Parameter and volterra-kernel estimation of bilinear systems Public Deposited

http://ir.library.oregonstate.edu/concern/graduate_thesis_or_dissertations/4t64gr483

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  • It has been established that bilinear models occur frequently in nature and offer some important advantages from the standpoint. of controllability, optimization and modeling. The estimation of bilinear systeim models from the Measurements of input-output data are discussed. In the first approach a parametric model of a discrete-time linear system is obtained by correlation analysis. The method is extended to bilinear systems using higher- order correlations, It is shown that for a pseudorandom binary input signal the computations in the estimation algorithm can be simplified. The estimates are asymptotically normal unbiased and consistent. The efficiency of the estimates is improved by least-squares fit on a parametric model involving correlation functions. A recursive formulation is given which makes the algorithm attractive for on-line implementation. These methods are compared with maximum-likelihood and least-squares parameter estimation for a model of a nuclear fission process. An experimental furnace to control the temperature of a sample is modeled. The power applied. to the furnace and the rate of air flow inside the chamber are the control variables. Only one input is perturbed at a time with a pseudorandom binary sequence and the linear and the bilinear models of the process are obtained from the input-output measurements. The identification results are used to design a feedforward-feedback programmable controller for the system with constant air flow rates. The second approach is to estimate the first and the second-order kernels in a Volterra series expansion of bilinear systems using correlation analysis. The kernels are estimated for a simulation model of a nuclear fission process. It is seen that the correlation method yields good estimates of the first -order kernel under noisy input -output measurements, However, the second-order kernel estimates are not satisfactory. A new approach to the estimation of the second and the higher-order kernels is then developed. The input-output relation of the bilinear system is represented by an integral-equation. A Wiener-Hopf type equation is obtained by crosscorrelation of the input and the output. An algorithm is given to estimate the unknown parameters in the bilinear operator. The estimation of the second-order kernel is significantly improved.
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