Fundamental Study on Adaptive Control Theory for Distributed Parameter System and its Application to Tempareture Control

本文研究了一种适用于描述工业加热炉或钢厂温度分布的分布参数系统的自适应数字控制的基础性研究。首先，提出了一种基于正则化方法和样条逼近方法的分布参数系统参数辨识方法。然后将该识别方法应用于日本德岛市附近地区的空气污染分布。在得到分布系统的估计参数后，将分布参数系统离散化为离散时间系统。对于离散时间分布参数系统，我们构造了各种自适应控制系统。其中，将自校正控制算法应用于加热炉温度控制。与常规的PID控制器相比，该控制器的控制效果良好。此外，我们还将广义预测控制算法应用于同样的问题，得到了稳定和鲁棒的控制结果。因此，本文的研究表明，自适应数字控制方法对分布参数系统和集中参数系统都具有很强的控制能力。

This Study is concerned with fundamental research for adaptive digital Control of a distributed Parameter system which is usefulfor description of temperature distribution in industrial Furnace or steel mill. first, we have proposed an parameter identification for distributed parameter systems by using regularization method and spline approximation method. Then the identification method has been applied to air pollution distribution in the vicinity of Tokushima City in Japan. after getting the estimated parameters of distributed systems, we have discretized the distributed parameter system into discrete-time system. For the discrete-time distributed parameter system we have constructed various kinds of adaptive control systems. Among them, we have applied the self-tuning control algorithm to control the temperature of heating furnace. The control results have been excellent compared with those by conventional PID controller. Furthermore, we have applied generalized predictive control algorithm to the same problem and obtained stable and robust control results. Therefore, the present study has shown that the adaptive digital control methods are powerful to control the distributed parameter systems as well as lumped parameter systems.