Research On Sliding Mode Control Of Fuzzy Bilinear Systems

Bilinear system is different from the general linear system and has its unique particularity.Its particularity is mainly shown in the following aspects: first,it only has more than the linear system the product of state variables and output variables,that is,the bilinear term,which is close to the linear system in form.It is not only simple in structure,but also easy to deal with.Second,for some unusual nonlinear systems,its ability to describe objects is much higher than that of traditional linear systems,so it has been applied in many fields.Combined with the T-S fuzzy model,the fuzzy bilinear system has a better ability to describe the nonlinear system.Many scholars devote themselves to the research of the control theory and control method of the fuzzy bilinear system.At present,the research of fuzzy bilinear system still has the following problems: 1.The performance of state feedback control is poor in the face of large disturbance or fault;2.For system faults,the research content is mostly passive fault-tolerant control,and the failure form is not clear.Therefore,in view of the above questions,On the basis of predecessors,this paper mainly studies the sliding mode control based on fuzzy bilinear system,and carries out related research mainly from the following aspects:(1)Based on the traditional sliding mode control method of continuous stirred reactor system(CSTR),the sliding mode surface and switching control item are optimized.The model of the system can be described by the Takagi-Sugeno(T-S)fuzzy bilinear model.Based on the fuzzy bilinear model,the sliding mode control method is given.The linear sliding mode surface is improved and the integral sliding mode surface is constructed.The equivalent control quantity and switching control quantity designed by this method can ensure the control accuracy of the system.By studying its stability,the sufficient conditions of global stability are obtained,and the controller parameters of the sliding surface are obtained.At the same time,seven fuzzy rules are constructed,and fuzzy inference is made to the switching gain term by using fuzzy method,so that the overall control is smoothed,and chattering phenomenon is avoided in the system state,so that the actual operation is realized.Finally,the simulation results of continuous stirred reactor demonstrate the effectiveness of the control method.(2)For the problem of controller singularity in sliding mode control of fuzzy bilinear systems,a class of event triggered sliding mode control is studied.The singular region with zero denominator of the controller is obtained,the event trigger threshold is selected,and the condition region to be met for event trigger is determined,so that the singular region is included in the condition region.The integral sliding mode surface is constructed,and the conventional sliding mode control law is obtained.On this basis,combined with the event trigger mechanism,the control law is extended,and the auxiliary control law is designed to make the system state transition smoothly when it is close to the singular region,ensure the stability of the system,and ensure that the state reaches the sliding mode surface normally.According to the designed event triggered sliding mode control law,considering the different situations that the system state approaches the singular region,combined with the Lyapunov stability condition,the reachability and stability of the system state are proved respectively.Finally,the effectiveness of the proposed method is verified by numerical simulation.(3)The sliding mode fault-tolerant control of fuzzy bilinear systems with multiplicative and additive actuators is studied respectively.Based on the fuzzy bilinear model and considering the actuator gain fault form,an adaptive fuzzy observer design scheme is presented.By designing the adaptive law of the fault matrix and solving the constraint condition of the observer correction term coefficient,the sufficient conditions for the stability of the error system in the actual state and estimated state are obtained.Then,based on this observer,a state sliding mode tolerant controller is designed,and the Lyapunov stability condition is used to prove that the fault tolerant controller can ensure the global asymptotic stability of the system in the case of failure.Finally,the effectiveness of the control method is verified by the simulation of a continuous stirred reactor considering the form of sudden failure.