Selection of Optimal Sampling Interval and Initial State for Precise Parameter Estimation

1 Selection of Optimal Sampling Interval and Initial State for Precise Parameter Estimation 

The optimality criteria based on which the conditions for the next experiment are determined are the same for dynamic and algebraic systems. However, for a dynamic system we determine the conditions not just of the next measure- 

Our selection of the initial state, x0, and the value of the manipulated variables vector, u(t) determine a particular experiment. Here we shall assume that the input variables u(t) are kept constant throughout an experimental run. Therefore, the operability region is defined as a closed region in the [xoj.xo, , Xo,n, U u2.u,]T -space. Due to physical constraints these independent variables are limited to a very narrow range, and hence, the operability region can usually be described with a small number of grid points. 

The main consideration for the choice of the most appropriate time interval is the availability of parameter sensitivity information. Kalogerakis and Luus (1984) proposed to choose the time interval over which the output vector (measured variables) is most sensitive to the parameters. In order to obtain a measure of the available sensitivity information with respect to time, they proposed the use of 

The procedure for the selection of the most appropriate time interval requires the integration of the state and sensitivity equations and the computation of lj(t), j=l.p at each grid point of the operability region. Next by plotting I/t), j=l.p versus time (preferably on a log scale) the time interval [t, tNp] where the information indices are excited and become large in magnitude is determined. This is the time period over which measurements of the output vector should be obtained. 

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