Global Stabilization Of Control Systems With Input Saturation And Multiple Input Delays

Saturation of physical input on hardware determines that the amplitude of control signal is always limited in many practical dynamic systems.Saturation is a potential problem for actuators of control systems.It often severely limits the performance of systems,resulting in inaccurate control and even unstable closed-loop systems.Therefore,it is necessary to study the stabilization of systems with input saturation.At the same time,in actual industrial systems such as aerospace systems,chemical systems and communication systems,the phenomenon of time delay is inevitable,especially multi-input time delay.If its existence is ignored in the design of the controller,it may lead to system overshoot and even system instability.Therefore,it is of great significance to study systems with input saturation and multiple input delays.In this paper,the global stabilization problem of control systems with input saturation and multiple input delays is studied,and some of the established theories are applied to solve the global stabilization problem of circular spacecraft rendezvous systems.The main contents are as follows:For continuous linear systems with multiple input delays,a new method is proposed to design a globally stable state feedback control law.Firstly,it is converted into a series of linear time-delay systems with a single input,and the two systems are decoupled by using the same eigenvalues before and after conversion,i.e.stability equivalence.For the decoupled system,a special state transformation with time delay is constructed and converted into a linear system with time delay in both the state and the input variables.For the conversion system,the feedback gain is designed by pole assignment under certain constraints,so that the closed-loop pole has the maximum state decay rate in a certain region while the system has the maximum state decay rate.Finally,the simulation comparison verifies the superiority of the proposed method.For continuous systems with input saturation and multiple input delays,a new method is proposed to design the stabilization control law.Firstly,it is converted into a series of linear systems with single input and input saturation.However,each subsystem is coupled to each other.For each subsystem controller,it does not need to be the global stabilization controller of the whole system.Therefore,the idea of recursion can be adopted for each subsystem by constructing a special state transformation with time delay,which can be converted into a system with time delay in both the state and the input variables.For the conversion system,a nonlinear control law with cascade saturation control is designed and a stability condition with less conservatism is established.Finally,the effectiveness of the proposed method is verified by simulation.For continuous feedforward systems with input saturation and multiple input delays,a new method is proposed to design a nonlinear stabilization control law.Firstly,it is converted into a series of nonlinear systems with single input and input saturation.Due to the existence of non-linear terms,a new special state transformation is constructed to transform it into a system with non-linear terms with time delay in both state and input variables.For the conversion system,a nonlinear control law with nested saturation is designed and a stability condition with less conservatism is established.Finally,the effectiveness of the proposed method is verified by simulation.The continuous system theory with input saturation and multiple input delays proposed above is applied to solve the global stabilization problem of circular spacecraft rendezvous system model.Firstly,the circular spacecraft rendezvous system model is transformed into a multi-input time-delay system described by the state equation,and then the global stabilization controller is designed by applying the theoretical results established in this paper.Finally,the simulation shows the practicability of the results established in this paper.