Modeling And State Estimation For Multirate Sampled-Data Systems

This thesis researchs on the modeling and state estimation algorithms of multirate sampled data systems with significant theory and potential values in applications. Based on some existing modeling theory and state estimation methods of multirate systems, the thesis mainly focuses on the state estimation algorithms of the dual-rate systems and non-uniformly sampled systems and the modeling of multi-input and multi-output systems, multi-input and single-output systems, single-input and multi-output systems. The main results are as follows:1. For the simple dual-rate system (the output sampling period equals to an integral multiple of the input updating period), the state-space model is deduced by the means of discretization. Based on the state-space model of simple dual-rate system and the Kalman filtering theory, a state estimation method with non-related noise is proposed, and the state filtering equations are obtained. The basic idea of the algorithm is to get the least estimation error by minimizing the estimated covariance matrix to obtain the optimal gain vector and covariance matrix.2. For the general dual-rate sampled-data system (the output sampling period does not equal to an integral multiple of the input updating period) is considers and its state-space model is estabilished. Based on the state-space model of general dual-rate system, the system with related noise is transformed into a system with non-related noise equally, and a state filtering algorithm of the lifted systems is derived based on the Kalman filtering principle.3. The state estimation algorithm is applyed to the non-uniformly updating and periodically sampling system and its state-space model is established. Recurring to the design ideas of certain observation, a state filtering algorithm with white noise in the system observing equation is detruced by minimizing the estimated covariance matrix based on the Kalman filtering theory.4. For the multirate and multivariables systems(the multi-input and multi-output system, the multi-input and single-output system, the single-input and multi-output system) the period of each output channel is not the same as that of each output channel, the model of the multirate and multivariables system is detruced by the means of discretization.The simulation results indicate that all models and state estimation algorithms based on the Kalman filtering principle are effective.