(622f) Effect of Uncertainty In Time Delay On Multi-Step-Ahead Predication Performance of Some Black Box Models

Multi-step-ahead prediction is part of several model based technologies. One of the most illustrative example is in model predictive control (MPC). In MPC, in many cases, the value of the control signal is calculated by penalizing the future deviation of the trajectory of the system output from a desired output trajectory. The future trajectory of the plant is predicted using the plant model. The most commonly used predictive models are the black box models. For linear time invariant systems, step response models, ARX and FIR models are commonly used. Orthonormal Basis Filter Based MPC is also becoming popular in literature. 

It is believed that the prediction performance of models depend on several factors, like the quality of the excitation signals used during identification test, model structure selection and model parameter estimation. While there are several possible model structures to select from, understanding the strengths and weaknesses of the various model structures greatly helps in selecting a structure for a specific application. One of the issues related to model structures is time delay. It is known that model structures like ARX, ARMAX and Box Jenkins need the time delay to be separately estimated and included in the model during the parameter estimation. Nevertheless, time delay estimation itself is not a trivial task and generally involves uncertainty in its accuracy. Therefore, it is essential to understand how uncertainties in time delay affect the multi-step-ahead prediction performance of the models. On the other hand, model structures like OBF, ARX-OBF, has inherent capability to estimate the time delay of the system because of their Pade’ like structures. They do not necessarily need a separate estimate of the time delay during model development.

In this paper, the effect of uncertainty in time delay on the prediction performance of various model structures is studied and compared to OBF based structures. The study includes both open-loop and closed-loop identification simulation case studies. The result shows that one-step-ahead prediction is not affected by the uncertainty for all types of structures. While as the number of steps-ahead and the uncertainty increases, the prediction performance of structures like ARX and ARMAX deteriorates much more than that of the OBF-Based model structures.