9.9 Controller Information Based Methods

As mentioned in the introduction, when information on dynamics of controllers used for stabilising the unstable plant is available, it could be used in the estimation procedure either directly or indirectly. In this section, two approaches to this effect are presented [8].

1. Using the input-output data between p1 and p3, an equivalent parameter set can be estimated. From this set of parameters, the open loop plant parameters can be retrieved from the equivalent parameters by using an appropriate transformation based on the knowledge of the controllers used for stabilisation. If the controller were a complex one, this method would not be feasible as it would be very difficult to retrieve the parameters from the equivalent parameters.

2. Alternatively, a combined mathematical model of the states obtained by combining the system model and the known feedback controllers can be formulated. Keeping the known parameters of the controller fixed in the model, the parameters of the plant can be estimated. This could result in a very high order state-space model of the combined system when complex controllers are used. In such cases, model reduction techniques could be employed to arrive at a workable solution.

In this section, these two approaches are investigated and the two-step bootstrap method is presented. The two-step bootstrap method utilises the knowledge of the controller and system in an indirect way. It enables smaller order models to be used and has the advantage that it can handle noisy input data. This approach has been...