CAJ | 학술논문

针对含两类分数阶微分项的悬架系统非线性振动，提出一种最优化控制方法，并得到最优反馈控制参数的取值范围。以一个带有两类分数阶微分项的非线性单自由度悬架系统为控制对象，引入线性控制参数，采用平均法得到系统的近似解，导出系统的幅频响应特性。分析系统作周期振动的定常解的稳定性，在保证系统存在稳定解的前提下，得到反馈控制参数的取值范围。分别以悬架系统的衰减率和稳定的反馈控制参数取值范围作为最优化控制的目标函数和约束条件，利用最优化方法得到最优反馈控制参数。研究了激励幅值及分数阶微分的变化对反馈控制参数的影响。仿真结果表明：引入控制参数能有效减小悬架系统的主共振幅值，减弱或消除其非线性振动特性；不同的分数阶阶次会对控制参数产生影响，进而影响系统的振动控制效果，其作用不可忽视。研究结果为悬架系统的优化设计提供了理论依据和设计参考。
침대함량류분수계미분항적현가계통비선성진동，제출일충최우화공제방법，병득도최우반궤공제삼수적취치범위。이일개대유량류분수계미분항적비선성단자유도현가계통위공제대상，인입선성공제삼수，채용평균법득도계통적근사해，도출계통적폭빈향응특성。분석계통작주기진동적정상해적은정성，재보증계통존재은정해적전제하，득도반궤공제삼수적취치범위。분별이현가계통적쇠감솔화은정적반궤공제삼수취치범위작위최우화공제적목표함수화약속조건，이용최우화방법득도최우반궤공제삼수。연구료격려폭치급분수계미분적변화대반궤공제삼수적영향。방진결과표명：인입공제삼수능유효감소현가계통적주공진폭치，감약혹소제기비선성진동특성；불동적분수계계차회대공제삼수산생영향，진이영향계통적진동공제효과，기작용불가홀시。연구결과위현가계통적우화설계제공료이론의거화설계삼고。
An optimal control method is presented for the nonlinear vibration system with two kinds of fractional-order derivative to gain the optimal range of feedback control parameters. The linear control parameters for a nonlinear single degree-of-freedom ( SDOF ) suspension system with two kinds of fractional-order derivative were introduced, the approximately solution and the amplitude-frequency response were obtained by averaging method. The system stability was analyzed and the range of feedback control parameters were gained on the premise of existence of stable solution of the system . Taking the attenuation ratio of suspension system and the stable feedback control parameters as objective functions and constraint conditions, respectively, the optimal control parameters were calculated by the optimization method. The simulation results show that the introduction of control parameters can effectively reduce the amplitude of primary resonance, weaken or eliminate the non-linear vibration characteristics of the suspension system. The fractional orders can have an impact on <br> control parameters, which affect the effect of vibration control, so the impact of fractional orders should be considered in the control problem. The study will provide a theoretical basis and reference for the optimal design of the suspension system.