Balanced Truncation of Networked Linear Passive Systems

This paper studies model order reduction of multi-agent systems consisting of identical linear passive subsystems, where the interconnection topology is characterized by an undirected weighted graph. Balanced truncation based on a pair of specifically selected generalized Gramians is implemented on the asymptotically stable part of the full-order network model, which leads to a reduced-order system preserving the passivity of each subsystem. Moreover, it is proven that there exists a coordinate transformation to convert the resulting reduced-order model to a state-space model of Laplacian dynamics. Thus, the proposed method simultaneously reduces the complexity of the network structure and individual agent dynamics, and it preserves the passivity of the subsystems and the synchronization of the network. Moreover, it allows for the a priori computation of a bound on the approximation error. Finally, the feasibility of the method is demonstrated by an example

Advanced Predictive Control Strategies for More Electric Aircraft

Next generation aircraft designs are incorporating increasingly complex electrical power distribution systems to address growing demands for larger and faster electrical power loads. This dissertation develops advanced predictive control strategies for coordinated management of the engine and power subsystems of such aircraft. To achieve greater efficiency, reliability and performance of a More Electric Aircraft (MEA) design static and dynamic interactions between its engine and power subsystems need to be accounted for and carefully handled in the control design. In the pursued approach, models of the subsystems and preview of the power loads are leveraged by predictive feedback controllers to coordinate subsystem operation and achieve improved performance of the MEA system while enforcing state and input constraints. More specifically, this dissertation contains the following key developments and contributions. Firstly, models representing the engine and power subsystems of the MEA, including their interactions, are developed. The engine is a dual-spool turbojet that converts fuel into thrust out of the nozzle and mechanical power at the shafts. Electrical generators extract some of this power and convert it into electricity that is supplied to a High Voltage DC bus to support connected loads, with the aid of a battery pack for smoothing voltage transients. The control objective in this MEA system is to actuate the engine and power subsystem inputs to satisfy demands for thrust and electrical power while enforcing constraints on compressor surge and bus voltage deviations. Secondly, disturbance rejection, power flow coordination, and anticipation of the changes in power loads are considered for effective MEA control. A rate-based formulation of Model Predictive Control (MPC) allowing for offset free tracking is proposed. Centralized control is demonstrated to result in better thrust tracking performance in the presence of compressor surge constraints as compared to decentralized control. Forecast of changes in the power load allows the control to act in advance and reduce bus voltage excursions. Thirdly, distributed MPC strategies are developed which account for subsystem privacy requirements and differences in subsystem controller update rates. This approach ensures coordination between subsystem controllers based on limited information exchange and exploits the Alternating Direction Method of Multipliers. Simulations demonstrate that the proposed approach outperforms the decentralized controller and closely matches the performance of a fully centralized solution. Finally, a stochastic approach to load preview based on a Markov chain representation of a military aircraft mission is proposed. A scenario based MPC is then exploited to minimized expected performance cost while enforce constraints over all scenarios. Simulation based comparisons indicate that this scenario based MPC performs similarly to an idealized controller that exploits exact knowledge of the future and outperforms a controller without preview.PHDAerospace EngineeringUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttps://deepblue.lib.umich.edu/bitstream/2027.42/150003/1/wdunham_1.pd