##### Article: Position and Current Control of an Interior Permanent-Magnet Synchronous Motor by Using Loop-Shaping Methodology: Blending of H ∞ Mixed-Sensitivity Problem and T–S Fuzzy Model Scheme
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ABSTRACT: This paper presents a robust mixed-sensitivity H-infinity controller design via loop-shaping methodology for a class of multiple-input multiple-output (MIMO) uncertain nonlinear systems. In order to design this controller, the nonlinear plant is first modeled as several linear subsystems by Takagi and Sugeno's (T-S) fuzzy approach. Both loop-shaping methodology and mixed-sensitivity problem are then introduced to formulate frequency-domain specifications. Afterward for each linear subsystem, a regional pole-placement output-feedback H-infinity controller is employed by using linear matrix inequality (LMI) approach. The parallel distributed compensation (PDC) is then used to design the controller for the overall system. Several experimental results show that the proposed method can effectively meet the performance requirements like robustness, good load disturbance rejection, and both tracking and fast transient responses even in the presence of parameter variations and load disturbance for the three-phase interior permanent-magnet synchronous motor (IPMSM). Finally, the superiority of the proposed control scheme is approved in comparison with the input-output linearization (I/O linearization) and the H-2/H-infinity controller methods.
Journal of Dynamic Systems Measurement and Control 09/2013; 135(5):051006. DOI:10.1115/1.4024200 · 0.98 Impact Factor