Parameter Estimation For A Class Of Dual-rate Sampled Data Systems

The system input and output are usually sampled in the same sampling rate for general discrete time system, but in actual process industry, it is impossible to identify the system parameters in same input and output sampling interval due to some restrictions on hardware. Multirate systems are widely studied and used in practical industry, it can solve the problem of parameter identification and output estimation for dual-rate systems. The dual-rate systems identification can be used to estimate the intersample output by using the obtained model and to monitor output variables. If the dual-rate models are obtained by the polynomial transformation technique, then it is required to find the corresponding fast single-rate models since they can be used to design the inferential control schemes and self-turning control strategies for multirate systems.Firstly, an identification model of a simple dual-rate system is derived by using the polynomial transformation technique. For dual-rate time-invariant CAR model, a dual-rate forgetting gradient algorithm is used to identify the parameters and estimate the missing output. Based on the output estimation, a single-rate model is derived from the dual-rate data. The matingle convergence theorem and stochastic process theory is usd to study the convergence properties. When the strong persistence excition condition is satisfied, the upper bound of the parameter estimation error is derived. The simulation example shows that the proper factor can result in a good convergence rate and reduce the computation burden.Secondly, for dual-rate systems whose corresponding single-rete models are CAR,CARMA,CARARMA models respectively, the dual-rate generalized forgetting gradient algorithm,daul-rate extended forgetting gradient algorithm and dual-rate generalized extended forgetting gradient algorithm are used to identify the system parameters. The basis is to use the estimate of the unknown noises to replace the unknown noise terms in identification models.Finally, for a class of dual-rate time-varying systems, based on the polynomial transform technique and the stochastic system theory, the convergence properties of forgetting factor least square algorithm are studied under the strong persistent excitation conditions. The upper bounds of the parameter estimation error(PEE) are presented. The analysis indicates that the mean square PEE upper bounds of the algorithm approach finite positive constants as the data length increases. The PEE upper bounds of deterministic time-invariant dual-rate systems, stochastic time-invariant dual-rate systems and deterministic time-varying dual-rate systems are also studied. Also, several simulation examples illustrates are given.