Cooperativity and Hierarchical MPC of State-Constrained Switched Power Flow Systems

Many energy systems require control frameworks that can manage dynamics spanning multiple timescales and can make decisions for both continuous and discrete inputs. This paper meets this need for a class of switched power flow systems modeled using graphs. Conditions are provided under which each mode of these models belongs to the class of cooperative systems. Leveraging properties of cooperative systems, a two-level hierarchical control framework is constructed in which an upper level controller governs slow dynamics to plan for long-term future behavior and select modes, while a lower level controller governs fast dynamics to improve performance and reject disturbances. The control framework guarantees satisfaction of state constraints while also ensuring that a minimum bound on the rate of energy transfer to the system can always be achieved. The applicability and efficacy of the approach is demonstrated in simulation on a fluid-thermal system representative of those found in aircraft.

[1]  Andrew G. Alleyne,et al.  Passivity and Decentralized MPC of Switched Graph-Based Power Flow Systems* , 2018, 2018 Annual American Control Conference (ACC).

[2]  Claus Danielson,et al.  Reconfigurable Model Predictive Control for Multievaporator Vapor Compression Systems , 2018, IEEE Transactions on Control Systems Technology.

[3]  D. West.  Introduction to Graph Theory , 1995 .

[4]  Andrew G. Alleyne,et al.  Dynamical Graph Models of Aircraft Electrical, Thermal, and Turbomachinery Components , 2018 .

[5]  Johan Löfberg,et al.  YALMIP : a toolbox for modeling and optimization in MATLAB , 2004 .

[6]  Franco Blanchini,et al.  Compartmental flow control: Decentralization, robustness and optimality , 2016, Autom..

[7]  Eduardo Sontag.  Nonlinear regulation: The piecewise linear approach , 1981 .

[8]  Hal L. Smith,et al.  Monotone Dynamical Systems: An Introduction To The Theory Of Competitive And Cooperative Systems (Mathematical Surveys And Monographs) By Hal L. Smith , 1995 .

[9]  Herschel C. Pangborn,et al.  Hierarchical control for multi-domain coordination of vehicle energy systems with switched dynamics , 2019 .

[10]  Daniel Liberzon,et al.  Switching in Systems and Control , 2003, Systems & Control: Foundations & Applications.

[11]  J. Stoustrup,et al.  Hierarchical Model Predictive Control for Plug-and-Play Resource Distribution , 2012 .

[12]  Matthew A. Williams.  A framework for the control of electro-thermal aircraft power systems , 2017 .

[13]  Ilya V. Kolmanovsky,et al.  Two-Layer Model Predictive Battery Thermal and Energy Management Optimization for Connected and Automated Electric Vehicles , 2018, 2018 IEEE Conference on Decision and Control (CDC).

[14]  Alberto L. Sangiovanni-Vincentelli,et al.  Optimal load management system for Aircraft Electric Power distribution , 2013, 52nd IEEE Conference on Decision and Control.

[15]  Andrew G. Alleyne,et al.  Experimental validation of graph-based modeling for thermal fluid power flow systems , 2016 .

[16]  Alex A. Kurzhanskiy,et al.  Mixed monotonicity of partial first-in-first-out traffic flow models , 2016, 2016 IEEE 55th Conference on Decision and Control (CDC).

[17]  Andrew G. Alleyne,et al.  Hierarchical Control for Electro-Thermal Power Management of an Electric Vehicle Powertrain , 2018, Volume 2: Control and Optimization of Connected and Automated Ground Vehicles; Dynamic Systems and Control Education; Dynamics and Control of Renewable Energy Systems; Energy Harvesting; Energy Systems; Estimation and Identification; Intelligent Transport.

[18]  Eduardo D. Sontag,et al.  Monotone and near-monotone biochemical networks , 2007, Systems and Synthetic Biology.

[19]  David Angeli,et al.  Monotone control systems , 2003, IEEE Trans. Autom. Control..

[20]  Andrew G. Alleyne,et al.  Experimental Validation of Graph-Based Hierarchical Control for Thermal Management , 2018, Journal of Dynamic Systems, Measurement, and Control.

[21]  Antoine Girard,et al.  Safety control with performance guarantees of cooperative systems using compositional abstractions , 2015, ADHS.

[22]  Debasish Chatterjee,et al.  Input-to-state stability of switched systems and switching adaptive control , 2007, Autom..

[23]  Mircea Lazar,et al.  Model predictive control of hybrid systems : stability and robustness , 2006 .

[24]  Franco Blanchini,et al.  Switched Positive Linear Systems , 2015, Found. Trends Syst. Control..

[25]  Kevin Barraclough,et al.  I and i , 2001, BMJ : British Medical Journal.

[26]  W. Marsden.  I and J , 2012 .

[27]  Franco Blanchini,et al.  Set-theoretic methods in control , 2007 .