CAJ | 학술논문

研究反馈增益系数对非线性磁悬浮控制系统稳定性的影响,给出了系统保持稳定时设计参数的取值范围.通过引入Hopf分岔的检验函数分析了磁悬浮控制系统动态Hopf分岔的产生条件,从而避免了分析系统稳定性时求解全部特征值的大量计算.以速度反馈增益为参量,运用规范型法和中心流形法,解析地确定出表征磁悬浮系统中Hopf分岔方向、周期解的稳定性及周期变化的特征量,以便通过向分岔的反方向调节反馈增益系数而实现系统的稳定.最后通过数值模拟验证了主要结果的可靠性.
연구반궤증익계수대비선성자현부공제계통은정성적영향,급출료계통보지은정시설계삼수적취치범위.통과인입Hopf분차적검험함수분석료자현부공제계통동태Hopf분차적산생조건,종이피면료분석계통은정성시구해전부특정치적대량계산.이속도반궤증익위삼량,운용규범형법화중심류형법,해석지학정출표정자현부계통중Hopf분차방향、주기해적은정성급주기변화적특정량,이편통과향분차적반방향조절반궤증익계수이실현계통적은정.최후통과수치모의험증료주요결과적가고성.
The influence of feedback control gains on the stability of nonlinear maglev system was investigated and the range of design parameters for maintaining the system to be stable was obtained. A test function for Hopf bifurcation was introduced to analyze the forming condition of Hopf bifurcation. In this way, the time-consuming of eigenvalue computation in the process of analyzing system stability is avoided. With the velocity feedback control gain as bifurcation parameter, the normal form theory and center manifold argument were applied to derive the explicit formulae, which determine the stability, direction and period of Hopf bifurcating periodic solutions of the maglev system. So, the asymptotically stable system can be achieved by adjusting parameters in the direction opposite to that of the Hopf bifurcation. The numerical simulation was performed to illustrate the validity of the main results.