Richard T. Meyer

Real-Time Model Predictive Control for Shipboard Power Management Using the IPA-SQP Approach

Shipboard integrated power systems, the key enablers of ship electrification, call for effective power management control (PMC) to achieve optimal and reliable operation in dynamic environments under hardware limitations and operational constraints. The design of PMC can be treated naturally in a model predictive control (MPC) framework, where a cost function is minimized over a prediction horizon subject to constraints. The real-time implementation of MPC-based PMC, however, is challenging due to computational complexity of the numerical optimization. In this paper, an MPC-based PMC for a shipboard power system is developed and its real-time implementation is investigated. To meet the requirements for real-time computation, an integrated perturbation analysis and sequential quadratic programming (IPA-SQP) algorithm is applied to solve a constrained MPC optimization problem. Several operational scenarios are considered to evaluate the performance of the proposed PMC solution. Simulations and experiments show that real-time optimization, constraint enforcement, and fast load following can be achieved with the IPA-SQP algorithm. Different performance attributes and their tradeoffs can be coordinated through proper tuning of the design parameters.

Modeling and Simulation of a Modern PEM Fuel Cell System

Recent trends and advances in hydrogen/air Proton Exchange Membrane Fuel Cells (PEMFC) are incorporated into a dynamic control oriented model. This type of model is important for development of control systems for PEMFC powered transportation where unpredictable and widely varying changes in power demand can be expected. Self humidification and low pressure operation are the two major changes to past systems. As a result, a high pressure air compressor, air cooler, and inlet gas humidifiers are no longer required. Also, the likelihood of cathode flooding is reduced. The overall fuel cell model consists of four basic sub-models: anode, cathode, fuel cell body, and cooling. Additionally, the oxidant supply blower, cooling pump, and cooling fan are explicitly incorporated. Mass and energy conservation are applied to each using a lumped parameter control volume approach. Empirical modeling is minimized as much as possible, however it is necessary for model manageability in a control context. Interactions between each subsystem and balance of plant components are clearly defined. The overall model is capable of capturing the transient behavior of the flows, pressures, and temperatures as well as net output power. The influence of the charge double layer effect on transient performance is also explored. Numerical simulations of the system are presented which illustrate the usefulness of the model. Finally, future control work is described.Copyright

A comparison of the embedding method with multiparametric programming, mixed-integer programming, gradient-descent, and hybrid minimum principle-based methods

In recent years, the embedding approach for solving switched optimal control problems has been developed in a series of papers. However, the embedding approach, which advantageously converts the hybrid optimal control problem to a classical nonlinear optimization, has not been extensively compared with alternative solution approaches. The goal of this paper is thus to compare the embedding approach with multiparametric programming, mixed-integer programming [mixed integer programming (MIP), commercial (CPLEX)], and gradient-descent-based methods in the context of five recently published examples: 1) a spring-mass system; 2) moving-target tracking for a mobile robot; 3) two-tank filling; dc-dc boost converter; and 5) skid-steered vehicle. A sixth example, an autonomous switched 11-region linear system, is used to compare a hybrid minimum principle method and traditional numerical programming. For a given performance index (PI) for each case, cost and solution times are presented. It is shown that there are numerical advantages of the embedding approach: lower PI cost (except in some instances when autonomous switches are present), generally faster solution time, and convergence to a solution when other methods may fail. In addition, the embedding method requires no ad hoc assumptions (e.g., predetermined mode sequences) or specialized control models. Theoretical advantages of the embedding approach over the other methods are also described; guaranteed existence of a solution under mild conditions, convexity of the embedded hybrid optimization problem (under the customary conditions on the PI), solvability with traditional techniques (e.g., sequential quadratic programming) avoiding the combinatorial complexity in the number of modes/discrete variables of MIP, applicability to affine nonlinear systems, and no need to explicitly assign discrete/mode variables to autonomous switches. Finally, common misconceptions regarding the embedding approach are addressed, including whether it uses an average value control model (no), whether it is necessary to tweak the algorithm to obtain bang-bang solutions (no), whether it requires infinite switching to implement embedded solution (no), and whether it has real-time capability (yes).

Hybrid model predictive power flow control of a fuel cell-battery vehicle

This paper considers optimal power flow control of a fuel cell-battery hybrid vehicle (FCHV) powertrain having three distinct modal configurations (modes): electric motor propelling/battery discharging, propelling/charging, and generating/charging. Each mode has a distinct set of dynamics and constraints. Using component dynamical/algebraic models appropriate to power management, the paper develops a supervisory-level switched system model as an interconnection of subsystems. Given the model, the paper sets forth a hybrid model predictive control strategy based on a minimization of a performance index (PI) that trades off tracking and fuel economy in each operational mode. Specifically the PI trades off velocity tracking error, battery state of charge variance, and hydrogen usage while penalizing frictional braking. The optimization is performed using an embedded system model and collocation with MATLABs fmincon to compute mode switches and continuous time controls thereby avoiding the computational complexity of alternate approaches based on, e.g., mixed integer programming. To demonstrate the approach, an example FCHV following trapezoidal and sawtooth drive profiles is simulated. PI weights are varied for reduced hydrogen use and higher final battery charge to illustrate various performance trade-offs.

Control of a PEM fuel cell cooling system

Previous research has assumed that a perfect Proton Exchange Membrane Fuel Cell (PEMFC) body temperature manager is available. Maintaining this temperature at a desired value can ensure a high reaction efficiency over all operation. However, fuel cell internal body temperature control has not been specifically presented so far. This work presents such control, using a Multiple Input Single Output (MISO) fuel cell cooling system to regulate the internal body temperature of a PEMFC intended for transportation. The cooling system plant is taken from a recently developed hydrogen/air PEMFC total system model. It is linearized and used to design a series of controllers via μ-synthesis. μ-synthesis is chosen since system nonlinearities can be handled as parameter uncertainties. A controller must coordinate the desired fuel cell internal temperature and commanded mass flow rates of the coolant and cooling air. Each linear controller is created for a segment of the expected current density range. Plant parameters are expected to vary over their linearized values in each segment. Also, a common set of μ-synthesis weighting functions has been developed to ease controller design at different operating points. Thus, the nonlinear cooling subsystem can be controlled with a series of current density scheduled linear controllers. Current density step change simulations are presented to compare the controller closed loop performance and open loop response which uses cooling system flow rates taken from an optimal steady state solution of the whole fuel cell system. Furthermore, a closed loop sinusoid response is also given. These show that the closed loop driven internal fuel cell temperature will vary little during operation. However, this will only be true over the range that the cooling system is required to be active.Copyright

Gas Turbine Engine Behavioral Modeling

This paper develops and validates a power flow behavioral model of a gas turbine engine (GTE) composed of a gas generator and free power turbine. The behavioral model is suitable for supervisory level (optimal) controller development of the engine itself or of electrical power systems containing gas-turbine-generator pairs as might be found in a naval ship or terrestrial electric utility plant. First principles engine models do not lend themselves to the supervisory level control development because of their high granularity. For the behavioral model, “simple” mathematical expressions that describe the engines internal power flows are derived from an understanding of the engines internal thermodynamic and mechanical interactions. These simple mathematical expressions arise from the balance of energy flow across engine components, power flow being the time derivative of energy flow. The parameter fit of the model to a specific engine such as the GE LM2500 detailed in this work utilizes constants and empirical fits of power conversion efficiencies obtained using data collected from a high-fidelity engine simulator such as the Gas Turbine Simulation Program (GSP). Transient response tests show that the two-norm normalized error between the detailed simulator model and behavioral model outputs to be 2.7% or less for a GE LM2500.

Notch filter and MPC for powered wheelchair operation under Parkinson's tremor

This paper considers a model predictive control (MPC) strategy for mitigating the effects of Parkinson tremors on a movement-sensing, joystick controlled battery powered wheelchair with regenerative braking to extend its range between charges. Regenerative braking transforms the wheelchair model into a (switched) hybrid system. The wheelchair is represented as a joystick controlled wheeled mobile robot (WMR) having four modes of operation, propelling and regenerative braking for each wheel. The joystick is presumed to provide velocity, orientation, and position commands. To enhance safety, velocity and acceleration saturation limits are imposed as constraints on the control activation. The paper delineates a notch filter to remove the main Parkinsons tremor followed by a model predictive control strategy to track velocity, orientation, and distance to a wall commands from the joystick. Results show significant feasible advantages for safe wheelchair operation by Parkinsons patients with tremor.

Behavioral modeling and optimal control of a vehicle mechanical drive system

This paper investigates the optimal power management of a vehicle powertrain that includes a diesel engine connected to a continuously variable transmission (CVT). A control-oriented, supervisory level powertrain model is developed using the interconnection of component dynamical/algebraic models applicable to power flow management. Of note, we perform a CVT power flow analysis and construct the corresponding power-flow-based model. Further, we introduce the use of Lyapunov energy functions into our modeling approach to mitigate solution singularities. Given the powertrain model, the paper sets forth power management based upon model predictive control that seeks to minimize vehicle velocity tracking error, fuel usage, and frictional braking, except during commanded deceleration, to avoid its use during positive engine power output. To demonstrate the validity of the approach, the controlled vehicle is simulated for a trapezoidal drive profile of 35 s. Results show that engine efficiency is greater than or equal to 30% for about 36% of the drive profile and velocity tracking 2-norm normalized error is about 1.5%.

Hybrid Optimal Power Management of a Ship

Power management of a ship’s electrical system has become important due to increasing loads from manpower-reducing automation, greater power requirements of advanced weapons and sensors, introduction of all electric propulsion, and the increasing cost of oil-based fossil fuels. A coordinated power management strategy of the ship’s electric power grid is desired to optimally allocate power flows and minimize fuel consumption. This paper develops such an optimal power management system for an interconnected, supervisory-level ship power system model based upon a ship power system test bed developed for the Office of Naval Research. The ship power system consists of two electrical generators, one rated at 59 kW to represent a gas turbine engine-generator pair and the other rated at 11 kW to represent a diesel generator, an 8 kW pulsed power load that represents the discharge and charge of a capacitor bank for an electromagnetic railgun system, and 37 kW ship propulsion system comprised of an induction motor coupled to the propeller shaft. The ship propulsion system’s induction motor has switched operation with two modes of operation, propelling and generating; the latter mode means that excess kinetic energy during ship slowing can be used to charge the capacitor bank for loads such as pulsed power loads. Given the switched system model, the paper sets forth a hybrid model predictive control strategy based on a minimization of a performance index that trades off fuel consumption, velocity tracking error, and electrical bus voltage error. The optimization is performed using a relaxed representation of the control problem (termed the embedding method) and collocation for discretization with traditional numerical programming to compute the mode and continuous control inputs. The methodology avoids the computational complexity associated with alternative approaches, e.g., mixed-integer programming. Numerical optimization is performed with MATLAB’s sqpLineSearch. To demonstrate the power management approach, a scenario is simulated where the ship is to follow a changing desired velocity while simultaneously maintaining the bus voltage at a desired value, keeping the 11 kW generator at a fuel efficient operating point, and minimizing the fuel use of the 59 kW generator.Copyright