Global Stabilization Of Control Systems With Input Saturation And Time-delay

Practical control systems are subject to input saturation.Ignoring the saturation nonlinearity in controller design can degrade the system performance of the resulting closedloop system when the saturation occurs and may even lead to instability.Because of the inherently nonlinear behavior of a control system with bounded controls,the stabilization problem is far from trivial.On the other hand,it is well known that time delay is also frequently encountered in engineering,and ignoring time delays can cause the performance deterioration even instability of the closed-loop system,particularly,if the delays are large enough.It is thus natural and essential to consider the problem of stabilization of control systems with input saturation and time-delay,which,as we can expect,is even more difficult that the problems of stabilizing control systems with input saturation or timedelay.This thesis studies the global stabilization of control systems with input saturation and time-delay.And the proposed approaches are used to solve the global stabilization problem of PVTOL aircraft system model.The main results are listed in the following.1.The global stabilization of ANCBC linear systems with input saturation and timedelay is considered.Based on some special canonical forms,several types of new nonlinear control laws consisting of nested/cascade saturation functions are proposed,and explicit conditions are proposed to guarantee the global stability of the closed-loop systems.Differently from the existing canonical forms,the new special canonical forms used in this thesis contain not only time delay in the input but also time delays in its state,which are essential in the recursive design since they lead to natural cancellation.Moreover,some free parameters are introduced into these controllers.Compared with the existing results,these advantages can help to improve the transient performance of the closed-loop system significantly.2.The problem of global stabilization of discrete-time multiple integrators by bounded and delayed controls is investigated.When the delay is absent in the control,we mainly deal with the problem of performance improvement,which will be achieved in two ways.On one hand,we establish two nonlinear controllers consisting of nested/cascade saturation functions where the saturation functions are state-dependent,which helps to increase the control energy and thus to improve the transient performance of the closedloop system.On the other hand,we establish some new constraints on the corresponding parameters that are less conservative than those in the existing results,which determines a larger range of parameters that can be well designed to improve the control performance.When the delay is present in the control,two types of nonlinear controllers consisting of nested/cascade saturation functions are proposed to achieve the global stabilization,and explicit conditions are proposed to guarantee the global stability of the closed-loop systems.Our solution is based on a special canonical form in which the delay is introduced to the state variable,helping to maintain the decoupled property in Teel's recursive design for delay-free systems,and thus can result in a simple analysis process.3.Based on the proposed results,the problems of global stabilization of continuous/discrete feedforward nonlinear systems by bounded and delayed controls are also investigated.We first consider two families of continuous feedforward nonlinear time-delay systems,whose linearized systems consist of a chain of integrators or identical oscillators.Based on two types of special canonical forms,several classes of nonlinear control laws consisting of nested/cascade saturation functions are respectively proposed to solve the problems,and explicit conditions are also given to guarantee the global stability of the closed-loop systems.For the nominal dynamics of the considered feedforward nonlinear systems,the proposed special canonical form contains time delays in its input and states,which allows us to cancel all the other state components at every step of the recursive design so that only a scalar system decoupled from the other state components is required to be handled in every step.This is different from the design in the existing results,which needs to consider a scalar time-delay system coupled with the former state components in every step of the recursive design.Moreover,the proposed controllers also contain some free parameters that can be well designed to improve the control performance.Secondly,the design approach proposed in this paper can deal with feedforward nonlinear systems whose nonlinearities contain not only the current states but also the delayed states,which are more general than the systems considered in the existing references.At last,the proposed design methods are extended to the discrete-time setting,which,to the best of our knowledge,seems not solved in the literature.4.Based on the theoretical results established in this thesis,we investigate the control problem of PVTOL aircraft model,which are subject to input saturation and delay.We first transform the PVTOL aircraft model system into a time-delay system in the form of state space description.Then,by using the proposed approaches in this thesis,nonlinear control laws are proposed to solve the global stabilization,and explicit conditions are also proposed to guarantee the global stability of the closed-loop systems.The simulation results show the effectiveness of the proposed approaches.