| With the development of industry,the controlled system becomes more and more diversified and complex in control engineering.In the actual control operation process,there are various uncertainties and nonlinearities.The existence of these uncertainties will often affect the performance of the system,and at the same time greatly increase the difficulty of controller design.It may lead to system oscillation,make the system unstable and unable to operate normally,and bring unnecessary harm and loss to factories and national finances.Therefore,it is of great theoretical significance and practical need to study the control problem of uncertain nonlinear systems for the safety guarantee of practical engineering.At present,most engineering projects have certain requirements on the control performance of the system on the premise of ensuring the stability of the system.Therefore,it is necessary to design a new control algorithm,ensure the stability of the system,improve the control performance and expand the applicable scope of the method.In this paper,sliding mode back-stepping control algorithm is designed for several kinds of uncertain nonlinear systems.The advantages of adaptive control and sliding mode back-stepping control are combined,and the adaptive control method is introduced into sliding mode back-stepping control,which expands the application range of sliding mode back-stepping control.Because of the introduction of disturbance observer,the research scope of uncertain nonlinear systems is further expanded and the research content is enriched.Next,this paper will study the sliding mode back-stepping control theory and related methods of uncertain nonlinear systems.The main work of this paper is as follows:(1)In chapter 2,aiming at a class of high-order semi-strict feedback nonlinear systems with uncertainties and unknown parameters,the unknown parameters in high-order semi-strict feedback nonlinear systems are treated by adaptive law.Then a new disturbance observer is designed to estimate external disturbances,It can not only estimate the external interference of the system,but also estimate the derivative of the virtual variable in each step.Finally,multivariable sliding surface is introduced,which can effectively avoid chattering and ensure the stability of closed-loop systems.(2)In chapter 3,the adaptive sliding mode back-stepping control method is adopted,and the tracking control problem of a class of unmatched uncertain nonlinear high-order systems is solved.The adaptive back-stepping method and sliding mode method are combined to realize the fast tracking problem of the system.Finally,the time when the state of the system reaches the sliding mode surface can be adjusted by adjusting the value of the gain parameter K,and the sgn function is replaced by the bipolar sigmoid function,which effectively reduces the chattering of the system.(3)In chapter 4,a sliding mode control method based on multi-power reaching law is designed for a class of uncertain nonlinear systems with matching and non-matching.The finite-time disturbance observer is used to deal with the uncertainties in the system,and the multivariable integral sliding mode surface is introduced to effectively avoid chattering in the sliding mode controller.(4)The maglev ball system in chapter 5 is a typical nonlinear unstable system.According to the characteristics of instability,we apply the methods in chapter 2 and chapter4 to this system,and solve the trajectory tracking problem of maglev ball system. |
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