Five 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.
4. Frequency responses comparison.
Identified and calculated closed loop systems are compared in the frequency domain by plotting the bode diagram of their magnitude frequency responses.
5. Vinnicombe Gap.
The Vinnicombe gap is used in order to quantify the distance between the identified and calculated closed loop systems: the result is an index of quality for the validation procedure.
See: Vinnicombe Gap.
For performing closed loop validation of the identified model one needs a good estimation of the closed loop system transfer function. The estimation of the closed loop transfer function is performed by means of an open loop identification algorithm. A statistical validation test on the residual output error (Whiteness test) assesses the quality of the estimation.
See: Closed loop identification module .
(file clvalid.htm)