Analytic exploration of safe basins in a benchmark problem of forced escape

Benchmark problems have been used to evaluate the performance of a variety of robust control design methodologies by many control engineers over the past 2 decades. A benchmark is a simple but meaningful problem to highlight the advantages and disadvantages of different control strategies. This paper verifies the performance of a new control strategy, which is called combined feedforward and feedback control with shaped input (CFFS), through a benchmark problem applied to a two-mass-spring system. CFFS, which consists of feedback and feedforward controllers and shaped input, can achieve high performance with a simple controller design. This control strategy has several unique characteristics. First, the shaped input is designed to extract energy from the flexible modes, which means that a simpler feedback control design based on a rigid-body model can be used. In addition, only a single frequency must be attenuated to reduce residual vibration of both masses. Second, only the dynamics between control force and the first mass need to be considered in designing both feedback and feedforward controllers. The proposed control strategy is applied to a benchmark problem and its performance is compared with that obtained using two alternative control strategies.

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Lexicographic Orders of Intuitionistic Fuzzy Values and Their Relationships

Mathematics ◽

10.3390/math7020166 ◽

2019 ◽

Vol 7 (2) ◽

pp. 166 ◽

Cited By ~ 19

Author(s):

Feng Feng ◽

Meiqi Liang ◽

Hamido Fujita ◽

Ronald Yager ◽

Xiaoyan Liu

Keyword(s):

Decision Making ◽

Comparative Analysis ◽

Scalar Product ◽

Multiple Attribute Decision Making ◽

Benchmark Problem ◽

Score Functions ◽

Intuitionistic Fuzzy ◽

Multiple Attribute ◽

Risk Investment ◽

Membership Score

Intuitionistic fuzzy multiple attribute decision making deals with the issue of ranking alternatives based on the decision information quantified in terms of intuitionistic fuzzy values. Lexicographic orders can serve as efficient and indispensable tools for comparing intuitionistic fuzzy values. This paper introduces a number of lexicographic orders by means of several measures such as the membership, non-membership, score, accuracy and expectation score functions. Some equivalent characterizations and illustrative examples are provided, from which the relationships among these lexicographic orders are ascertained. We also propose three different compatible properties of preorders with respect to the algebraic sum and scalar product operations of intuitionistic fuzzy values, and apply them to the investigation of compatible properties of various lexicographic orders. In addition, a benchmark problem regarding risk investment is further explored to give a comparative analysis of different lexicographic orders and highlight the practical value of the obtained results for solving real-world decision-making problems.

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