6.2.2 ReducedOrder State Estimator via SylvesterObserver Equation
The design of the reducedorder state estimator via the Sylvesterobserver equation approach uses the following template.
1. Choose an stable matrix .
2. Transform to the upper observerHessenberg form , where is an unreduced block upper Hessenberg matrix and (see Section 4.2 for details).
3. Solve the reducedorder Sylvesterobserver equation for a fullrank matrix , choosing the matrix appropriately.
4. Find , an estimate of , as , where and is given by .
A singleoutput recursive bidiagonal scheme due to Datta (1989) to solve the reducedorder Sylvesterobserver equation in step 3 is available using the function ReducedOrderEstimator with the option value MethodRecursiveBidiagonal. In this scheme, the matrix , where , is computed recursively row by row starting with and choosing the matrix as an upper bidiagonal matrix with the diagonal entries as poles of the state estimator. The rows of can be computed either sequentially or in parallel. A block version of this scheme is available with the option value MethodRecursiveBlockBidiagonal. For details, see Datta and Sarkissian (2000).
Another scheme, due to Van Dooren (1984), is the multioutput recursive triangular scheme and is available with the option value MethodRecursiveTriangular. This scheme computes and in the form
,
where the diagonal entries , ... , of the matrix are the userchosen poles of the estimator. The scheme computes the unknown entries of , , and simultaneously row by row, starting from the top row, using certain recursive formulas. A block version of this scheme is also available with the option value MethodRecursiveBlockTriangular. For details, see Van Dooren (1984) or Datta (2003). For other algorithms for solving the reducedorder Sylvesterobserver equation, see Bischof, Datta, and Purkayastha (1996), Datta and Saad (1991), and Carvalho and Datta (2001).
Design of the reducedorder state estimator via the Sylvesterobserver equation.
This constructs the reducedorder state estimator of the steam power system via the Sylvesterobserver equation approach using the recursive scheme.
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This finds the estimates of the state variables.
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This constructs the reducedorder state estimator of the steam power system via the Sylvesterobserver equation approach using the block recursive scheme.
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This obtains the estimates of the states by feeding the input and the measured output to the reducedorder state estimator.
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The graph shows the relative error of the estimated states with respect to the simulated true states for the recursive scheme (solid line) and the block recursive scheme (dashed line).
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