Patent Publication Number: US-2023160347-A1

Title: Adaptive model predictive control for hybrid electric propulsion

Description:
CROSS-REFERENCE TO RELATED APPLICATION 
     This application is a continuation application of U.S. Application No. 16/783,512 filed Feb. 6, 2020, which claims the benefit of priority to U.S. Provisional Application No. 62/802,263 filed Feb. 7, 2019, the disclosures of which are incorporated herein by reference in their entirety. 
    
    
     BACKGROUND 
     The subject matter disclosed herein generally relates to rotating machinery and, more particularly, to a method and an apparatus for model predictive control for hybrid electric propulsion. 
     A hybrid electric propulsion system for an aircraft can include a gas turbine engine and at least one electric motor that supplements performance of the gas turbine engine. Gas turbine engines and electric motors typically have separate control laws to manage gas turbine power and electric power. Separate control laws can increase challenges in effectively managing events, such as rapid transients, thermal-mechanical stress, component lifespan, and/or other control goals. 
     BRIEF DESCRIPTION 
     According to one embodiment, a hybrid electric propulsion system includes a gas turbine engine having at least one compressor section and at least one turbine section operably coupled to a shaft. The hybrid electric propulsion system includes an electric motor configured to augment rotational power of the shaft of the gas turbine engine. A controller is operable to determine hybrid electric propulsion system parameters based on a composite system model and sensor data from one or more sensors, determine a prediction based on the hybrid electric propulsion system parameters and the composite system model, determine a model predictive control optimization for a plurality of hybrid electric system control effectors based on the prediction using a plurality of reduced-order partitions of the composite system model, and actuate the hybrid electric system control effectors based on the model predictive control optimization. 
     In addition to one or more of the features described above or below, or as an alternative, further embodiments may include where the controller is further configured to update a plurality of composite system model states of the composite system model based on detection of one or more faults. 
     In addition to one or more of the features described above or below, or as an alternative, further embodiments may include where the controller is further configured to update one or more reduced-order values based on the reduced-order partitions of the composite system model states of the composite system model. 
     In addition to one or more of the features described above or below, or as an alternative, further embodiments may include where the one or more reduced-order values are reduced-order Jacobian values based on a plurality of Jacobian equations associated with the composite system model. 
     In addition to one or more of the features described above or below, or as an alternative, further embodiments may include where the reduced-order partitions include partitions of a propulsion system model including a gas turbine engine model, a mechanical power transmission model, and an electrical power system model that preserve a plurality of dominant states for each partition. 
     In addition to one or more of the features described above or below, or as an alternative, further embodiments may include where the composite system model includes the propulsion system model, an optimization objective function, and a plurality of constraints. 
     In addition to one or more of the features described above or below, or as an alternative, further embodiments may include where the Jacobian equations associated with the composite system model include a plurality of model sensitivity matrices that are updated based on the detection of one or more faults. 
     In addition to one or more of the features described above or below, or as an alternative, further embodiments may include where the model predictive control optimization uses the model sensitivity matrices to determine a set of changes to the hybrid electric system control effectors that optimizes the optimization objective function over a finite time horizon while maintaining the constraints. 
     In addition to one or more of the features described above or below, or as an alternative, further embodiments may include an electric generator configured to extract power from the shaft, wherein the composite system model includes a plurality of electrical and mechanical physics-based models of at least the gas turbine engine, the electric motor, the electric generator, and one or more mechanical power transmissions. 
     According to an embodiment, a hybrid electric propulsion system includes a gas turbine engine, an electrical power system, a mechanical power transmission operably coupled between the gas turbine engine and the electrical power system, a plurality of hybrid electric system control effectors operable to control a plurality of states of one or more the gas turbine engine and the electrical power system, and means for controlling the hybrid electric system control effectors based on a model predictive control that is dynamically updated during operation of the hybrid electric propulsion system. 
     In addition to one or more of the features described above or below, or as an alternative, further embodiments may include where the means for controlling the hybrid electric system control effectors includes a controller operable to determine a plurality of hybrid electric propulsion system parameters based on a composite system model and a plurality of sensor data from one or more sensors, determine a prediction based on the hybrid electric propulsion system parameters and the composite system model, determine a model predictive control optimization for the hybrid electric system control effectors based on the prediction using a plurality of reduced-order partitions of the composite system model, and actuate the hybrid electric system control effectors based on the model predictive control optimization. 
     According to an embodiment, a method for controlling a hybrid electric propulsion system includes determining, by a controller, a plurality of hybrid electric propulsion system parameters based on a composite system model and a plurality of sensor data from one or more sensors, determining, by the controller, a prediction based on the hybrid electric propulsion system parameters and the composite system model, determining, by the controller, a model predictive control optimization for a plurality of hybrid electric system control effectors based on the prediction using a plurality of reduced-order partitions of the composite system model, and actuating, by the controller, the hybrid electric system control effectors based on the model predictive control optimization. 
     A technical effect of the apparatus, systems and methods is achieved by performing model predictive control for a hybrid electric propulsion system. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
       The patent or application file contains at least one drawing executed in color. Copies of this patent or patent application publication with color drawing(s) will be provided by the Office upon request and payment of the necessary fee. 
       The following descriptions should not be considered limiting in any way. With reference to the accompanying drawings, like elements are numbered alike: 
         FIG.  1    is a partial cross-sectional illustration of a gas turbine engine, in accordance with an embodiment of the disclosure; 
         FIG.  2    is a schematic diagram of a hybrid electric propulsion system with physical power flow connections (electrical and mechanical power), in accordance with an embodiment of the disclosure; 
         FIG.  3    is a schematic diagram of control signal paths of a hybrid electric propulsion system propulsion system, in accordance with an embodiment of the disclosure; 
         FIG.  4    is a block diagram of a model predictive control system for a hybrid electric propulsion system, in accordance with an embodiment of the disclosure; 
         FIG.  5    is a flow chart illustrating a method, in accordance with an embodiment of the disclosure; 
         FIG.  6    is a flow chart illustrating a method, in accordance with an embodiment of the disclosure; and 
         FIG.  7    is a flow chart illustrating a method, in accordance with an embodiment of the disclosure. 
     
    
    
     DETAILED DESCRIPTION 
     A detailed description of one or more embodiments of the disclosed apparatus and method are presented herein by way of exemplification and not limitation with reference to the Figures. 
       FIG.  1    schematically illustrates a gas turbine engine  20 . The gas turbine engine  20  is disclosed herein as a two-spool turbofan that generally incorporates a fan section  22 , a compressor section  24 , a combustor section  26  and a turbine section  28 . The fan section  22  drives air along a bypass flow path B in a bypass duct, while the compressor section  24  drives air along a core flow path C for compression and communication into the combustor section  26  then expansion through the turbine section  28 . Although depicted as a two-spool turbofan gas turbine engine in the disclosed non-limiting embodiment, it should be understood that the concepts described herein are not limited to use with two-spool turbofans as the teachings may be applied to other types of turbine engines including three-spool architectures. 
     The exemplary engine  20  generally includes a low speed spool  30  and a high speed spool  32  mounted for rotation about an engine central longitudinal axis A relative to an engine static structure  36  via several bearing systems  38 . It should be understood that various bearing systems  38  at various locations may alternatively or additionally be provided, and the location of bearing systems  38  may be varied as appropriate to the application. 
     The low speed spool  30  generally includes an inner shaft  40  that interconnects a fan  42 , a low pressure compressor  44  and a low pressure turbine  46 . The inner shaft  40  is connected to the fan  42  through a speed change mechanism, which in exemplary gas turbine engine  20  is illustrated as a geared architecture  48  to drive the fan  42  at a lower speed than the low speed spool  30 . The high speed spool  32  includes an outer shaft  50  that interconnects a high pressure compressor  52  and high pressure turbine  54 . A combustor  56  is arranged in exemplary gas turbine  20  between the high pressure compressor  52  and the high pressure turbine  54 . An engine static structure  36  is arranged generally between the high pressure turbine  54  and the low pressure turbine  46 . The engine static structure  36  further supports bearing systems  38  in the turbine section  28 . The inner shaft  40  and the outer shaft  50  are concentric and rotate via bearing systems  38  about the engine central longitudinal axis A which is collinear with their longitudinal axes. 
     The core airflow is compressed by the low pressure compressor  44  then the high pressure compressor  52 , mixed and burned with fuel in the combustor  56 , then expanded over the high pressure turbine  54  and low pressure turbine  46 . The turbines  46 ,  54  rotationally drive the respective low speed spool  30  and high speed spool  32  in response to the expansion. It will be appreciated that each of the positions of the fan section  22 , compressor section  24 , combustor section  26 , turbine section  28 , and fan drive gear system  48  may be varied. For example, gear system  48  may be located aft of combustor section  26  or even aft of turbine section  28 , and fan section  22  may be positioned forward or aft of the location of gear system  48 . 
     The engine  20  in one example is a high-bypass geared aircraft engine. In a further example, the engine  20  bypass ratio is greater than about six (6), with an example embodiment being greater than about ten (10), the geared architecture  48  is an epicyclic gear train, such as a planetary gear system or other gear system, with a gear reduction ratio of greater than about 2.3 and the low pressure turbine  46  has a pressure ratio that is greater than about five. In one disclosed embodiment, the engine  20  bypass ratio is greater than about ten (10:1), the fan diameter is significantly larger than that of the low pressure compressor  44 , and the low pressure turbine  46  has a pressure ratio that is greater than about five 5:1. Low pressure turbine  46  pressure ratio is pressure measured prior to inlet of low pressure turbine  46  as related to the pressure at the outlet of the low pressure turbine  46  prior to an exhaust nozzle. The geared architecture  48  may be an epicycle gear train, such as a planetary gear system or other gear system, with a gear reduction ratio of greater than about 2.3:1. It should be understood, however, that the above parameters are only exemplary of one embodiment of a geared architecture engine and that the present disclosure is applicable to other gas turbine engines including direct drive turbofans. 
     A significant amount of thrust is provided by the bypass flow B due to the high bypass ratio. The fan section  22  of the engine  20  is designed for a particular flight condition--typically cruise at about 0.8 Mach and about 35,000 feet (10,688 meters). The flight condition of 0.8 Mach and 35,000 ft (10,688 meters), with the engine at its best fuel consumption—also known as “bucket cruise Thrust Specific Fuel Consumption (‘TSFC’)”—is the industry standard parameter of lbm of fuel being burned divided by lbf of thrust the engine produces at that minimum point. “Low fan pressure ratio” is the pressure ratio across the fan blade alone, without a Fan Exit Guide Vane (“FEGV”) system. The low fan pressure ratio as disclosed herein according to one non-limiting embodiment is less than about 1.45. “Low corrected fan tip speed” is the actual fan tip speed in ft/sec divided by an industry standard temperature correction of [(Tram °R)/(518.7 °R)]^0.5. The “Low corrected fan tip speed” as disclosed herein according to one non-limiting embodiment is less than about 1150 ft/second (350.5 m/sec). 
     While the example of  FIG.  1    illustrates one example of the gas turbine engine  20 , it will be understood that any number of spools, inclusion or omission of the gear system  48 , and/or other elements and subsystems are contemplated. Further, rotor systems described herein can be used in a variety of applications and need not be limited to gas turbine engines for aircraft applications. For example, rotor systems can be included in power generation systems, which may be ground-based as a fixed position or mobile system, and other such applications. 
       FIG.  2    illustrates a hybrid electric propulsion system  100  (also referred to as hybrid gas turbine engine  100 ) including a gas turbine engine  120  operably coupled to an electrical power system  210  as part of a hybrid electric aircraft. One or more mechanical power transmissions  150  (e.g.,  150 A,  150 B) can be operably coupled between the gas turbine engine  120  and the electrical power system  210 . The gas turbine engine  120  can be an embodiment of the gas turbine engine  20  of  FIG.  1    and includes one or more spools, such as low speed spool  30  and high speed spool  32 , each with at least one compressor section and at least one turbine section operably coupled to a shaft (e.g., low pressure compressor  44  and low pressure turbine  46  coupled to inner shaft  40  and high pressure compressor  52  and high pressure turbine  54  coupled to outer shaft  50  as depicted in  FIG.  1   ). The electrical power system  210  can include a first electric motor  212 A configured to augment rotational power of the low speed spool  30  and a second electric motor  212 B configured to augment rotational power of the high speed spool  32 . Although two electric motors  212 A,  212 B are depicted in  FIG.  2   , it will be understood that there may be only a single electric motor or additional electric motors (not depicted). The electrical power system  210  can also include a first electric generator  213 A configured to convert rotational power of the low speed spool  30  to electric power and a second electric generator  213 B configured to convert rotational power of the high speed spool  32  to electric power. In some embodiments, the electric motors  212 A,  212 B can be configured as a motor or a generator depending upon an operational mode or system configuration, and thus the electric generators  213 A,  213 B may be omitted. In the example of  FIG.  2   , the mechanical power transmission  150 A includes a gearbox operably coupled between the inner shaft  40  and a combination of the first electric motor  212 A and first electric generator  213 A. The mechanical power transmission  150 B can include a gearbox operably coupled between the outer shaft  50  and a combination of the second electric motor  212 B and second electric generator  213 B. In embodiments where the electric motors  212 A,  212 B are configurable between a motor and generator mode of operation, the mechanical power transmission  150 A,  150 B can be a clutch or other interfacing element(s). 
     The electrical power system  210  can also include motor drive electronics  214 A,  214 B operable to condition current to the electric motors  212 A,  212 B (e.g., DC-to-AC converters). The electrical power system  210  can also include rectifier electronics  215 A,  215 B operable to condition current from the electric generators  213 A,  213 B (e.g., AC-to-DC converters). The motor drive electronics  214 A,  214 B and rectifier electronics  215 A,  215 B can interface with an energy storage management system  216  that further interfaces with an energy storage system  218 . The energy storage management system  216  can be a bi-directional DC-DC converter that regulates voltages between energy storage system  218  and electronics  214 A,  214 B,  215 A,  215 B. The energy storage system  218  can include one or more energy storage devices, such as a battery, a super capacitor, an ultra capacitor, and the like. 
     A power conditioning unit  220  and/or other components can be powered by the energy storage system  218 . The power conditioning unit  220  can distribute electric power to support actuation and other functions of the gas turbine engine  120 . For example, the power conditioning unit  220  can power an integrated fuel control unit  222  to control fuel flow to the gas turbine engine  120 . The power conditioning unit  220  can power a plurality of actuators  224 , such as one or more of a low pressure compressor bleed valve actuator  226 , a low pressure compressor vane actuator  228 , a high pressure compressor vane actuator  230 , an active clearance control actuator  232 , and other such effectors. Collectively, any effectors that can change a state of the gas turbine engine  120  and/or the electrical power system  210  may be referred to as hybrid electric system control effectors  240 . Examples of the hybrid electric system control effectors  240  can include the electric motors  212 A,  212 B, electric generators  213 A,  213 B, integrated fuel control unit  222 , actuators  224  and/or other elements (not depicted). 
       FIG.  3    is a schematic diagram of control signal paths  250  of the hybrid electric propulsion system  100  of  FIG.  2    and is described with continued reference to  FIGS.  1  and  2   . A controller  256  can interface with the motor drive electronics  214 A,  214 B, rectifier electronics  215 A,  215 B, energy storage management system  216 , integrated fuel control unit  222 , actuators  224 , and/or other components (not depicted) of the hybrid electric propulsion system  100 . In embodiments, the controller  256  can control and monitor for fault conditions of the gas turbine engine  120  and/or the electrical power system  210 . For example, the controller  256  can be integrally formed or otherwise in communication with a full authority digital engine control (FADEC) of the gas turbine engine  120 . In embodiments, the controller  256  can include a processing system  260 , a memory system  262 , and an input/output interface  264 . The controller  256  can also include various operational controls, such as a model predictive control  266  that controls the hybrid electric system control effectors  240  as further described herein. 
     The processing system  260  can include any type or combination of central processing unit (CPU), including one or more of: a microprocessor, a digital signal processor (DSP), a microcontroller, an application specific integrated circuit (ASIC), a field programmable gate array (FPGA), or the like. The memory system  262  can store data and instructions that are executed by the processing system  260 . In embodiments, the memory system  262  may include random access memory (RAM), read only memory (ROM), or other electronic, optical, magnetic, or any other computer readable medium onto which is stored data and algorithms in a non-transitory form. The input/output interface  264  is configured to collect sensor data from the one or more system sensors ( FIG.  4   ) and interface with various components and subsystems, such as components of the motor drive electronics  214 A,  214 B, rectifier electronics  215 A,  215 B, energy storage management system  216 , integrated fuel control unit  222 , actuators  224 , and/or other components (not depicted) of the hybrid electric propulsion system  100 . The controller  256  provides a means for controlling the hybrid electric system control effectors  240  based on a model predictive control  266  that is dynamically updated during operation of the hybrid electric propulsion system  100 . The means for controlling the hybrid electric system control effectors  240  can be otherwise subdivided, distributed, or combined with other control elements. 
     Referring now to  FIG.  4   , a block diagram of a control system  300  is depicted, in accordance with an embodiment of the disclosure. The control system  300  includes the model predictive control  266  that may be embodied within the controller  256  of  FIG.  3    and configured to interface with the hybrid electric propulsion system  100 . The model predictive control  266  includes a composite system model  302  and computational modules to perform a state estimation  304 , state and output prediction  306 , determine reduced-order values (e.g., reduced-order Jacobian equations)  308 , and constrained optimization  310 . The composite system model  302  can include a propulsion system model  312 , an optimization objective function  314 , a plurality of constraints  316 , and Jacobian equations  318  associated with the composite system model  302 . The propulsion system model  312  can include a gas turbine engine model  320  of the gas turbine engine  120 , a mechanical power transmission model  322  of the mechanical power transmission  150 , and an electrical power system model  324  of the electrical power system  210 . 
     The composite system model  302  can provide model states  326 , as well as modeled sensor values  327 , to state estimation  304  which also receives sensor data from sensors  330  of the hybrid electric propulsion system  100 . The state estimation  304  can produce updated state estimates  328 , which are provided to update the composite system model  302 . In some embodiments, the state estimation block  304  also receives Jacobian values from composite system model  302 . These Jacobian values are sensitivities of modeled sensor values  327  to changes in model states  326  and inputs. The Jacobian values are used by the state estimation algorithm within block  304  to compute updated state estimates that align modeled sensor values  327  with the actual sensor data  330 . More specifically, in some embodiments, the state estimation algorithm within block  304  is an instance of moving horizon constrained estimation. 
     From a control architecture perspective, the hybrid electric propulsion system  100  can have multiple potential solutions to achieving a given propulsion system thrust goal. This provides opportunities for real-time optimization of transient and steady-state system performance. For example, the optimization objective function  314  can be configured to use electric power only during rapid accelerations, preserving engine life by lowering peak thermal-mechanical stresses that would otherwise be larger during rapid, fuel-only transients. A control law for this example can smoothly transition from transient electric power-assist to continuous, quasi-steady gas turbine engine supplied power, while maintaining all engine and electric system variables within safe limits as defined in the constraints  316 . 
     Associated with the power distribution challenges, the hybrid electric propulsion system  100  can be significantly more complex than a non-hybrid system, and subject to a larger number of failure modes. The performance advantages realized through hybridization can be accompanied by improvements in control system adaptability and tolerance to failures, such as detected and isolated propulsion system failures  332 . The control system embodied in the model predictive control  266  can make a combination of continuous and discrete decisions through predictions over a plurality of future time steps, for instance, to modulate effectors (e.g., fuel, DC motor power) and/or make discrete decisions, such as power provision versus power extraction. In a prediction step, the propulsion system model  312  can be used to predict future responses of the system states and outputs by the state and output prediction  306 , which can be based on current values of the hybrid electric system control effectors  240 . In a corrector step, the constrained optimization  310  can use model sensitivity matrices (e.g., Jacobian equations  318  reduced as reduced-order values  308 ) to determine a set of changes to the hybrid electric system control effectors  240  as optimal effector commands  334  that optimize objective function  314 , over a finite time horizon, while maintaining the hybrid electric propulsion system  100  within safe limits (e.g., constraints  316 ). The objectives and constraints may also be functions of current and future system inputs, states, and outputs, thus requiring objective and constraint sensitivities, in addition to model sensitivity matrices, to accurately predict/correct system trajectories and satisfy constraints. For example, in one embodiment, a battery state of charge objective can be a function of the difference of predicted propulsion system thrust and thrust required/requested by an airframe. In another example embodiment, a compressor pressure ratio constraint may be a function of predicted future compressor air flow rate. The sensitivity matrices of the Jacobian equations  318  and further reduced as reduced-order values  308  can be computed during operation of the hybrid electric propulsion system  100  rather than a priori in order to maximize adaptability of model predictive control  266  to failures  332 . Propulsion system goals and airframe commands  336  can be updated during operation to change the optimization objective function  314  in order to adapt the model predictive control  266  to changing mission objectives. 
     For more efficient real-time operation, computational cost of the model predictive control  266  can be reduced by lowering the computational the cost of iteratively computing inverses of the model sensitivity matrices. Therefore, there can be a technical benefit to reducing the size of the sensitivity matrices through state order reduction. In order to splice predictions from a full order model, with optimal corrections computed from reduced order sensitivities, it can be beneficial to retain the identity of physics states in both full and reduced order models. Some hybrid electric propulsion architectures, such as a parallel architecture, have strong but sparse coupling between the aero-thermodynamic propulsion subsystem and the electric power subsystem, through, for example, a gearbox connecting an electric motor to a turbo-machinery shaft. Aside from sparse mechanical coupling points, the remaining and dominant dynamic states of the electrical subsystem (e.g., energy storage system temperature, state of charge) may be largely independent of the dominant dynamic states of the gas turbine engine subsystem. This structure of a dynamic model can be characterized as a sparse and nearly block-diagonal structure that can help inform selection of dynamic states for reduced order Jacobians and potentially can leverage efficient sparse matrix algorithms. 
     In embodiments, the propulsion system model  312  represents a multi-physics model including aero-thermodynamic, mechanical, and electrical dynamics. State partitioning of the propulsion system model  312  can preserve a quasi-block diagonal structure. A reduced order set of dominant dynamic states for each partition can be determined that preserves state physical identity. The selected reduced order states are used to compute reduced order Jacobians  308  from analytic Jacobian equations of the composite system model  318 . The reduced-order Jacobian values  308  are then provided to the constrained optimization  310 , which computes optimal effector commands given a set of propulsion system goal and airframe commands  336 , objectives  314  and constraints  316 , and current estimated state of the engine  328 . 
     Referring now to  FIG.  5    with continued reference to  FIGS.  1 - 4   ,  FIG.  5    is a flow chart illustrating a method  400  for off-board modeling and analysis, in accordance with an embodiment. The method  400  may be performed, for example, by a computer system external to the hybrid electric propulsion system  100  to construct a composite propulsion system model  302 , generate analytic Jacobian equations  318  for the composite system model, and select a set of reduced order model states for reduced order Jacobians  308  for the model predictive control  266  of  FIG.  4   . For purposes of explanation, the method  400  is described primarily with respect to the hybrid electric propulsion system  100  of  FIG.  2   ; however, it will be understood that the method  400  can be performed with respect to other configurations (not depicted). 
     At block  402 , a physics-based hybrid electric propulsion system model is constructed that corresponds to design characteristics of the hybrid electric propulsion system  100 , as an initial configuration of the propulsion system model  312 . At block  404 , propulsion system constraint exceedance equations can be determined based on propulsion system constraint equations  406  to determine values for the constraints  316 . At block  408 , analytic Jacobian equations are generated for the composite system model  302  and implemented as software in the target controller  256  as the Jacobian equations  318 , which can include first-order partial derivatives for a collection of dynamic states, adjustments, goals, limits, and the like. At block  410 , the analytical Jacobian equations for the composite system model  302  can be loaded as the Jacobian equations  318  into the controller  256 . At block  412 , the physics-based hybrid electric propulsion system model of block  402  can be partitioned in dynamic states based on a coupling analysis. At block  414 , a reduced set of physics states can be selected for each partition based on singular value analysis and time scale separation. At block  416 , the reduced set of physics states for each partition can be provided as a set of state indices to load in the controller  256  for producing the reduced-order values  308 . 
     Referring now to  FIG.  6    with continued reference to  FIGS.  1 - 5   ,  FIG.  6    is a flow chart illustrating a method  500  for controlling of a hybrid electric propulsion system, in accordance with an embodiment. The method  500  may be performed, for example, by the hybrid electric propulsion system  100  of  FIG.  2   . For purposes of explanation, the method  500  is described primarily with respect to the hybrid electric propulsion system  100  of  FIG.  2   ; however, it will be understood that the method  500  can be performed on other configurations (not depicted). 
     Method  500  pertains to the controller  256  executing embedded code for the model predictive control  266  to compute optimal hybrid propulsion system control effectors  518  and actuate these effectors  520 . At block  504 , it can be determined whether this is the first pass of the model predictive control  266 . If this is not the first pass, then at block  506 , the model states  326  are calculated from last pass model state values, by numerical integration of differential equations  402 ,  404  of the composite system model  302 , within the controller  266 . Block  506  also calculates Jacobians  318 . The composite system model  302 , represented in part by differential equations  402 ,  404 , and the corresponding Jacobians  318 , are adaptive to detected failure states  332 . For example, a detected open circuit failure of motor drives  214 A or  214 B triggers a structural and/or parametric change to the composite system model  302  and corresponding Jacobians  318 , reflecting physics of the failure state. Model state values from block  506  are used to calculate reduced order Jacobian values in block  508 . Block  512  receives the model states from block  506  and computes updated state estimates  328 , based on modeled sensor values  327  and propulsion system sensor data  330 . At block  508 , the controller  256  can calculate the reduced-order values  308  (e.g., reduced-order Jacobian values) based on reduced order partitions defined by a reduced order set of physics states. Indices for the reduced order set of physics states are set in controller  256  at initialization, as defined in block  416  of  FIG.  5    and block  510  of  FIG.  6   . At block  512 , the controller  256  can determine an estimate of hybrid electric propulsion system states based on sensor data from sensors  330  and modeled sensor values  327  and model states  326  of the composite system model  302 . Initialization  514  of the composite system model  302  can be performed on the first pass of the model predictive control  266 . 
     At block  516 , the controller  256  can execute the model predictive control  266  to determine the state and output prediction  306 . At block  518 , the controller  256  can execute the model predictive control  266  to determine the constrained optimization  310  for optimal effector commands  334  of the hybrid electric system control effectors  240  based on the reduced-order Jacobian values  308  of block  508 . At block  520 , the hybrid electric system control effectors  240  can be actuated based on the optimal effector commands  334 . The method  500  can loop back to block  504  to continue with real-time control and updates as the hybrid electric propulsion system  100  operates. 
     Referring now to  FIG.  7    with continued reference to  FIGS.  1 - 6   ,  FIG.  7    is a flow chart illustrating a method  600  for control of a hybrid electric propulsion system, in accordance with an embodiment. The method  600  may be performed, for example, by the hybrid electric propulsion system  100  of  FIG.  2   . For purposes of explanation, the method  600  is described primarily with respect to the hybrid electric propulsion system  100  of  FIG.  2   ; however, it will be understood that the method  600  can be performed on other configurations (not depicted). 
     At block  602 , controller  256  can determine an estimate of a plurality of hybrid electric propulsion system parameters based on a composite system model  302  and a plurality of sensor data from sensors  330  using the state estimation  304 . At block  604 , the controller  256  can determine a model predictive control state and a prediction using the state and output prediction  306  based on the hybrid electric propulsion system parameters and the composite system model  302 . At block  606 , the controller  256  can determine a model predictive control optimization for a plurality of hybrid electric system control effectors  240  by the constrained optimization  310  based on the model predictive control state and the prediction using a plurality of reduced-order partitions of the composite system model  302 . At block  608 , the controller  256  can actuate the hybrid electric system control effectors  240  based on the model predictive control optimization. 
     In embodiments, the controller  256  can be configured to update a plurality of composite system model states of the composite system model  302  based on detection of one or more faults, such as detected and isolated propulsion system failures  332 . The controller  256  can be further configured to update one or more reduced-order values  308  based on the reduced-order partitions of the composite system model states of the composite system model  302 . The one or more reduced-order values  308  can be reduced-order Jacobian values based on a plurality of Jacobian equations  318  associated with the composite system model  302 . The reduced-order partitions can include partitions of a propulsion system model  312  including a gas turbine engine model  320 , a mechanical power transmission model  322 , and an electrical power system model  324  that preserve a plurality of dominant states for each partition. The composite system model  302  can include the propulsion system model  312 , an optimization objective function  314 , and a plurality of constraints  316 . The Jacobian equations  318  associated with the composite system model  302  can include a plurality of model sensitivity matrices that are updated based on the detection of one or more faults. The model predictive control optimization can use the model sensitivity matrices to determine a set of changes to the hybrid electric system control effectors  240  that optimizes the optimization objective function  314  over a finite time horizon while maintaining the constraints  316 . 
     While the above description has described the flow process of  FIG.  7    in a particular order, it should be appreciated that unless otherwise specifically required in the attached claims that the ordering of the steps may be varied. Also, it is clear to one of ordinary skill in the art that, the stability enhancement provided by the dynamic torque and power capability of the coupled electric motor system described herein can be combined with and enhance other surge control features, such as surge control valves, variable stators, and fuel flow control. 
     The term “about” is intended to include the degree of error associated with measurement of the particular quantity based upon the equipment available at the time of filing the application. 
     The terminology used herein is for the purpose of describing particular embodiments only and is not intended to be limiting of the present disclosure. As used herein, the singular forms “a”, “an” and “the” are intended to include the plural forms as well, unless the context clearly indicates otherwise. It will be further understood that the terms “comprises” and/or “comprising,” when used in this specification, specify the presence of stated features, integers, steps, operations, elements, and/or components, but do not preclude the presence or addition of one or more other features, integers, steps, operations, element components, and/or groups thereof. 
     While the present disclosure has been described with reference to an exemplary embodiment or embodiments, it will be understood by those skilled in the art that various changes may be made and equivalents may be substituted for elements thereof without departing from the scope of the present disclosure. In addition, many modifications may be made to adapt a particular situation or material to the teachings of the present disclosure without departing from the essential scope thereof. Therefore, it is intended that the present disclosure not be limited to the particular embodiment disclosed as the best mode contemplated for carrying out this present disclosure, but that the present disclosure will include all embodiments falling within the scope of the claims.