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Multi-objective optimized fuzzy-PID controllers for fourth order nonlinear systems

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Figure

Fig. 1. Structure of the ball–beam system.
Fig. 2. The block diagram of fuzzy-PID control for the ball–beam system.
Fig. 4. Membership functions of PFIM for the ball–beam system.
Fig. 5. Three-dimensional Pareto fronts of objective functions 1, 2 and 3 for the ball–beam system.
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