Research On Fault Detection And Fault Estimation Algorithm Of H2AT System Based On Fuzzy Observer

Spinal Cord Injury(SCI)is usually caused by a burst fracture of the spine and dislocation of the vertebral body.Paraplegic patients with SCI lose all sensitivity and activity below their thoracic vertebrae.At present,there is no effective means to cure SCI.The recovery of limb function of SCI patients mainly depends on various rehabilitation exercise training.Among them,maintaining sitting balance is one of the main contents of rehabilitation training,but SCI patients are prone to fall when maintaining sitting balance due to lack of muscle assistance.From the biomechanical point of view,sitting control is mainly related to the stability between the lumbar spine and the sacrum joint segment,considering the pressure on the patient’s lumbar spine,this paper uses the Head-Two-Arms-Trunk(H2AT)model to simulate the sitting balance control of SCI patients.Considering that there are uncertain factors such as component aging and external interference during the use of the sitting balance assist device,there are unknown system failures in the use of the device.These faults will directly affect the accuracy of information obtained by the sitting balance assist device for SCI patients when maintaining sitting balance,thereby affecting the effect of limb rehabilitation training in the later stage.Therefore,when assisting SCI patients to maintain sitting balance,necessary fault detection and fault estimation must be carried out on the sitting balance assist device to realize the recovery of limb motor function of SCI patients.Since the H2AT system is used to simulate the sitting balance control of SCI patients,the fault detection and fault estimation problems of H2AT system are studied based on the observer method.Considering the complex nonlinear characteristics of H2AT system,this paper adopts TS fuzzy control theory and uses the sector nonlinear method to express H2AT system as TS fuzzy model.For the fuzzy H2AT system model,due to the existence of unmeasurable nonlinear terms,there is an unmeasurable membership function in its TS fuzzy model,which makes the design of the system observer much more complicated.In view of this,nonlinear partition is adopted to divided nonlinear terms in H2AT system into three parts,namely measurable nonlinear terms independent of control inputs,measurable nonlinear terms and unmeasurable nonlinear terms related to control inputs.The measurable and unmeasurable nonlinear terms related to the control inputs are regarded as the local nonlinear sub-models of the fuzzy model,and only the measurable nonlinear terms unrelated to the control inputs are treated with the sector nonlinear method.A special fuzzy model with local nonlinear subsystem,N-TS fuzzy model is established.Based on this model,the observer-based fault detection and fault estimation problem of H2AT system with unmeasurable antecedent variables is transformed into observer-based fault detection and fault estimation problem of H2AT system with measurable antecedent variables.Using N-TS fuzzy modeling method to model H2AT system can not only avoid the appearance of unmeasured antecedent variables,but also reduce the number of fuzzy rules of the system and reduce the burden of offline computation.The specific research work of this paper is as follows:1.The corresponding descriptor nonlinear model is established according to the dynamics equation of H2AT system.In order to facilitate the research of system fault diagnosis algorithm,the descriptor nonlinear model can be simplified as a nonlinear model.Then,the TS fuzzy model and N-TS fuzzy model are established respectively for the generalized nonlinear model and nonlinear model.Analysis and design of fault detection and fault estimation algorithm for H2AT system based on N-TS fuzzy model.2.For the research of fault detection algorithm of H2AT system,based on N-TS fuzzy model of H2AT system,a fault detection method based on unknown input observer is proposed.Combined with H_-/H_∞theory,the fault sensitivity performance and interference robustness performance of the system are analyzed.The comprehensive convex condition of the fault detection algorithm is given in the form of linear matrix inequality(LMI)to realize the fault detection of H2AT system.3.For nonlinear H2AT system with unknown inputs,in order to achieve simultaneous estimation of system faults and unmeasured states,system faults and unmeasured states are represented as the“new”system states by system reconstruction method.Based on the observer of unknown inputs,combined with the differential mean value theorem and Lyapunov theory,the synthetic convex conditions of the fault estimation algorithms for H2AT system are given in LMI form.4.Aiming at the nonlinear H2AT descriptor system with unknown input,in order to estimate the system fault and unmeasurable state simultaneously,the system state is extended,and a"new"system state is obtained by expressing the system fault and unmeasurable state of H2AT descriptor system.Based on Luenberger observer,combined with differential mean value theorem and Lyapunov theory,the comprehensive convex condition of observer design is given in the form of LMI.