Uncertainty is inherent and unavoidable in almost all engineering systems. It is of essential significance to deal with uncertainties by means of reliability approach and to achieve a reasonable balance between reliab...Uncertainty is inherent and unavoidable in almost all engineering systems. It is of essential significance to deal with uncertainties by means of reliability approach and to achieve a reasonable balance between reliability against uncertainties and system performance in the control design of uncertain systems. Nevertheless, reliability methods which can be used directly for analysis and synthesis of active control of structures in the presence of uncertainties remain to be developed, especially in non-probabilistic uncertainty situations. In the present paper, the issue of vibration con- trol of uncertain structures using linear quadratic regulator （LQR） approach is studied from the viewpoint of reliabil- ity. An efficient non-probabilistic robust reliability method for LQR-based static output feedback robust control of un- certain structures is presented by treating bounded uncertain parameters as interval variables. The optimal vibration con- troller design for uncertain structures is carried out by solv- ing a robust reliability-based optimization problem with the objective to minimize the quadratic performance index. The controller obtained may possess optimum performance un- der the condition that the controlled structure is robustly re- liable with respect to admissible uncertainties. The proposed method provides an essential basis for achieving a balance between robustness and performance in controller design ot uncertain structures. The presented formulations are in the framework of linear matrix inequality and can be carried out conveniently. Two numerical examples are provided to illustrate the effectiveness and feasibility of the present method.展开更多
基金supported by the National Natural Science Foundation of China(51175510)
文摘Uncertainty is inherent and unavoidable in almost all engineering systems. It is of essential significance to deal with uncertainties by means of reliability approach and to achieve a reasonable balance between reliability against uncertainties and system performance in the control design of uncertain systems. Nevertheless, reliability methods which can be used directly for analysis and synthesis of active control of structures in the presence of uncertainties remain to be developed, especially in non-probabilistic uncertainty situations. In the present paper, the issue of vibration con- trol of uncertain structures using linear quadratic regulator （LQR） approach is studied from the viewpoint of reliabil- ity. An efficient non-probabilistic robust reliability method for LQR-based static output feedback robust control of un- certain structures is presented by treating bounded uncertain parameters as interval variables. The optimal vibration con- troller design for uncertain structures is carried out by solv- ing a robust reliability-based optimization problem with the objective to minimize the quadratic performance index. The controller obtained may possess optimum performance un- der the condition that the controlled structure is robustly re- liable with respect to admissible uncertainties. The proposed method provides an essential basis for achieving a balance between robustness and performance in controller design ot uncertain structures. The presented formulations are in the framework of linear matrix inequality and can be carried out conveniently. Two numerical examples are provided to illustrate the effectiveness and feasibility of the present method.
