本論文第一部份首先探討相關文獻所提出的灰色模型，選擇與工程相關方面的例子來進行模型之檢測，並進一步結合傅立葉殘差修正法來做模型精度的改進。隨後討論建模維數和採樣區間對灰色預測模型的影響。
第二部份討論灰色理論在控制工程上的應用。利用灰色理論結合增量式PID控制法則來控制延遲系統及非線性系統。在控制線性延遲系統方面，以調整灰色預測器之預測步數為主要方法；而在非線性系統方面，則調整灰色預測器的累加生成次數及預測步數，觀察其對系統動態響應的影響。根據以上的模擬結果，顯示出本文所提出的灰色模型及其各種參數的調整方式，在控制系統設計上結果良好。

The first part of the thesis discusses the usability of the grey prediction models presented on associated literatures, and then the Fourier residual error method is cooperated into the grey prediction model to improve the model precisions. Some engineering examples are introduced to show the influence of the dimension and the sampling time on the grey prediction model.
The second part discusses the application of grey prediction theory on the control engineering. It tries to invent a new method by combining the grey theory with the incremental PID control scheme to make the control laws for time-delay systems and nonlinear systems. To control a linear time-delay system the main idea is to adjust the predictive step of the grey prediction controller. For nonlinear systems we observe the influence on system dynamic responses caused by various accumulative number and predictive step of the grey prediction controller. According to the simulation it shows the feasibility of the proposed method in controller design.

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