Three different validation tests for models operation in closed loop are given:
1. Uncorrelation test:
The statistical validation test for closed loop identification is developed in a similar way as the open loop uncorrelation test, with the difference that a closed loop predictor incorporating the plant model is used to obtain the residual closed loop output error : the uncorrelation between this closed loop output error and the closed loop prediction in then tested.
2. Time domain validation:
The real output of the system in closed loop operation and the simulated output of the closed loop system (computed with the given model and controller) are compared. The loss function is also given.
3. Poles closeness validation:
If the identified model allows to construct a good predictor of the closed loop system for a given controller used during identification, this will imply that the poles of the true closed loop system and those of the closed loop predictor are close.
An indication upon the quality of the identified model then result from the comparison of the computed closed loop poles with the poles of the true closed loop system (which can be identified). One can use the Vinnicombe gap for a quantitative evaluation of the difference. For this one has to use "clvalid1" function.
See: Closed loop identification module .
(file clvalid.htm)