On State-Predictive Servo Controllers for Time-Delay Systems and Their Application to Blood Pressure Control

In this thesis, a design method of the state-predictive servo system for the plant with a pure delay is proposed and applied to the blood pressure control of living bodies using a hypotensive drug. The state-predictive controller is one of the representative controllers that takes the pure delay of the plant into account, and is effective in control of the plant with comparatively long delay. The thesis consists of three parts. In the first part, a design method of the state-predictive two-degree-of-freedom LQI servo system is studied. First, a design method of the two-degree-of-freedom LQI servo system in the delay-free case is extended to the case where the plant includes a pure delay. This method enables the designer to determine the tracking characteristics for step references and the feedback characteristics for step disturbances optimally with respect to independent quadratic performance indices, respectively. Then, the properties of the designed state-predictive two-degree-of-freedom servo system is clarified, and the optimal observer that minimizes the deterioration of the maximally attainable disturbance rejection ability is derived. This result about the optimal observer, in combination with the two-degree-of-freedom design method derived at the beginning, constitutes the complete solution to the optimal design problem of the state-predictive two-degree-of-freedom LQI servo system for step references and step disturbances. In the second part, a robust stability condition of the state-predictive control system is derived under the assumption that the gain and the delay time of the plant model include uncertainties. A method to calculate the stability margin is also established. In the state-predictive controller, the present state of the lumped-parameter part of the plant is predicted using a dynamical model of the plant. So, the performance of the controller much depends upon the accuracy of the model. Hence, in the design of state-predictive controllers, the robust stability analysis is essential. The robust stability condition derived here gives. a practically complete solution to this problem for the case of scalar plants in the sense that the controller is ready for the worst case. Namely, the uncertainties of the plant model of scalar plants can be reduced to the uncertainties in the gain and the phase, and the assumption that there exists the uncertainty in the delay time corresponds to the case of the worst phase shift for a given gain. In the third part l the state-predictive servo controller is applied to the blood pressure control of living bodies using a hypotensive drug. The final purpose of the research is to apply the obtained result to the blood pressure control of pa~ients under surgical operation and to reduce blood loss, to reduce blood transfusion and to avoid the side"effect of blood transfus~on. To attain these effects, the blood pressure must be kept within a narrow range. Since the responses of the blood pressure of living bodies to a hypotensive drug include a considerably large pure delay, the control system must be designed by a method taking the dead time of the responses to the hypotensive drug into accotintso that highly accurate control is performed. This circumstance motivated the useof a state-predictive servo controller. The control system was applied to a dog experimentally and proved to achieve satisfactorily accurate and robust performance needed in the application to the surgical operations.