Method and system of dynamic model identification for monitoring and control of dynamic machines with variable structure or variable operation conditions
A method and system for forming a dynamic model for the behavior of machines from sensed data. The method and system generates a dynamic model of the machine by applying a canonical variate analysis (CVA) method to subspace system identification extending to parameter varying (LPV) systems and nonlinear (NL) systems in order to make implementation of the computation feasible and accurate.
1. A method of controlling or modifying engine dynamic response characteristics, comprising:
observing, with at least one sensor, an engine in operation; and
at least one of controlling and modifying engine dynamic response characteristics of the engine based upon a generated dynamic model of engine behavior, wherein a canonical variate analysis CVA is performed according to the equation:
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wherein y t is a linear prediction of a present output, α i and β i are parameter-varying coefficients, p t+i is a parameter varying scheduling function, y t+i and u t+i are dimensions of identity matrices, t is time, v t is a white noise process of a covariance matrix, l is an order of the autoregressive input-output linear parameter-varying process.
2. The method of controlling or modifying engine dynamic response characteristics of claim 1 , further comprising recording data from the at least one sensor about at least one characteristic of the engine in operation.
3. The method of controlling or modifying engine dynamic response characteristics of claim 2 , further comprising fitting at least one of an autoregressive input-output linear parameter-varying dynamic model and an autoregressive input-output nonlinear parameter-varying dynamic model, each model having a state order above a predetermined threshold, to the recorded engine data.
4. The method of controlling or modifying engine dynamic response characteristics of claim 3 , further comprising removing effects of future inputs from future outputs to generate corrected future outputs by using at least one of the fitted autoregressive input-output linear parameter-varying dynamic model and the fitted autoregressive input-output nonlinear parameter-varying dynamic model.
5. The method of controlling or modifying engine dynamic response characteristics of claim 4 , further comprising performing, a canonical variate analysis (CVA) between the corrected future outputs and past outputs of at least one of the fitted autoregressive input-output linear parameter-varying dynamic model and the fitted autoregressive input-output nonlinear parameter-varying dynamic model.
6. The method of controlling or modifying engine dynamic response characteristics of claim 1 , further comprising constructing at least one of a dynamic linear parameter varying state-space model and a dynamic nonlinear parameter varying state-space model based on the performed CVA.
7. The method of controlling or modifying engine dynamic response characteristics of claim 6 , further comprising generating a dynamic model of engine behavior.