Operating point adjustment procedure for a class of continuous-time bilinear models

Modelling and data-based identification of heating element in continuous-time domain

“…orig. [9], it is possible to operate the base-line adjusted model at any operating point (not just zero base-line), while preserving the dynamical response of the nonlinear model from any other point of operation, but this is beyond the scope of the current article.…”

“…For example, it is not possible to pre-process the measured input-output signals by means of subtracting mean values or initial values prior to parameter estimation and then attempt to estimate the nonlinear model parameters. Of course, this is a common practice when estimating linear transfer function model parameters, however identification of nonlinear models is, in general, not possible in this way (with some exceptions, see [9]). It is going to be shown, however, that it is possible to simulate the identified nonlinear model (1) at zero operating point while the obtained dynamical response is identical to the one which would be obtained at the original point of operation.…”

“…This is not an issue in the case of linear models, however the values of nonlinear model parameters depend on the point of operation. The procedure of tackling this issue is discussed in [8,9] for the case of identification of bilinear and Hammerstein-bilinear models. Due to the close connection of the considered nonlinear model, cf.…”

“…Section 3.4. Subsequently, if the base-line components are removed (subtracted) from the the input-output signals of model (1) then also the offset term o is effectively removed, see [9], and the following nonlinear, base-line adjusted, model can be derived…”

“…Finally, the nonlinear dynamic behaviour of the identified heating element model throughout the operational envelope is discussed, together with the implications for parameter estimation and simulation of such model, see Sub-section 3.5. Motivated by [9], it will be shown that the dynamic behaviour of the considered nonlinear model at given operating point can be replicated at zero operating point, which has further applications in system identification and simulation of such system models (which are, however, not shown here).…”