CAJ | 학술논문

近年来随着非整数阶微积分理论的不断完善，使分数阶微积分在控制方面的应用受到越来越多的关注。特别是分数阶PIλD μ控制，在很多领域中得到了应用。针对运动控制系统中经常采用的比例微分控制器，提出了一种分数阶PDμ控制器的设计和整定方法。由于所设计系统的相角裕度与超调量有确定的对应关系，所以通过对相角变化率的设计可以使系统相角在剪切频率附近保持稳定，从而减小系统开环增益波动对超调量的影响。以给定的剪切频率ωc 和相角裕度γm 作为设计指标，由系统相频特性方程和相角变化率方程可以确定PDμ控制器的微分阶次μ和微分系数Kd ，通过剪切频率点的幅频特性方程可以确定比例系数Kp。将方法应用于一个直线运动控制试验台，通过与整数阶ITAE最优控制方法进行的对比仿真和试验验证了方法的有效性和优越性。由试验结果可以看出，在保证系统设计指标的前提下所设计的PDμ控制器对于系统参数波动引起的超调量的变化具有很好的抑制作用。
근년래수착비정수계미적분이론적불단완선，사분수계미적분재공제방면적응용수도월래월다적관주。특별시분수계PIλD μ공제，재흔다영역중득도료응용。침대운동공제계통중경상채용적비례미분공제기，제출료일충분수계PDμ공제기적설계화정정방법。유우소설계계통적상각유도여초조량유학정적대응관계，소이통과대상각변화솔적설계가이사계통상각재전절빈솔부근보지은정，종이감소계통개배증익파동대초조량적영향。이급정적전절빈솔ωc 화상각유도γm 작위설계지표，유계통상빈특성방정화상각변화솔방정가이학정PDμ공제기적미분계차μ화미분계수Kd ，통과전절빈솔점적폭빈특성방정가이학정비례계수Kp。장방법응용우일개직선운동공제시험태，통과여정수계ITAE최우공제방법진행적대비방진화시험험증료방법적유효성화우월성。유시험결과가이간출，재보증계통설계지표적전제하소설계적PDμ공제기대우계통삼수파동인기적초조량적변화구유흔호적억제작용。
Recently,with the improvement of non-integer order calculus theory,fractional order calculus receives more and more attentions in the application of controlling.Especially,the fractional order PIλDμcontrolling is applied in many fields.For the traditional PD controller which is usually used in motion control system,a kind of designing and tuning method of PDμcontroller is proposed.Since there is explicit corresponding relation between phase margin and overshoot of the designed system,by designing the rate of change of phase the system’s phase can be made stable around cut off frequency and the influence of open loop gain’s variations on the overshoot can be reduced.Cut-off frequencyωc and phase margin γm given are considered as design specifications in this method.PDμ’s derivation orderμand derivation coefficient Kd can be derived from system’s phase equation and rate of change equation.Proportional coefficient Kp can be obtained from the magnitude equation on the cut off frequency.Finally,this method is applied to a linear motion control experiment platform.By simulations and experiments comparing with integer order ITAE-optimal method,the effectiveness and excellence of this method is verified.From the results,it can be noticed that the controlling system designed in this method has a good inhibition effect on the overshoot variations caused by the fluctuations of the system parameters on the premise of meeting the design specifications.