Coordinating multiple optimization-based controllers: new opportunities and challenges

Transcription

1 Coordinating multiple optimization-based controllers: new opportunities and challenges James B. Rawlings and Brett T. Stewart Department of Chemical and Biological Engineering University of Wisconsin Madison Dynamics and Control of Process Systems 27 June 6, 27 Rawlings and Stewart (UW) MPC: Status and Future DYCOPS 27 1 / 22 Outline 1 MPC at the Large Scale Large, networked systems 2 Conclusions and Future Outlook Rawlings and Stewart (UW) MPC: Status and Future DYCOPS 27 2 / 22

2 Electrical power distribution Rawlings and Stewart (UW) MPC: Status and Future DYCOPS 27 3 / 22 Chemical plant integration Material flow Energy flow Rawlings and Stewart (UW) MPC: Status and Future DYCOPS 27 4 / 22

3 MPC at the Large Scale Most large-scale systems consist of networks of interconnected/interacting subsystems Chemical plants, electrical power grids, water distribution networks,... Traditional approach: Decentralized control Wealth of literature from the early 197 s on improved decentralized control (Sandell-Jr., Varaiya, Athans, and Safonov, 1978; Siljak, 1991; Lunze, 1992) Well-known that poor performance may result if the interconnections are not negligible Rawlings and Stewart (UW) MPC: Status and Future DYCOPS 27 5 / 22 MPC at the Large Scale Steady increase in available computational power has provided the opportunity for centralized control Most practitioners view centralized control of large, networked systems as impractical and unrealistic Centralized control law grows exponentially with system size Difficult to tailor a centralized controller to meet operational objectives A divide and conquer strategy is essential for control of large, networked systems (Ho, 25) Centralized control: A benchmark control framework for comparing and assessing other control formulations Rawlings and Stewart (UW) MPC: Status and Future DYCOPS 27 6 / 22

4 Nomenclature: Consider Two Interacting Units Objective functions Φ 1 (u 1, u 2 ), Φ 2 (u 1, u 2 ) and Φ(u 1, u 2 ) = w 1 Φ 1 (u 1, u 2 ) + w 2 Φ 2 (u 1, u 2 ) decision variables for units u 1 Ω 1, u 2 Ω 2 Decentralized Control Communication-based Control (Nash equilibrium) Cooperation-based Control (Pareto optimal) Centralized Control (Pareto optimal) min Φ1 (u 1 ) u 1 Ω 1 min Φ 1 (u 1, u 2 ) u 1 Ω 1 min Φ(u 1, u 2 ) u 1 Ω 1 min Φ2 (u 2 ) u 2 Ω 2 min Φ 2 (u 1, u 2 ) u 2 Ω 2 min Φ(u 1, u 2 ) u 2 Ω 2 min Φ(u 1, u 2 ) u 1,u 2 Ω 1 Ω 2 Rawlings and Stewart (UW) MPC: Status and Future DYCOPS 27 7 / 22 Noninteracting systems u b Φ 2 (u) n, d, p a -1 Φ 1 (u) u 1 Rawlings and Stewart (UW) MPC: Status and Future DYCOPS 27 8 / 22

5 Weakly interacting systems.5 Φ 2 (u) b p n, d -.5 u 2-1 a Φ 1 (u) u 1 Rawlings and Stewart (UW) MPC: Status and Future DYCOPS 27 9 / 22 Moderately interacting systems 2 u b Φ 2 (u) p Φ 1 (u) a d n u 1 Rawlings and Stewart (UW) MPC: Status and Future DYCOPS 27 1 / 22

6 Strongly interacting (conflicting) systems Φ 2 (u) p Φ 1 (u) a u 2 b d u 1 Rawlings and Stewart (UW) MPC: Status and Future DYCOPS / 22 Strongly interacting (conflicting) systems u n Φ 2 (u) Φ 1 (u) u 1 Rawlings and Stewart (UW) MPC: Status and Future DYCOPS / 22

7 Application chemical plant D, x Ad, x Bd MPC 3 MPC 1 MPC 2 F purge F, x A F 1, x A1 H b H r Hm F m, x Am, x Bm Q F r, x Ar, x Br A B B C A B B C F b, x Ab, x Bb, T (Venkat, Rawlings, and Wright, 26b), (Venkat, Hiskens, Rawlings, and Wright, 26a) Rawlings and Stewart (UW) MPC: Status and Future DYCOPS / 22 Two Reactor Chain with Nonadiabatic Flash Performance of different MPC frameworks H m Time H b Time setpoint Cent-MPC Comm-MPC FC-MPC (1 iterate) setpoint Cent-MPC Comm-MPC FC-MPC (1 iterate) F 1 D Time Time Cent-MPC Comm-MPC FC-MPC (1 iterate) Cent-MPC Comm-MPC FC-MPC (1 iterate) Rawlings and Stewart (UW) MPC: Status and Future DYCOPS / 22

8 Conclusions In this talk, we evaluated two candidate distributed MPC strategies for systemwide control that maintain the existing unit control structure. Pure communication-based MPC is unreliable and can produce closed-loop instability. Cooperation-based MPC gives nominal closed-loop stability for any number of iterations. On iteration to convergence, cooperation-based MPC achieves optimal (centralized) control performance. Distributed target calculation as an alternative to centralized target calculation for large-scale systems. Extension of the FC-MPC algorithm to handle asynchronous operation of subsystem-based MPCs. Rawlings and Stewart (UW) MPC: Status and Future DYCOPS / 22 Future Outlook Power network control using distributed MPC 1. Future directions: a wealth of unexplored issues remain. Methods that minimize information exchange. Methods that are robust to disruption in information exchange. Methods to identify significant interactions from closed-loop data (minimal modeling). Extensions to nested (hierarchical) systems, nonlinear models,... 1 In collaboration with Professor Ian A. Hiskens, Department of Electrical and Computer Engineering, University of Wisconsin-Madison Rawlings and Stewart (UW) MPC: Status and Future DYCOPS / 22

9 Reducing Information Exchange Subsystem l Subsystem i Subsystem j U i D i Two sets Nearest upstream neighbors Nearest downstream neighbors U i = {upstream of i} {plant} D i = {downstream of i} {plant} Reduction of interactions to subsystems i and j U i D i Use state model x + i = f (x i, x l ) + g(u) l U i Rawlings and Stewart (UW) MPC: Status and Future DYCOPS / 22 Reducing Information Exchange 1 4 The reduced subproblem requires upstream states and downstream inputs Communication is reduced over the whole plant 2 3 Material/Energy Input trajectory State trajectory Rawlings and Stewart (UW) MPC: Status and Future DYCOPS / 22

10 Hierarchies of Cooperating MPCs RTO Φ Φ MPC 1 MPC 2 Optimizers pass objective information vertically Cooperation between steady-state optimizers and dynamic controllers Rawlings and Stewart (UW) MPC: Status and Future DYCOPS / 22 Acknowledgments Support from the U.S. National Science Foundation through grant CTS Collaboration with and support from Aspentech, Eastman, ExxonMobil and Shell Global Solutions. Dr. Aswin N. Venkat, Shell Global Solutions. Rawlings and Stewart (UW) MPC: Status and Future DYCOPS 27 2 / 22

11 Further Reading I Y.-C. Ho. On Centralized Optimal Control. IEEE Trans. Auto. Cont., 5 (4): , 25. J. Lunze. Feedback Control of Large Scale Systems. Prentice-Hall, London, U.K., N. R. Sandell-Jr., P. Varaiya, M. Athans, and M. Safonov. Survey of decentralized control methods for larger scale systems. IEEE Trans. Auto. Cont., 23(2):18 128, D. D. Siljak. Decentralized Control of Complex Systems. Academic Press, London, ISBN A. N. Venkat, I. A. Hiskens, J. B. Rawlings, and S. J. Wright. Distributed output feedback MPC for power system control. In Proceedings of the 45th IEEE Conference on Decision and Control, San Diego, California, December a. Rawlings and Stewart (UW) MPC: Status and Future DYCOPS / 22 Further Reading II A. N. Venkat, J. B. Rawlings, and S. J. Wright. Implementable distributed model predictive control with guaranteed performance properties. In Proceedings of the American Control Conference, Minneapolis, Minnesota, June b. Rawlings and Stewart (UW) MPC: Status and Future DYCOPS / 22