State Estimation And Fault Detection Of The Non-smooth Sandwich Systems

Dead-zone, backlash, and hysteresis are widely existing in electrical, communication, andindustrial system as typical non-smooth nonlinear characteristics. Moreover, thesenon-smooth and non-linear characteristics usually embedded between two linear parts toconstruct the non-smooth sandwich systems. However, in the past research works, thesecharacteristics are usually neglected and the non-smooth sandwich systems are simplified aslinear systems. This simplification must lead to model uncertainty and bring disadvantages aswe are constructing the observer for the systems. Taking all these non-smooth and nonlinearcharacteristics into consideration, the non-smooth state space equation can be constructed andthe corresponding non-smooth observers also can be proposed. Therefore, the systems can bedescribed more precisely and their states can be estimated more quickly and accurately. It isof great importance for the future application. For these purposes, the paper is carried out asthe following five parts.1. Based on the characteristics of the systems, non-smooth state-space equations areconstructed for the sandwich system with dead-zone, backlash, and hysteresis by theseparation principle, respectively. These non-smooth state-space equations provide thefundamental for the constructing the non-smooth observers.2. According to the non-smooth state-space equation, the non-smooth state estimationobservers are proposed to estimate the states of the system. Based on the analysis of thelogical relationships among dead-zone, backlash, and hysteresis, the structure and designprinciple of the non-smooth observers are presented. The comparisons of simulation andexperimental results between the proposed non-smooth schemes and the conventionalmethods are illustrated. It shows that the proposed non-smooth approaches are much betterthan the conventional ones in estimation performances.3. The convergences of the non-smooth observers are analyzed and the correspondingconvergence theorems are proved. Following the logical relationships among dead-zone,backlash, and hysteresis and starting from the estimation error analysis, the correspondingconvergence theorems and its proof are presented. The convergence analysis can help us tounderstand the working process and application condition of the non-smooth observers.4. Considering the model uncertainties and external disturbances, a novel robust stateestimation observer is proposed to estimate the states of the sandwich systems. Byintroducing the “general disturbance” concept and minimizing the Frobenius norm of theTFM （Transform Function Matrice） from the general disturbance to the estimation error （J） on basic operation zone, the gain matrice of the robust state estimation observer are obtainedand the observers are robust to the general disturbance including exogenous disturbances,noise and modeling uncertainties. After that, the simulation and experimental results arepresented. The comparisons between the proposed robust schemes and the conventionalmethods are illustrated. It is demonstrated that the proposed robust approaches can track thestates of the non-smooth sandwich systems more accurately comparing to the conventionalones.5. The paper applies the robust fault detection observers to the fault detection of thenon-smooth sandwich systems. By zeros assignment and minimizing theH_{∞, F}/H_-,Findicator on the basic operation zone, novel robust fault detection observers are proposed toestimate the output for sandwich systems in order to generate the robust residual for faultdetection. The residuals generated by the novel robust fault detection observer are insensitiveto the general disturbances while sensitive to the faults. After that, the simulation results arepresented. The comparisons between the proposed robust schemes and the conventionalmethods are illustrated. It is demonstrated that the proposed robust fault detection approachescan detect the actuator and sensor faults accurately and quickly which the conventionalobservers can not detect at all. Therefore, missing and false alarms are effectively avoided bythis method.The above research results of item2,4and5can be used for state estimation in thewidely existing non-smooth nonlinear sandwich systems in electrical, communication andmechanical system. The observers not only can estimate the measurable states but also canestimate the immeasurable interval states of the non-smooth sandwich systems. Theseestimated states are significantly important for the future applications of control and faultdiagnosis of the non-smooth sandwich systems.