Optimal Control For Time-Delay Systems With External Disturbances

Almost all practical control systems work under persistent disturbances, which can degrade the system performance, or even cause instability of the system. Due to the time lag in variable measurement and signal transmission, the phenomena of time delay are frequently encountered in many control systems, such as time delays in temperature control of oil pipe, network-induced delays in networked control systems, and so on. This problem has attracted considerable attention recently. Time-delay systems are infinite-dimensional systems described by functional differential equations. Therefore, it is very difficult for the stability analysis and control algorithm design for them. Up to now, many problems are still open in this field. Therefore, the study of time-delay systems is still a focus, and will remain interesting for many researchers in the future.Offshore platforms are typical time-delay systems subjected to persistent external disturbances. Vibration control becomes a very important research subject in ocean engineering. Time delay in control input is inevitable and is also an important problem in the active control of offshore platforms. Therefore, the optimal control problem for time-delay systems with disturbances is of both theoretical significance and practical values.This thesis first gives an outlook on the state-of-the-art of optimal control for time-delay systems. Further research work is given later. The main contents are given as follows:1. First, the development history of the optimal control for time-delay systems is reviewed. Then, the zero steady-state error control method based on the internal model principle and the study of optimal control based on quadratic average performance index for systems with external disturbances are given. Finally, the contents of this thesis are listed.2. The optimal control for linear systems with control time delay affected by sinusoidal disturbances is considered. Optimal rejection with zero steady-state error is realized by designing an optimal regulator. First, the system with control time delay is transformed into one without time delay through the Artstein transform. Then based on the internal model principle, a disturbance compensator is designed such that the plant model with external disturbances is transformed into an augmented system without disturbances. Consequently, the problem of disturbance rejection with zero steady-state error becomes the problem of designing an optimal controller for the augmented plant without disturbances. By using the optimal control theory, an optimal feedback control law with zero steady-state error is obtained.3. An optimal sinusoidal disturbance attenuation problem for linear systems with both state and input delays is considered. By the Artstein transform, the original system is first transformed into one without explicit input delays. Then, an approximation sequence is constructed. By viewing the time-delay term as an actuator term in each iteration step, the optimal control problem reduces to a sequence of nonhomogeneous linear two-point boundary value (TPBV) problems whose solution sequences uniformly converge to the solutions of the original TPBV problem. An iterative algorithm for the suboptimal control law is given.4. The main work of this thesis is summarized and prospects on this research work in the future are presented.