Aiming at the problem of unstable buffering process of electromagnetic buffer (EMB) under intensive impact load, a three-segment electromagnetic buffer is proposed. The inner tube and air-gap of EMB are divided into three segments. The finite element analysis and impact test results show that the resultant resistance force (RRF) curve has two hump-shaped peaks, which is the reason for the unstable buffering process. In order to stabilize the buffering process, a multi-objective optimization design method of EMB based on Nash game theory is proposed. Firstly, the optimization model is established by taking the two peaks of the RRF curve and the maximum buffer displacement as the optimization objectives. Secondly, the multi-objective optimization model is transformed into a game model by sensitivity analysis and fuzzy clustering. Then, a Nash equilibrium solution strategy of EMB Nash game model based on symmetric elitist information exchange is proposed, which integrates gene expression programming (GEP) surrogate model and genetic algorithm (GA) as an optimization solver. Finally, the Nash equilibrium of the game model is obtained. The results show that the smoothness of the RRF curve has been significantly improved, which proves the effectiveness of the game strategy.
Graphic abstractIn this paper, adaptive–adaptive robust boundary control is proposed for uncertain mechanical systems with inequality constraints. First, inequality constraints are taken into consideration, which are derived from the system or environment constraints on state bounds and control input bounds. Moreover, the original system with inequality constraints is transformed into a novel system with merely equality constraints by constraint reorganization techniques. Second, an adaptive robust control with a two-layer adaptive law is initiated. Here, the lower-layer adaptive law is used to overcome the (possibly rapidly time-varying) system uncertainty, which is bounded but unknown. Additionally, the adaptive law design parameters are chosen online by the upper-layer adaptive law, rather than according to the empirically set fixed values. Finally, the performance of the controller with uniform boundedness and uniform ultimate boundedness is theoretically and experimentally verified. The control strategy allows the electric cylinder-driven pitch system to achieve highly accurate and error-controllable motion within the motor drive capability.
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