Intelligent Mechanical Earth by HィイD22ィエD2/HィイD2∞ィエD2 Control : Experiment and Digital Signal Processing

This control experiment based upon a new concept called mechanical earthand theoretical work on H - 22 D2/H - D2∞- D2 control as well as digital signal processing forimplementation. More specifically，our main toptics have been as follows:1. We have completed the polynomial ILQ设计理论a special kind of H D22 D2 controland solved the inverse problem of sample -data LQ control numerically，in relation to the digital signal processing for implementation.2.我们已经开发了控制法律which combines quadratic stabilization with dominant pole placement3.我们已经开发了，这是一个特定的决策，这是indeed implementable.3a design method for dynamic state feedback law which achieves H D2∞D2 control and partial poleplacement simultaneously.4. In H - D22 - D2/H - D2∞- D2 control，我们已经给了单一的问题一个numerical solution；i . e .,the case where the performance index does not satisfy standard assumptions.5. When implementing acontrol law,我们需要转换between continuus - and discrete-time signals sampling.我们已经分析了the effect of this transformation in terms of γ-positive realness （an extention of H D2∞D2）control) . however,further investigation such as phase property has not been performed.6. In view of an excellentfrequency property possessed by H D22 D2 or LQ control，我们已generalized the poly-nomial ILQ method into a method for achieving stability marginassignment and partial pole placement simultaneously.7.我们已经建立了一个实验设置andperformed control experiment.虽然我们可以确认控制系统的功能，我们已经发现了我们的加速器传感器和piezo actuator不支持我们objective. Further investigation is needed for a practical control system。

This research consists of control experiment based upon a new concept called mechanical earth, and theoretical work on HィイD22ィエD2/HィイD2∞ィエD2 control as well as digital signal processing for implementation. More specifically, our main toptics have been as follows :1. We have completed the polynomial ILQ design theory, a special kind of HィイD22ィエD2 control, and solved the inverse problem of sampled-data LQ control numerically, in relation to the digital signal processing for implementation.2. We have developed a control law which combines quadratic stabilization with dominant pole placement, and shown theoretically that under some coudition this is indeed implementable.3. We have developed a design method for dynamic state feedback law which achieves HィイD2∞ィエD2 control and partial pole placement simultaneously.4. In HィイD22ィエD2/HィイD2∞ィエD2 control, we have partially given a numerical solution for the singular problem ; I.e., the case where the performance index does not satisfy standard assumptions.5. When implementing a control law, we need to transform between continuous- and discrete-time signals via sampling. We have analyzed the effect of this transformation in terms of γ-positive realness (an extention of HィイD2∞ィエD2 control). However, further investigation such as phase property has not been fully performed.6. In view of an excellent frequency property possessed by HィイD22ィエD2 or LQ control, we have generalized the poly-nomial ILQ method into a method for achieving stability margin assignment and partial pole placement simultaneously.7. We have composed an experimental setup and performed control experiment. Although we could confirm the function of the control system, we have found out. That the acceleration sensor and the piezo actuator are not sufficient to our objective. Further investigation is needed for a practical control system.