(188v) Closed-Loop Re-Identification of Multi-Rate System Using N4SID and Zone MPC

ByungJun Park, Se-Kyu Oh and Jong Min Lee

School of Chemical and Biological Engineering, Institute of Chemical Processes,

Seoul National University, 1 Gwanak-ro, Gwanak-gu, Seoul 08826, South Korea

Changes in operating conditions or process units are common in industry and these changes result in the performance degradation of model predictive control (MPC). The quality of model plays a key part in maintaining the control performance of MPC, and it is desirable to re-identify the model under closed-loop rather than to perform open-loop plant tests. Multi-rate (MR) systems involve variables sampled at different rates, and they are difficult to identify under closed-loop without additional persistent excitation of the inputs, leading to poor regulation performance. In addition, most existing methods for closed-loop identification of MR systems involve polynomial transformation, which is not compatible with popular model forms for MPC such as step response and state space models.

This work presents a closed-loop re-identification method that provides a state-space model of multi-rate system suitable for MPC. The proposed approach consists of three major steps: First, a lifting technique is exploited to convert the multi-rate system to an augmented single-rate system [1]. Second, a modified MPC scheme, i.e., zone MPC, to strike a balance between input excitation and output regulation is introduced [2]. Finally, N4SID, the subspace identification algorithm, is employed to identify a state-space model [3]. This procedure, however, does not consider dynamic characteristics of systems like steady-state gain and settling time and structural characteristics due to using the lifting technique. This work modifies the N4SID algorithm to reflect steady-state, settling time and structural characteristic of the lifted model. First, the feedthrough matrix for the augmented state-space model is represented as a lower triangular form that is included as a linear constraint. Second, steady-state gain and settling time are explicitly included as constraints. Because the evaluation of steady-state gain involves matrix inversion, C(sI-A)^-1B+D, A and C are first identified without those two constraints and then B and D are identified with the constraints. This two-stage identification is computationally more robust and efficient than the standard N4SID algorithm that identifies A, B, C and D simultaneously.

Both single-input single-output linear time invariant (LTI) system and multiple-input multiple-output LTI system are illustrated as numerical examples. It is verified that the estimated lifted state-space model by the modified N4SID algorithm describe the dual-rate input-output data better than that of the standard N4SID. Results also show that the suggested scheme successfully improves the model accuracy while regulating the outputs within acceptable bounds.

References

[1] Z. Y. P. Qin, S. Kanae, “Identification of lifted models for general dual-rate sampled-data systems based on input-output data”, Proceedings of the IASTED Asian Conference Modelling and Simulation (2007) 6–12.

[2] L. F. M. Oscar A.Z. Sotomayor, Darci Odloak, “Closed-loop model re-identification of processes under MPC with zone control”, Control Engineering Practice 17 (2009) 551–563.

[3] B. D. M. P. Van Overschee, “N4sid: Subspace algorithms for the identification of combined deterministic-stochastic systems”, Automatica 30 (1994) 75–93