Researches For Linear System With Time Delay In Frequency Domain

Time delay system is one of the kernel problems in the control theory. In the industrial processes, most of the plant has the characteristic of the time delay, which refuses the plant to get the ideal control response by using the normal algorithm, such as PID. So, it is very difficulty to control the processes with time delay.As we know, the control theory by using transfer function in the frequency domain is very clear and easy to understand for studying the linear time invariant system. Recently, most conclusions for the linear system with time delay have been achieved in the frequency domain, especially the Smith predictor in continuous system and the Dahlin algorithm in the discrete system. But both of them have some disadvantages, so some researchers want to improve them and hope to get the ideal control response.In the industrial processes, we should design and use the controller with the characteristic of simple structure, low order and easy to implement. From this point of view and based on the research of the Smith predictor and its seriously improved algorithm, the dissertation studies some of the problems in the linear system with time delay and make the contributions as follow: 1) We make an overview on the improvement process of the linear systemwith time delay in the classic frequency domain control and predictivecontrol in detail, especially introduce the Smith predictor and its improvement.2) We provide two kinds of discrete PID control theories for the linear system with time delay to apply the disturbance rejection:a) Using the discrete double PI controllers and the IMC structure, the first algorithm can achieve the robust control for the load disturbance with non-steady state error.b) Dealing with the output by proportion controller directly, and then feedback to the input of the plant, the second algorithm can cancel the effect of the load disturbance. Its principle corresponds to applying the feed-forward control to the load disturbance.3) We provide the discrete PID control structure for the unstable process with integrator and time delay by using an internal feedback loop to stable the original plant. And we provide the design of the controllers finally.4) After studying the multivariable and multi-time delay system in the frequency domain and basing on the adjoint matrix, we introduce an adjustable diagonal matrix to get the anticipant decouple plant. Compare with the Smith predictor, which is extended in the multivariable and multi-time delay system, the new algorithm overcome the disadvantage that the model should match the process exactly. In addition, the structure is very simple and the design of the decoupler and the controller is very simple too.Finally, we make a conclusion and propose of the future research directions.