Research Of Tracking Control For Nonaffine System Based On Adaptive Fuzzy Theory

In many practical engineering,the controlled objects such as chemical reaction control system,flight control system,etc.are nonaffine nonlinear system.Due to the limitation of practical condition,in general it is difficult to develop an accurate mathematical model for the nonaffine system.Therefore,designing controller for nonaffine uncertain system is research topic with important theory significance and significant practical value.As the adaptive fuzzy control approach has the unique property of function approximation,it can effectively deal with the control problem of uncertain nonaffine system.Based on the analyzing and summarizing the research results of nonaffine system at home and abroad,utilizing Nussbaum function,Backstepping technique,small gain theorem and Lyapunov-krasocskii quadratic functional methods,this thesis systematically studies tracking control strategies for several types of uncertain nonaffine nonlinear systems.Aiming at single input and single output(SISO)nonaffine nonlinear system tracking controller design problem,in case of the state variable measurable and immeasurable adaptive fuzzy controller design methods are proposed.As the control direction is unknown,when using fuzzy logic systems(FLSs)to approximate unknown nonlinearity,the controller singularity problem may occur because the update direction is uncertainty.However,the improved method to solve the singularity will lead the control input chattering problem.By utilizing the Nussbaum function indirect adaptive fuzzy controller and adaptive laws are developed.Using the Lyapunov stability theorem,the stability of the controlled system is proved.Meanwhile,the controller can guarantee that the system tracking error convergence.The simulation results verify the effectiveness of the proposed control scheme.According to the cases that system states are measurable or immeasurable,and system has a strict-feedback form,three adaptive fuzzy control schemes have been developed for SISO nonaffine nonlinear system with unknown dead-zone input.The unknown dead-zone nonlinearity is firstly divided into a linear part and a bounded disturbance-like term and the nonaffine form of the system is transformed into an affine form.Whereafter,the FLSs are utilized to approximate the uncertain nonlinear parts,and the corresponding parameter adaptive laws are given out.The robust control technique is employed to dead with the unknown part which is composed of higher-order infinite term,the disturbance-like term and the optimal approximation error.Considering the control objective,appropriate Lyapunov candidate functions have been constructed to prove the convergence of the system trackingerror and the boundedness of signals in closed-loop system.By applying the designed controllers to simulation examples,the simulation results demonstrate the feasibility of the control strategies.Considering the SISO strict feedback nonaffine nonlinear system is with unknown dead-zone input and unknown control gain direction,an adaptive fuzzy backstepping control approach is proposed first.In each step of backstepping technique design procedure,all the unknown nonlinear functions are treated as a collectivity which is directly approximated by FLSs.The adaptive parameter is used to estimate the upper bound of the norm of the optimal approximation weight parameter vector.As the sign of the control gain is unknown,the Nussbaum function property is introduced to design the virtual control law,actual control law and the parameter adaptive law.By choosing the Lyapunov function and using the Nussbaum function theorem,it is proved that the controller can ensure the stability of system.Based on the above analysis,an adaptive fuzzy control approach with Nussbaum function is developed for the system with unknown time varying delay.Along with the design of Lyapunov candidate function,Lyapunov-krasocskii quadratic functional method is used to construct the append term to compensate the nonlinear part which contain the state variable with time delay.Finally,the stability of the system is proved,and it is easy to get the conclusion that tracking error is convergence and all signals in closed-loop system are bounded.According to the analysis of simulation,the effectiveness of control scheme is validated.An adaptive fuzzy output feedback controller design method based on small gain theorem is developed for multiple-input and multiple-output(MIMO)nonaffine time delay system with unmodeled dynamical.As the system states are immeasurable,a state observer is constructed to estimate the system state variables.The filtered signal of the Butterworth low filter are utilized to avoid the algebraic loop problem which may encountered in the implementation of the controller caused by the system pure feedback form.Then,the observe value and the filtered signal are employed as the input of FLSs which are introduced to directly approximate the unknown nonlinear part.Adaptive parameters are used to estimate the unique upper bound of all the norms of the optimal approximation weight parameter vector.At last the actual control input and the adaptive law are designed.Through the choosing of the appropriate Lyapunov function and combining the small gain theorem,the controlled system is proved to be Input-to-State Practically Stable.The validity of the control approach is illustrated by the simulation results.Considering that the values of MIMO nonaffine time delay system outputs contain disturbance,an adaptive fuzzy output feedback control strategy is proposed.By usingLyapunov-Razumikhin Lemma to cope with the time varying delay system state,the constraint that the derivative of time delay term must be less than one is relaxed.As the system states cannot be measured,and it is hard to get the accurate value of the system outputs,i.e.,the measured output value is with unknown disturbance,the information of the outputs cannot be used as the input of the state observer.By utilizing the expand dimension idea the measurement of the system outputs are transformed as a new system states.Like the iterative learning observer method,a new state observer is constructed.By using the observe information and the filtered signals,the system controller is designed.Utilizing Lyapunov stable theorem the system stability is proved.Finally,the controller is directly applied to control a simulation model,and the results demonstrated the feasibility of the control scheme.