Extended Use of the Parameter Observer on a Class of Second-Order Systems

: The paper extends the use of a parameter observer (PO) from first-order to second-order observed systems. A procedure for identifying a linking relationship between the coefficients of a second-order linear system is proposed, based on experiment. The link relation uses link parameters provided by POs from processing the free response of the observed system. By combining the connection relations obtained from several experiments carried out on the system, after the controlled modification of its coefficients, it is possible to calculate the coefficients of the second-order system or the primary parameters that appear in their expressions. The application of the method is illustrated for time-invariant systems. The examples include both tutorial examples and mathematical models of some physical systems. In this context, the suitability of the RLC series circuit as an equivalent model of a capacitor is discussed. The limitations due to the sensitivity of the calculation formulas in relation to the estimation errors of the link parameters, respectively the spectrum of the signal at the PO input, e.g., the voltage at the capacitor terminals, are highlighted.