Memoryless Feedback Stabilization And Application For Control Systems With Unknown Input Delay

The phenomenon of time delay is very common in the control system,such as engineering control system,network control system,biological system,mathematical physics system,and so on.The existence of time delay often has a negative impact on the stability and performance of the system,and even leads to instability.Systems with input time-delay are an important class of timedelay systems,and its research on some related issues has been widely concerned by scholars at home and abroad.Because the system with input delay is an infinite dimensional control system,the controller design and stability analysis of the input time delayed system is a difficult problem in the field of control,which has important theoretical research significance and practical application value.In this paper,the control system with unknown input delay is studied from two aspects: linear system and nonlinear system.For a class of linear systems with unknown input delay,a memoryless state feedback controller is designed by using truncated predictor feedback method to achieve global asymptotic stability of the closed-loop system.Then,for a class of nonlinear systems with unknown input delay,a memoryless feedback controller based on linearization method is designed to achieve local asymptotic stability of the closed-loop nonlinear system.Finally,the above research results are applied to the pitch reduction control of high-speed catamaran.In this paper,the four aspects of main results include:(1)For a class of linear system with unknown input delay,in order to avoid the realization problem caused by the traditional Smith predictor controller,which is infinite dimensional,we design a memoryless state feedback controller based on the truncated predictor.By the Razumikhin theorem,it is proved that the closed-loop control system is globally asymptotically stable when the unknown input delay is in a certain range,whose explicit expression is given.(2)For a class of nonlinear systems with unknown input delay,a memoryless state feedback controller based on truncated predictor is designed by using linearization method and nonlinear separation property.We prove that the memoryless state feedback controller can make the nonlinear system with input delay be locally asymptotically stable.In addition,this result is further extended to the case where the eigenvalues of linearized systems lie on the left closed complex plane.(3)For a class of nonlinear systems with unknown input delay,the problem of local stabilization by memoryless output feedback is studied.A memoryless output feedback controller is designed for the linearization systems with input delay.When the unknown input delay is in a certain range,it is proved that the designed memoryless output feedback controller can realize the local asymptotic stability of MIMO nonlinear systems by the use of Razumikhin theorem and the local feedforward complete lemma for nonlinear time-delay systems.In addition,this result still holds for the case where the eigenvalues of the linearization system are located on the left closed complex plane.(4)For the pitch reduction control problem of high-speed catamaran under the influence of unknown input time delay,the nonlinear mathematical model of catamaran is linearized,and the model of catamaran with T-wing is established.Using the above research results,a memoryless feedback controller is designed to realize the local asymptotic stability of the pitch reduction control system.The simulation results verify the effectiveness of the proposed control scheme.In this paper,linear and nonlinear time delay systems are studied.For control systems with unknown input delay,a memoryless feedback controller is designed that can make the system asymptotically stable.The unknown input delay value is combined with the known input time delay and other parameters,and an explicit expression for the range of unknown input delay is given.Design a memoryless feedback controller that can effectively control the system within the constraint range of unknown input delay.In addition,the above research results are also applied to the pitch reduction control of high-speed catamaran.