Research on the development for the design method of robust servo systems from the viewpoint of the inverse problem and its application to a magnetic levitation system

本研究的目的是建立一种从逆问题的角度出发的鲁棒伺服系统设计方法，并将其应用于磁悬浮系统的控制问题，以阐明其有效性和存在的问题，并在必要时进一步改进该方法。为了达到这一目的，我们将自己开发的鲁棒ILQ设计方法应用于去年以Y形铁板为悬浮载体的磁悬浮系统的控制问题。结果，我们成功地在一个设定值上应用阶跃变化控制了它的非常稳定的悬浮和姿态。然而，我们发现，当施加脉冲扰动时，由于非线性和建模中忽略的振动模式引起的建模误差导致了不稳定运动的发生。我们今年首先尝试解决这一问题，并针对两种建模误差采取措施。针对以往的建模误差，本文采用精确线性化技术代替近似线性化技术建立了磁悬浮系统的模型，并设计了控制系统并进行了控制实验。因此，它的性能有所提高。然而，由脉冲扰动引起的不稳定运动并没有被抑制。另一方面，针对前者的建模误差，采用了H_*控制理论，在控制系统设计中可以将其考虑在内，并对控制系统进行了设计。在此基础上，设计了一种控制器，通过在设定值上施加小阶跃变化来抑制脉冲扰动引起的不稳定运动。然而，它不能设计与一个大阶跃变化的设定值的应用。为了正确地掌握精确线性化技术的有效性，我们在一个非常刚性的鱼叉形悬浮飞行器上进行了类似的悬浮控制实验，验证了基于精确线性化模型的仿真结果与基于线性近似模型的实验结果更加一致。在此基础上，本文扩展了ILQ伺服系统最优设计方法。到目前为止，该设计方法只考虑了阶跃参考输入，因此得到的控制器阶数较低，不利于控制系统性能的提高。因此，我们在今年推广了基于参考输入的ILQ伺服优化设计方法，并开发了其CAD。少

The purpose of this research is that we develop a design method of robust servo systems from the viewpoint of the inverse problem and apply it to a control problem of a magnetic levitation system in order to clarify its effectiveness and its problem and furthermore improve the method if necessary. In order to achieve this purpose, we applied the Robust ILQ design method developed by us to the control problem of the magnetic levitation system with a Y shape iron plate as a levitation vehicle last year. As a result we succeeded in a control experiment of its very stable levitation and attitude with an application of step change in a set point. We, however, found it that an unstable motion happened due to the modelling errors which was arisen from nonlinearity and modes of vibration neglected in modelling when an impulse disturbance was applied. We first try to solve this problem this year and take measures against two kinds of modelling errors. Against the former modelling error we made … More a model of the magnetic levitation system by using exact linearization technique, which is useful as was pointed out recently, instead of approximate linearization technique and then design a control system and did a control experiment. As a result its performance was a little improved. The unstable motion caused by an impulse disturbance, however, was not suppressed. On the other hand against the former modelling error we use H_* control theory, which can take it into account in the control system design, and design the control system. Then a controller was designed in order to suppress the unstable motion caused by an impulse desturbance with an application of small step change in a set point. It, however, could not be designed with an application of large step change in a set point. In order to grasp the effectiveness of exact linearization technique correctly, we did a similar levitation control experiment with a very rigid barbel shape levitation vehicle and verified that a simulation result and an experimental result based on the exactly linearized model was more consistent than that based on the linear approximation model. Based on the above-mentioned information we extended the ILQ optimal servo system design method this year. So far this design method have taken only a step reference input into consideration and a controller obtained by using the method therefore had low order and it prevented the performance of the control system from being improved. Hence, we generalized ILQ optimal servo design method with respect to the reference input and developed its CAD this year. Less