Delayed Output Feedback Of Time-delay Systems With Applications To Spacecraft Control

Time-delay phenomena exist widely in various systems,such as mechanical transmission systems,chemical process systems,industrial metallurgical systems,aerospace systems,networked control systems and so on.On the one hand,the existence of timedelay can lead to performance degradation or even instability of systems.On the other hand,some unexpected performances can be obtained by skillfully utilizing time-delay.In recent years,the problem of time-delay has attracted wide attention and research.As a classical method to compensate time-delay,Smith predictor can handle the systems with pure input delay well.However,the Smith predictor is invalid when the non-time-delay part of the original system is unstable.As an alternative method to overcome the aforementioned problem,the predictor feedback controller constitutes a state-like feedback using the current states and the past input during a period of time.Nevertheless,the states are not completely measurable or difficult to be measured for many systems.As a result,the application of the predictor feedback controller is limited.To solve this problem,this thesis proposes a control method for linear time invariant continuous systems with multiple input delays,which is referred as delayed output feedback(DOF)control.Compared with other methods used to compensate time-delay,the greatest feature of the DOF control is that it only uses the current and past input and output information,so it is easier to be implemented.To overcome the instability problem arisen by the numerical implementation of the distributed delay terms contained in DOF control,this thesis gives an LPF-based DOF control.In addition,this thesis proposes the DOF control for discretetime systems,time-varying systems systematically.Finally,design the DOF control for a spacecraft rendezvous system and a three-axes magnetic moment attitude control system with the theory presented in this thesis.The main research work is as follows:Chapter 1 declares the background and significance of this subject.The knowledge closely related to the subject,such as time-delay systems,output feedback,spacecraft rendezvous and three-axes magnetic moment attitude control,is presented.The main research work of this thesis is summarized.Chapter 2 proposes the DOF control and the LPF-based DOF control for linear time invariant continuous systems with multiple input delays.By introducing a state transformation,systems with multiple input delay are transformed into equivalent non-time-delaysystems firstly.The states of the equivalent systems are constructed from the current and past input and output information by the motion equations of the systems.Then the constructed sates are used to form feedback and the DOF control is obtained.To solve the instability problem arisen by the numerical implementation of distributed delay terms involved in the DOF control,this chapter proposes an LPF-based DOF control.It is proven that there is always a sufficiently high numerical integration precision such that the LPF-based DOF control system can maintain asymptotic stability after numerical implementation.By constructing an augmented system,the design problem of the LPF is transformed into a state feedback stabilization problem.Finally,the effectiveness of the proposed method is verified by numerical simulations.Chapter 3 proposes the DOF control for linear time invariant discrete-time systems with single input delay and multiple input delays.For systems with a single input delay,using only the input and output information at some discrete points of the current and the past,the future states are constructed with the motion equations of the systems.Then the corresponding DOF control is obtained by the feedback of the constructed states.For a system with multiple input delays,it is firstly transformed into an equivalent nontime-delay system by a model reduction method.Then the conclusion of systems with a single input delay is extended to systems with multiple input delays.The DOF control for discrete-time systems doesn't contain distributed delay terms,thus avoids the problem of instability problem arisen by numerical implementation.The chapter also proposes the delayed output feedback control used to state observation error reconstruction.Compared with state feedback controls which are based on traditional observers,the delayed output feedback control used to state observation error reconstruction weakens the stability requirement of the observer itself and the observation(prediction)process of states is deadbeat.So the control system has better dynamic performance.For systems with a single input time-delay,the second type of delayed output feedback control used to state observation error reconstruction is also proposed in this chapter,which can significantly reduce the computational complexity of the controller when the input and output delays are large.The numerical simulations prove that the theoretical method proposed in this chapter is effective.Chapter 4 provides the DOF control for single input delay systems with a timevarying input matrix,general time-varying continuous systems with multiple input delays and time-varying discrete-time systems with multiple input delays.For general time-varying continuous systems,the definition of Gram matrix for observability is redefined in this chapter,and its non-singularity is analyzed.Aiming at the safe numerical implementation of the distributed time-delay terms in the DOF control for time-varying continuous systems,this chapter proposes a time-varying LPF-based DOF control.By designing time-varying LPF parameters Af(t)and Bf(t),which involve free parameters,the design problem of LPF is transformed into a state feedback stabilization problem of general time-varying systems.To solve the problem that time-varying systems are difficult to achieve stabilization through pole placement,parametric DRE method and Lyapunov equation method are used in this chapter to design the feedback gain.Using this method to design feedback gain,the input amplitude can be effectively controlled and saturation can be avoided.In addition,the DOF control for the time-varying discrete-time system is constructed by using the motion equations of the time-varying discrete-time systems,which only utilizes the input and output information of the current and the past.Moreover,it avoids the numerical implementation problem.Chapter 5 is the application of the theoretical methods proposed in Chapter 2–Chapter 4 to spacecraft rendezvous systems and three-axes magnetic moment attitude control systems.Firstly,the kinematics and dynamics of spacecraft rendezvous systems and three-axes magnetic moment attitude control systems are modeled in this chapter,and then they are linearized reasonably according to the need of DOF control design.The continuous or discrete-time DOF control for rendezvous systems and three-axes magnetic moment attitude control systems are designed by using the theoretical methods proposed in Chapter 2–Chapter 4.The simulation results show that the designed DOF controls can accomplish the rendezvous task and attitude control task well,and effectively solve the problem that the relative velocity between spacecrafts is difficult to be measured accurately.The time-delay of the actuators and sensors is effectively compensated,and the saturation of actuators is avoided.Moreover,the designed DOF control has good robustness to the uncertainties of system structure,parameters,input delay and rounding errors in the process of controller implementation.This chapter is a preliminary attempt of the theoretical methods proposed in this thesis to the spacecraft control,which provides a reference for solving some problems in the spacecraft orbit and attitude control.