Kalman Filter Based Soft Sensor Of Singular Nonlinear Systems For Chemical Processes

Most chemical process models are singular systems.Although the state estimation of singular systems has made great achievements in linear systems,there are few research results of state estimation for singular nonlinear systems.Discrete Kalman filter of singular linear systems and discrete extended Kalman filter of singular nonlinear systems are deduced and the simulation results of the second dense bed of FCCU regenerator prove the feasibility of the singular discrete Kalman filter.Continuous Kalman filter of singular linear systems and continuous Kalman filter of singular nonlinear systems are also deduced and the simulation results of the second dense bed prove the feasibility of the singular continuous Kalman filter.The Euler’s method are widely used in the discretization of the continuous systems and there are few other methods in the discretization of the continuous systems.The continuous-discrete Kalman filter of singular nonlinear systems by Trapezoidal method and the continuous-discrete Kalman filter of singular nonlinear systems by Runge-Kutta method are deduced.Simulation results of different discretization methods for fast time-varying acetylene hydrogenation reactor soft sensor with different sampling periods are showed in the paper.The slow time-varying phenomenons widely exist in chemical processes.In a running cycle of a chemical plant the performance of the chemical plant declines gradually because of the change of slow time-varying parameter.The change of slow time-varying parameter affects the performance of control system.So the online estimation of slow time-varying parameter is meaningful.For acetylene hydrogenation reactor,the time unit of catalyst deactivation is ’day’,but the time unit of unmeasurable disturbances is ’second’.Because of the different time scales of slow time-varying characteristics and controlled variables,the design of slow time scale soft sensor and fast time scale soft sensor for acetylene hydrogenation reactor is needed based on singular extended Kalman filter.The simulations show that,when slow time-varying characteristics and controlled variables are augmented as state variable on slow and fast time scales respectively,the singular extended Kalman filter can estimate the catalyst activity with day as time unit and controlled variables with second as time unit correctly.The estimated values converge to the model values and the soft sensor has good dynamic performance.This method can be widely used in the chemical processes with the slow time-varying phenomenon.