Systems and methods for control allocation for electric vertical take-off and landing aircraft - Patents.com

Abstract

To provide techniques for minimizing noise generated by electric propulsion units of an electric VTOL aircraft.SOLUTION: A method of controlling an electric aircraft that has a plurality of actuators including a plurality of electric propulsion units includes: receiving force and moment commands for the electric aircraft; determining control commands for the plurality of actuators based on the desired force and moment commands by solving an optimization problem that comprises a noise minimization term for minimizing noise generated by the electric propulsion units; and controlling the plurality of actuators according to the determined control commands to meet the force and moment commands for the electric aircraft.SELECTED DRAWING: Figure 1B

Description

[Technical field]

[0001] CROSS-REFERENCE TO RELATED APPLICATIONS This application claims priority to and the benefit of U.S. Application No. 17 / 157,580, filed January 25, 2021, which is incorporated by reference herein in its entirety.

[0002] The present disclosure relates generally to control of aircraft, and more particularly, to control of electric vertical take-off and landing aircraft. [Background technology]

[0003] A vertical take-off and landing (VTOL) aircraft is an aircraft that can take off and land vertically, hover, and provide the ability to transport travelers directly to their destination. Helicopters are VTOL aircraft that generate lift entirely through their rotors. Some VTOL aircraft have wings and a propulsion system that allows the wings to provide the lift required during forward flight. Some winged VTOL aircraft use separate propulsion systems for vertical thrust for use during take-off and landing, and forward thrust for use during cruise. Other winged VTOL aircraft use tiltable propulsion systems that tilt between vertical and forward thrust positions. Electric VTOL aircraft use electric propulsion units to provide thrust for vertical and forward flight. Many electric VTOL aircraft include movable electric propulsion units that can change the thrust vector of the propulsion units, such as from an upward direction for vertical lift to a forward direction for forward flight. Many electric VTOL aircraft are overactuated, in that there are more degrees of freedom of actuators than degrees of freedom of movement. Control allocation is the problem of distributing control effort among multiple actuators in an overactuated system. Electric VTOL aircraft often contain more propulsion units and other actuators than conventional aircraft, which strongly influence multiple control axes, and therefore may pose greater control allocation problems than conventional aircraft. Summary of the Invention

[0004] According to some embodiments, systems and methods for control allocation in electric VTOL aircraft include considering rotor acoustics when controlling actuators of the aircraft. According to various embodiments, the control allocation includes solving an optimization objective function that includes satisfying force and moment commands as a primary objective and tuning rotor acoustics as a secondary objective. In some embodiments, rotor acoustics is tuned by minimizing edgewise flight, varying rotor speed across a set of rotors, and / or minimizing propeller tip speed.

[0005] According to some embodiments, a system and method for control allocation in an electric VTOL aircraft includes considering the charge of the battery packs when controlling actuators of the aircraft. In some embodiments, the electric VTOL aircraft includes multiple battery packs electrically isolated from one another to power one or more electric propulsion units. The control allocation may include solving an optimization objective function that includes satisfying force and moment commands as a primary objective and balancing the energy usage of the battery packs as a secondary objective. In some embodiments, electric propulsion units powered by battery packs with greater charge are preferentially utilized.

[0006] According to various embodiments, a method for controlling an electric aircraft with multiple actuators including multiple electric propulsion units includes receiving force and moment commands for the electric aircraft, determining control commands for the multiple actuators based on desired force and moment commands by solving an optimization problem including a noise minimization term to minimize noise generated by the electric propulsion units, and controlling the multiple actuators in accordance with the determined control commands to satisfy the force and moment commands for the electric aircraft.

[0007] In any of these embodiments, controlling the plurality of actuators in accordance with the determined control commands may include operating at least a first electric propulsion unit of the plurality of electric propulsion units at a different speed than at least a second electric propulsion unit of the plurality of electric propulsion units to spread frequencies of the plurality of electric propulsion units across a wider frequency band.

[0008] In any of these embodiments, electric propulsion units closer to the aircraft fuselage may operate at slower speeds than electric propulsion units further from the fuselage to reduce noise in the fuselage.

[0009] In any of these embodiments, the electric propulsion units may operate at different speeds during straight flight.

[0010] In any of these embodiments, at least a portion of the plurality of electric propulsion units may be tiltable, and controlling the plurality of actuators in accordance with the determined control commands may include at least one of tilting the electric propulsion units and adjusting the attitude of the aircraft to minimize time of edgewise flight.

[0011] In any of these embodiments, controlling the plurality of actuators in accordance with the determined control commands may include setting a pitch of blades of the at least one electric propulsion unit to minimize a speed of the at least one electric propulsion unit.

[0012] In any of these embodiments, the electric aircraft may be a vertical take-off and landing aircraft.

[0013] In any of these embodiments, the electric aircraft may be manned.

[0014] In any of these embodiments, the electric aircraft may include multiple electric propulsion units on either side of the aircraft fuselage.

[0015] According to various embodiments, a system for controlling an electric aircraft including a plurality of actuators including a plurality of electric propulsion units includes one or more processors, a memory, and one or more programs stored in the memory for execution by the one or more processors for: receiving desired force and moment commands for the electric aircraft; determining control commands for the plurality of actuators based on the desired force and moment commands by solving an optimization problem including a noise minimization term to minimize noise generated by the electric propulsion units; and controlling the plurality of actuators in accordance with the determined control commands to satisfy the desired force and moment commands for the electric aircraft.

[0016] According to various embodiments, a method of controlling an electric aircraft including a plurality of actuators, including a plurality of electric propulsion units and a plurality of battery packs powering the plurality of electric propulsion units, includes receiving desired force and moment commands for the electric aircraft; monitoring an energy state of the plurality of battery packs, where at least a first battery pack of the plurality of battery packs is electrically isolated from at least a second battery pack of the plurality of battery packs; determining control commands for the plurality of actuators based on the desired force and moment commands by solving an optimization problem including an energy balance term for balancing energy draws of the electric propulsion units according to the monitored energy state of the plurality of battery packs; and controlling the plurality of actuators according to the determined control commands to satisfy the desired force and moment commands of the electric aircraft.

[0017] In any of these embodiments, the first battery pack may have lower remaining energy than the second battery pack, and the first electric propulsion unit powered by the first battery pack may operate at lower power than the second electric propulsion unit powered by the second battery pack.

[0018] In any of these embodiments, the first battery pack and the second battery pack may have the same energy capacity.

[0019] In any of these embodiments, the first electric propulsion unit and the second electric propulsion unit may have the same power rating.

[0020] In any of these embodiments, the energy balance term may include a set of preferred operating conditions for the multiple electric propulsion units, and the preferred operating conditions for an electric propulsion unit powered by a battery pack with a lower remaining energy may be lower than the preferred operating conditions for an electric propulsion unit powered by a battery pack with a higher remaining energy.

[0021] In any of these embodiments, the energy balance term may include a set of penalties for deviating from preferred operating conditions, and the penalty for an electric propulsion unit connected to a lower energy battery pack may be higher than the penalty for an electric propulsion unit connected to a higher energy battery pack.

[0022] In any of these embodiments, the optimization problem may include a noise minimization term to minimize the noise generated by the electric propulsion unit.

[0023] In any of these embodiments, the electric aircraft may be a vertical take-off and landing aircraft.

[0024] In any of these embodiments, the electric aircraft may be manned.

[0025] In any of these embodiments, the electric aircraft may include multiple electric propulsion units on either side of the aircraft fuselage.

[0026] According to various embodiments, a system for controlling an electric aircraft including a plurality of actuators including a plurality of electric propulsion units includes one or more processors, a memory, and one or more programs stored in the memory for execution by the one or more processors, the program for receiving desired force and moment commands for the electric aircraft; monitoring an energy state of a plurality of battery packs, where at least a first battery pack of the plurality of battery packs is electrically isolated from at least a second battery pack of the plurality of battery packs; determining control commands for the plurality of actuators based on the desired force and moment commands by solving an optimization problem including an energy balance term for balancing energy draw of the electric propulsion units according to the monitored energy state of the plurality of battery packs; and controlling the plurality of actuators according to the determined control commands to satisfy the desired force and moment commands of the electric aircraft. [Brief description of the drawings]

[0027] The present invention will now be described, by way of example only, with reference to the accompanying drawings, in which:

[0028] [Figure 1A] FIG. 1A illustrates a VTOL aircraft in a forward flight configuration in accordance with various embodiments.

[0029] [Figure 1B] FIG. 1B illustrates a VTOL aircraft in a takeoff and landing configuration in accordance with various embodiments.

[0030] [Figure 2A] , [Figure 2B] 2A and 2B illustrate power distribution architectures for powering electric propulsion units of an aircraft according to various embodiments.

[0031] [Diagram 3]FIG. 3 is a block diagram of a method for control allocation for an electric aircraft according to some embodiments.

[0032] [Figure 4] FIG. 4 is a functional block diagram of a control system for controlling actuators of an electric aircraft in accordance with various embodiments.

[0033] [Diagram 5] FIG. 5 is a functional block diagram of a system for control allocation including multi-stage optimization with frequency division according to various embodiments.

[0034] [Figure 6] FIG. 6 illustrates an example computing system 700 in accordance with various embodiments. DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

[0035] According to various embodiments, a system and method for control allocation for an electric VTOL aircraft includes considering rotor acoustics and / or battery pack energy balancing when distributing control effort of actuators of the aircraft. According to various embodiments, the control allocation includes solving an optimization objective function that includes satisfying force and moment commands as a primary objective and regulating rotor acoustics and / or balancing battery pack energy as secondary objectives.

[0036] According to various embodiments, the electric VTOL aircraft includes multiple electric propulsion units on each side of the aircraft's fuselage. The electric propulsion units include rotor-driven propellers, and the acoustic noise generated by the aircraft can be reduced by operating the rotors at different speeds to spread the combined frequencies over a larger frequency band, which can reduce the amplitude of any single frequency and result in a lower perceived noise. In some embodiments, the acoustics of the rotors can be tuned by minimizing the tip speed of the propellers while providing the required thrust. This can be done by determining the rotor speed and propeller pitch that achieves the lowest tip speed for the required thrust. In some embodiments, at least a portion of the electric propulsion units are tiltable, and the acoustics of the rotors can be tuned by utilizing thrust vectoring and flight trajectories to minimize the time of edgewise flight. In some embodiments, the acoustics of the rotors can be tuned by balancing the thrust distribution to minimize excessive demands on any one rotor.

[0037] According to various embodiments, the electric VTOL aircraft includes multiple battery packs electrically isolated from one another to provide electricity to different portions of the multiple electric propulsion units. In some embodiments, the control allocation includes energy balancing of the battery packs, which may be achieved by minimizing the use of electric propulsion units connected to battery packs having a lower charge relative to other battery packs. According to various embodiments, minimizing the use of electric propulsion units connected to lower charge battery packs may be achieved by reducing the preferred state of the electric propulsion units in the control allocation optimization objective function and / or increasing the penalty for deviation from the preferred state.

[0038] In the following description of the disclosure and embodiments, reference is made to the accompanying drawings, in which is shown, by way of illustration, specific embodiments that may be practiced. It will be understood that other embodiments and examples may be practiced and changes may be made without departing from the scope of the disclosure.

[0039] It will further be understood that, as used in the following description, the singular forms "a," "an," and "the" are intended to include the plural forms unless the context clearly dictates otherwise. It will also be understood that the term "and / or," as used herein, refers to and encompasses any and all possible combinations of one or more of the associated listed items. It will also be understood that, as used herein, the terms "includes," "including," "comprises," and / or "comprising" specify the presence of stated features, integers, steps, operations, elements, components, and / or units, but do not exclude the presence or addition of one or more other features, integers, steps, operations, elements, components, units, and / or groups thereof.

[0040] As used herein, the term "proprotor" refers to a controllable pitch propeller that can provide thrust for vertical lift and forward propulsion by varying the pitch of the propeller.

[0041] As used herein, the term "battery pack" means any combination of electrically connected batteries (i.e., battery cells) and can include multiple batteries arranged in series, parallel, or in a series and parallel combination.

[0042] 1A and 1B show a VTOL aircraft 100 in a cruise configuration and a vertical take-off and landing configuration, respectively, according to various embodiments. Exemplary embodiments of a VTOL aircraft according to various embodiments are described in U.S. Application No. 16 / 878,380, entitled "Vertical Take-Off and Landing Aircraft," filed May 19, 2020, the entire contents of which are incorporated herein by reference.

[0043] The aircraft 100 includes a fuselage 102, wings 104 attached to the fuselage 102, and one or more rear stabilizers 106 attached to the rear of the fuselage 102. The aircraft 100 includes multiple rotors 112 and multiple propeller rotors 114 (collectively referred to herein as EPUs). The EPUs (112, 114) generally include electric motors that drive multiple blades and motor controllers to control / drive the motors. In some embodiments, the pitch of the blades of one or more EPUs may be controlled in flight. In some embodiments, the EPU may include multiple partial motors that may together drive independent fans and may be controlled by multiple separate motor controllers.

[0044] Rotor 112 is attached to wing 104 and configured to provide lift for vertical takeoff and landing. Prop rotor 114 is attached to wing 104 and is tiltable between a lift configuration, shown in FIG. 1B, which provides a portion of the lift required for vertical takeoff and landing and hovering, and a propulsion configuration, shown in FIG. 1A, which provides forward thrust to the aircraft 100 for horizontal flight. As used herein, a prop rotor lift configuration refers to the orientation of any prop rotor in which the prop rotor thrust is primarily providing lift to the aircraft, and a prop rotor propulsion configuration refers to the orientation of any prop rotor in which the prop rotor thrust is primarily providing forward thrust to the aircraft.

[0045] According to various embodiments, the rotors 112 are configured to provide lift only, with all propulsion provided by the propeller rotors. Thus, the rotors 112 may be in a fixed position. During takeoff and landing, the propeller rotors 114 are tilted into a lift configuration in which their thrust is directed downward to provide additional lift. In some embodiments, the rotors 112 are tiltable for thrust vectoring.

[0046] For forward flight, the propeller rotors 114 tilt from their lift configuration to their thrust configuration. In other words, the tilt of the propeller rotors 114 varies from a range of tilt positions where the propeller thrust is directed upward to provide lift during vertical takeoff and landing to a range of tilt positions where the propeller thrust is directed forward to provide forward thrust to the aircraft 100. The propeller rotors tilt about an axis 118 that is perpendicular to the forward direction of the aircraft 100. When the aircraft 100 is in fully forward flight, lift may be provided entirely by the wings 104 and the rotors 112 may be stopped. The blades 120 of the rotors 112 may be locked in a low-drag position for aircraft cruise. In some embodiments, the rotors 112 each have two blades 120 locked to cruise in a minimum-drag position with one blade directly ahead of the other, as shown in FIG. 1A. In some embodiments, the rotors 112 have more than two blades. In some embodiments, the prop rotor 114 includes more blades 116 than the rotor 112. For example, as shown in Figures 1A and 1B, the rotors 112 may include two blades each, and the prop rotors 114 may include five blades each. According to various embodiments, the prop rotors 114 can have between two and five blades.

[0047] According to various embodiments, the aircraft includes only one wing 104 on each side of the fuselage 102 (or a single wing extending across the entire aircraft), with at least a portion of the rotors 112 located aft of the wing 104 and at least a portion of the propeller rotors 114 located forward of the wing 104. In some embodiments, all of the rotors 112 are located aft of the wing 104 and all of the propeller rotors are located forward of the wing 104. According to some embodiments, all of the rotors 112 and the propeller rotors 114 are wing-mounted, i.e., there are no fuselage-mounted rotors or propellers. According to various embodiments, all of the rotors 112 are located aft of the wing 104 and all of the propeller rotors 114 are located forward of the wing 104. According to some embodiments, all of the rotors 112 and the propeller rotors 114 are disposed inboard of the wing tips 109.

[0048] According to various embodiments, the rotors 112 and the propeller rotors 114 are attached to the wing 104 by a boom 122. The boom 122 may be attached under the wing 104, on the top of the wing, and / or integrated into the wing profile. According to various embodiments, one rotor 112 and one propeller rotor 114 are attached to each boom 122. The rotors 112 may be attached to the aft end of the boom 122 and the propeller rotors 114 may be attached to the forward end of the boom 122. In some embodiments, the rotors 112 are attached to a fixed position on the boom 122. In some embodiments, the propeller rotors 114 are attached to the forward end of the boom 122 via a hinge 124. The propeller rotors 114 are attached to the boom 122 such that when in its propulsion configuration, the propeller rotors 114 are aligned with the body of the boom 122, forming a continuous extension of the front end of the boom 122 that minimizes drag for forward flight.

[0049] According to various embodiments, the aircraft 100 may include multiple wings on each side of the aircraft 100, only one wing on each side of the aircraft 100, or a single wing extending across the aircraft 100. According to some embodiments, the at least one wing 104 is a high wing attached to the upper side of the fuselage 102. According to some embodiments, the wing includes control surfaces 150, such as flaps and / or ailerons, arranged via one or more control surface actuators (not shown). According to some embodiments, the wing may have curved wing tips 109 to reduce drag during forward flight. According to some embodiments, the rear stabilizer 106 includes control surfaces 152, such as one or more rudders, one or more elevators, and / or one or more combined rudder-elevators arranged via one or more control surface actuators (not shown). The wing may have any suitable design. In some embodiments, the wing has a tapered leading edge 123, for example as shown in the embodiment of FIG. 1A. In some embodiments, the wing has a tapered trailing edge.

[0050] FIG. 2A illustrates a power distribution architecture for powering the EPUs (112, 114) of the aircraft 100, according to various embodiments. Although FIGS. 1A-2A illustrate twelve EPUs (numbered 1-12 in FIG. 2A) mounted on the wing 104, an aircraft according to various embodiments may have any suitable number of EPUs, including 4, 6, 8, 10, 14, 18, 20, or more. The EPUs are powered by a number of battery packs 200. In the embodiment illustrated in FIG. 2A, there are six battery packs 200, numbered 1-6. Each battery pack 200 powers only a portion of the EPUs. In the embodiment illustrated, each battery pack 200 powers two EPUs. The grouping of battery packs and EPUs according to the embodiment illustrated in FIG. 2A is enumerated in FIG. 2B. Battery pack 1 powers EPUs 1, 12, battery pack 2 powers EPUs 2, 11, and so on. Each battery pack 200 is connected to a respective portion of the EPU via a dedicated distribution bus, e.g., buses 202, 204. Thus, the distribution bus 202 of one battery pack 1 is not electrically connected to the distribution bus 204 of battery pack 2.

[0051] Because the battery packs 200 are electrically isolated from each other, an electrical failure in one battery pack or its power distribution does not affect the operation of the other EPUs and battery packs. Only the EPUs powered by the failed battery pack or power distribution are affected. Thus, there is no single point of failure in the delivery of aircraft power. Furthermore, because the battery packs and power distribution circuitry are isolated from each other, there is no need for diodes to prevent current from flowing from one battery pack to another. This can result in significant weight savings and increased efficiency compared to systems with parallel battery packs.

[0052] According to various embodiments, the particular EPUs powered by a given battery pack may be selected to reduce destabilizing effects caused by loss of electricity to the EPUs if the battery pack fails. According to various embodiments, to reduce roll, pitch or yaw moments that may be caused by loss of power to an EPU powered by a battery pack, EPUs located on either side of one or more axes of symmetry of the collection of EPUs are powered by the same battery pack. For example, EPUs in the same relative position on either side of the longitudinal axis 280 of the aircraft may be powered by a first battery pack, so that if one of the battery packs fails, minimal roll moments will result because the thrust provided by the remaining EPUs remains uniform about the longitudinal axis. Similarly, in some embodiments, when a set of EPUs is positioned at least partially forward of the leading edges of a pair of wings and an EPU is positioned at least partially aft of the trailing edges of a pair of wings, the sets may be such that the EPUs on both sides of the wings and on both sides of the longitudinal axis 280 are powered by the same battery pack such that minimal roll and pitch moments are produced in the event of a battery pack failure (as shown in FIG. 2A ).

[0053] According to various embodiments, each battery pack 200 powers at least a portion of at least one propeller rotor 114 and at least a portion of at least one rotor 112. In the embodiment of FIG. 2A, the rotors and propeller rotors in opposite positions are driven by the same battery pack 200. Thus, the outermost propeller rotor 114 on the left side of the aircraft fuselage 102 (EPU1 in FIG. 2A) is powered by the same battery pack (battery pack 1 in FIG. 2A) as the outermost rotor 112 on the right side of the fuselage 102 (EPU12). Similarly, the outermost EPUs of the other pair (EPU6 and EPU7 in FIG. 2A) are powered by the same battery pack (battery pack 6). The grouping need not be limited to EPUs in exactly opposite positions. For example, EPU1 may be grouped with EPU11 instead of EPU12.

[0054] The number of EPUs powered by a given battery pack may be more than two. For example, in some embodiments, the number of EPUs per battery pack may be three, four, five, six, or any other suitable fraction of the number of layers of EPUs. According to various embodiments, there may be a different number of EPUs in each group. For example, one group may have two EPUs (two EPUs powered by a battery pack) and another group may have four EPUs (four EPUs powered by different battery packs). The number of battery packs can be from two. In various embodiments, the number of battery packs is at least three, at least four, at least five, at least six, at least seven, at least eight, or more.

[0055] FIG. 3 is a block diagram of a method 300 for control allocation for an electric aircraft according to some embodiments. The method 300 can be used for control allocation of an electric aircraft, such as the aircraft 100 of FIG. 1A. The method 300 determines commands for a plurality of actuators for the aircraft. The plurality of actuators can include one or more actuators associated with each of a plurality of electric propulsion units of the aircraft and can include one or more control surface actuators of the aircraft. As described further below, the method 300 can include control allocation utilizing overactuation of the aircraft to optimize rotor acoustic noise and / or battery pack energy balance. According to some embodiments, the method 300 utilizes extra degrees of freedom available due to the number and configuration of electric propulsion units to reduce acoustic noise while meeting desired forces and moments of the aircraft. According to some embodiments, the aircraft includes a plurality of battery packs that independently power the electric propulsion units, and the method 300 utilizes the extra degrees of freedom to balance the energy of the battery packs.

[0056] In step 302, force and moment commands for the electric aircraft are received, which may include receiving force and moment commands from an upstream computing module of the aircraft, such as a flight control system, which may generate the force and moment commands from pilot inputs. The force and moment commands may be desired forces and moments to be applied to the aircraft via operation of one or more of the aircraft's various actuators.

[0057] As used herein, an "actuator" is any subsystem of an aircraft that provides a degree of freedom to control the aircraft. For example, the rotor of each EPU is an actuator, and the degree of freedom is the rotational speed of the blades. One or more EPUs may include other actuators, such as a rotor tilt system to provide thrust vectoring, and / or a propeller blade pitch system to adjust the pitch of the propeller blades. Thus, for example, the aircraft 100 of FIGS. 1A and 1B may include up to three actuators (rotor speed, blade pitch, and rotor tilt) per propeller rotor 114 and up to two actuators (rotor speed, blade pitch) per rotor 112, providing up to 30 actuators for the EPUs in the illustrated EPU configuration (24 actuators in an embodiment in which the rotor blade pitch is not adjustable). Other actuators may include wing control surface actuators, such as control surface 150 of FIG. 1A, and / or the tail of the aircraft, such as control surface 152 of FIGS. 1A and 1B. In some embodiments, there are ten control surface actuators, making the total number of actuators available for control allocation by method 300 thirty-four.

[0058] In step 304, control commands for at least some of the aircraft's actuators are determined by solving an optimization problem that includes minimizing a cost function that satisfies the force and moment commands from step 302 while also seeking to achieve one or more sub-objectives, which may include reducing acoustics generated by the aircraft's EPU and / or balancing energy usage of multiple battery packs that power the electric propulsion unit. The control commands include control commands for actuators of the aircraft's EPU, which may include, for example, rotor speed, propeller blade pitch, and / or rotor tilt (e.g., for a propeller rotor).

[0059] According to some embodiments, one or more secondary objectives include adjusting noise generated by the electric propulsion units of the aircraft, as illustrated by optional block 306 of FIG. 3. According to various embodiments, noise reduction may be achieved by reducing the tip speed of the propellers of one or more EPUs. According to some embodiments, the tip speed of the propellers of the EPUs may be reduced while providing the required thrust by adjusting the propeller pitch. In some embodiments, noise reduction may be achieved by distributing the load across the EPUs to reduce load peaks in any one EPU.

[0060] In some embodiments, noise reduction may be achieved by operating the EPUs at different speeds such that the acoustic frequencies generated by the EPUs are spread across a wider frequency band, which may be perceived by the human ear as less noisy. In some embodiments, the EPUs closer to the fuselage operate at a lower speed than the EPUs further from the fuselage to reduce the amount of noise generated closer to the fuselage and its passengers. In some embodiments, the frequency spread is mirrored across the centerline of the aircraft, such that EPUs in the same location on either side of the aircraft are operated at the same speed to maintain thrust balance, such as during straight flight. For example, the two innermost prop rotors 114 on either side of the example aircraft 100 of FIG. 1A may operate at the slowest speed of all prop rotors, while the two outermost prop rotors 114 on either side of the aircraft 100 may operate at the highest speed of all prop rotors while maintaining balanced thrust about the yaw axis.

[0061] In some embodiments, at least some of the EPUs are tiltable, and the acoustics of rotor noise can be tuned by utilizing thrust vectoring to minimize the time of edgewise flight. The cost function in step 304 can assign a relatively high cost to operating one or more tiltable EPUs in their pure vertical thrust positions, when the force and moment commands allow it, such that minimization of the cost function tends to move the tiltable EPUs away from their pure vertical thrust positions more quickly than strictly necessary to satisfy the force and moment commands. According to some embodiments, thrust vectoring used to reduce acoustic noise can be countered by attitude adjustments via actuation of control surfaces.

[0062] According to some embodiments, one or more secondary objectives include balancing the energy consumption of the electric propulsion units based on the energy state of the aircraft's multiple battery packs, as indicated by optional block 308 of method 300. In some embodiments, the aircraft includes multiple battery packs that independently power different EPUs and may be electrically isolated from one another. The energy state of the battery packs may be monitored and the EPUs may be controlled, via control allocation in step 304, such that the EPUs powered by the lower energy battery packs are used less than the EPUs powered by the higher energy battery packs. For example, with respect to the embodiment shown in FIG. 2A and FIG. 2B, battery pack 1 may have relatively less charge than battery pack 2 at some point during flight, and in order to balance the energy of the battery packs, according to various embodiments, one or more of the EPUs powered by battery pack 1 may be operated in a relatively lower power state, and one or more EPUs connected to battery pack 2 may be operated in a relatively higher power state to compensate for at least a portion of the lost thrust from the one or more EPUs connected to battery pack 1.

[0063] In some embodiments, a relatively low charge can refer to an overall low charge, such as when battery packs have the same energy capacity but one has less remaining charge than the other. In some embodiments, the charge can be relatively low compared to the capacity of each battery pack. For example, battery pack 2 in Figures 2A and 2B may have a lower capacity than battery pack 1, but a relatively higher charge than battery pack 1 (e.g., 90% for battery pack 2 and 80% for battery pack 1).

[0064] In some embodiments, one or more EPUs connected to a lower energy battery pack operate at a lower power than one or more EPUs connected to a higher energy battery pack. For example, referring to FIG. 2A and FIG. 2B, at least one EPU connected to battery pack 1 and at least one EPU connected to battery pack 2 may have the same power rating, and the EPU connected to battery pack 1 may operate at a lower power than the EPU connected to battery pack 2. In some embodiments, the one or more EPUs connected to the lower energy battery pack are operated at a lower power relative to a nominal power for a given aircraft operating condition, which may or may not be a lower power than one or more EPUs connected to a higher energy battery pack that are operated at a higher power relative to a nominal power for a given aircraft operating condition. For example, the EPUs connected to the lower energy battery pack may have a higher power rating than the EPUs connected to the higher energy battery pack, and the EPUs connected to the lower energy battery pack may operate at a relatively low power that is even higher than the relatively high power of the EPUs connected to the higher energy battery pack.

[0065] In step 310, at least a portion of the aircraft's actuators are operated according to the control commands determined in step 304 to satisfy desired force and moment commands for the electric aircraft. For example, various actuators associated with multiple electric propulsion units are operated according to the determined control commands. Depending on the sub-objectives sought in the optimization of step 304, which may include adjusting EPU acoustic noise, battery pack energy balance, or both, step 310 may achieve not only the desired forces and moments for the aircraft, but also a relatively low degree of aircraft acoustic noise and / or battery pack energy balance.

[0066] FIG. 4 is a functional block diagram of a control system 400 for controlling actuators of an electric VTOL aircraft, such as aircraft 100, according to various embodiments. The system 400 includes a control allocation module 402 that generates actuator commands 404 based on various inputs 406. As described further below, the control allocation module 402 determines the actuator commands 404 by minimizing an objective function that includes one or more primary objectives, such as meeting commanded aircraft forces and moments, and one or more secondary objectives, which may include minimizing acoustic noise and / or minimizing battery pack usage. The control system 400 may be implemented by a microprocessor-based controller that executes software code stored on a storage medium to perform the functions described herein. The control system 400 may also be implemented in hardware or a combination of hardware and software. The control system 400 may be implemented as part of a flight control system of the aircraft. It should be understood that many of the conventional functions of a control system are not shown in FIG. 4 for ease of explanation.

[0067] Inputs 406 to the control allocation module 402 may include one or more of force and moment commands 408, actuator states 410, safe operating envelope protection limits 412, scheduling parameters 414, aerodynamic parameters 416, battery states 418, and optimizer parameters 420. The force and moment commands 408 include up to six force and moment commands, which may include x, y, and z force commands, x, y, and z moment commands. As known in the art, the force and moment commands may be derived from operator commands (or autopilot commands, or commands from an autonomous controller for non-piloted aircraft) and aircraft states (e.g., speed, acceleration, altitude, attitude). The force and moment commands 408 are generated by an upstream controller (not shown) and provided to the control allocation module 402.

[0068] Actuator status 410 may include actuator hardware limits such as travel limits, speed limits, response time limits, and may include actuator health indicators that may indicate degradation in actuator performance that may limit a given actuator's ability to satisfy actuator commands. Actuator status 410 may be used to determine boundaries (e.g., min / max) for individual actuator commands. Battery status 418 is the remaining energy in the aircraft's battery packs and may be monitored when control allocations include balancing the energy state of the battery packs according to various embodiments.

[0069] The safe operating envelope protection limits 412 may include command limits that prevent operation outside the flight safe operating envelope, which defines the operating limits of the aircraft, including speed and acceleration based limits, as known in the art.

[0070] The scheduling parameters 414 are speed-related parameters used to define the allocation problem. The aerodynamic parameters 416 are parameters derived from aerodynamic and acoustic modeling and can be based on actuator Jacobian matrices and actuator states. The aerodynamic parameters 416 may be a function of the scheduling parameters 414. The optimizer parameters 420 are parameters used to define the optimization problem, as described further below. The optimizer parameters 420 can include axis weights that define the relative prioritization of force and moment axes. The optimizer parameters 420 can also include individual actuator weights that define the relative importance of different actuators in the control allocation problem. In some embodiments, the optimizer parameters 420 are a function of the scheduling parameters 414.

[0071] The control allocation module 402 may include a limit calculation module 430, a parameter interpolation module 432, and an optimization module 434. The limit calculation module 430 calculates limits for individual actuator commands based on the actuator states 410 and the safe operating envelope protection limits 412. In normal operation, the minimum command limit for a given actuator includes the maximum of the minimum hardware-based limit and the minimum flight safe operating envelope limit, and the maximum command limit for a given actuator includes the minimum of the maximum hardware-based limit and the maximum flight safe operating envelope limit. In the event of an actuator failure, the command limit for the failed actuator corresponds to the failure mode (e.g., a non-responsive control surface actuator position or a failed rotor at 0 RPM).

[0072] The parameter interpolation module 432 may be configured to determine parameters that vary with the scheduling parameters based on the speed of the aircraft, as described above. The value of a given parameter (e.g., an aerodynamic parameter or an optimizer parameter) may be determined from a lookup table for the parameter based on the scheduling parameters associated with the current speed of the aircraft, as follows: x out =F(x table ,v) Where: x out : Output of x under condition v x table Lookup data for :x v: Scheduling parameters

[0073] In some embodiments, the parameter interpolation module 432 can determine one or more parameters associated with one or more secondary objectives, such as battery pack energy balancing. For example, the parameters used for battery pack energy balancing can be determined from a lookup table of parameters based on the battery state 418 and the scheduling parameters, as follows: x out =F(x table ,v,E batt ) Where: x out : Output of x under condition v x table Lookup data for :x v: Scheduling parameters E batt : remaining battery energy

[0074] The optimization module 434 executes a nonlinear optimization algorithm that minimizes the sum of a primary objective 440 and a secondary objective 442. The primary objective 440 seeks to satisfy the force and moment commands 408 and may prioritize axis commands in case of saturation. The secondary objective 442 seeks to satisfy other operational goals when the force and moment solution space includes a combination of multiple actuator commands. The secondary objective 442 may include terms for adjusting rotor acoustics and / or balancing energy usage, as described further below. Other operational goals that may be included in the secondary objective 442 may include prioritizing certain actuators and minimizing deviations from one or more preferred actuator states.

[0075] The optimization module 434 minimizes an objective function that includes a primary objective 440 and a secondary objective 442. The following is an example of an objective function:

number

[0076] In various embodiments, the optimization module 434 finds a set of actuator commands u that minimizes the objective function of Equation 1. min≦u≦max

[0077] In Equation 1, the first function JPEG0007675262000002.jpg1874 corresponds to the primary objective 440. W includes weights for prioritizing certain force and moment axes and is determined by the interpolation module 432 based on the optimizer parameters 420. B is the actuator Jacobian matrix determined by the interpolation module 432 based on the aerodynamic parameters. FM req are the force and moment commands.

[0078] The second function in Eq. JPEG0007675262000003.jpg1882 corresponds to secondary objective 442 and contains the null space of the Jacobian matrix B. ε contains weights for the relative prioritization of the actuators and is determined by the interpolation module 432 based on optimizer parameters 420. u0 contains the preferred operating state of the actuators and is determined by the interpolation module 432 based on the aerodynamic parameters 416.

[0079] The secondary objective function in Equation 1 is the l2 norm, which minimizes the deviation of the actuator from the desired operating state. We also use the l1 norm to minimize the control effort and the l2 norm to minimize the maximum command. ∞ Other minimization functions can be used, such as the norm.

[0080] According to various embodiments, energy balancing for multiple electric propulsion units powered by electrically isolated battery packs is included as a secondary objective based on adjusting at least one of the weights ε and the preferred operating states u0 of the actuators based on the battery state 418. For example, the weights ε of actuators associated with lower energy battery packs may have a higher value (higher penalty for deviating from the preferred state) than the weights of actuators associated with higher energy battery packs. Additionally or alternatively, the preferred operating states u0 of actuators associated with lower energy battery packs may have a lower value than the preferred operating states u0 of actuators associated with lower energy battery packs.

[0081] According to various embodiments, tuning of the acoustics of the aircraft's electric propulsion units is included as a secondary objective by applying preferred operating conditions u0 that minimize the acoustics received in the cabin. For example, at any given aircraft speed, the preferred operating speeds of the rotors and / or propellers are spread over a range of frequencies, following the method outlined in

[0039] , to reduce the noise perceived by the passengers.

[0082] The optimization module 434 calculates the actuator command limits u determined by the limit calculation module 430. min Tou max Subject to the requirement that u be between and, we find a set of actuator commands u that minimizes the objective function in Eq.

[0083] According to various embodiments, the objective function can be solved by formulating the objective function as a quadratic problem and using a quadratic program solver to solve the quadratic problem. Examples of suitable quadratic program solvers include interior point, active set, conjugate gradient, and augmented Lagrangian solvers.

[0084] FIG. 5 is a functional block diagram of a system 500 for control allocation including multi-stage optimization with frequency division according to various embodiments. The control allocation of system 500 includes a first control allocation step performed based on low frequency force and moment commands and a second control allocation step performed based on high frequency force and moment commands. System 500 can ensure that high frequency commands are not generated for slow actuators that cannot respond to high frequency commands. Similar to system 400 of FIG. 4, system 500 can provide control allocation that seeks to achieve one or more secondary objectives, such as reduced noise and / or battery pack energy balance, at a lower computational cost compared to single step optimization.

[0085] In the system 500, a number of inputs 502 are provided to a force and comment command filter 508. The number of inputs 502 include force and moment commands 504 and may include optimizer parameters 506. The filter 508 filters low frequency force and moment commands 510 from the unfiltered force and moment commands 504. The filter 508 may filter the low frequency force and moment commands based on a filter cutoff frequency and a gain, which may be predefined parameters that may be based on scheduling parameters. Actuator dynamics and / or power consumption may be used to determine the filter behavior. For example, actuator response time may be used to determine an appropriate filter cutoff frequency such that relatively low frequency actuator commands are generated for relatively slow actuators, i.e., actuators having a relatively long response time. According to various embodiments, the group of low speed actuators may include actuators for controlling tilt of an electric propulsion unit and actuators for controlling blade pitch, while the group of high speed actuators may include electric propulsion unit motors for controlling blade speed and one or more control surface actuators. According to various embodiments, the actuator states, safe operating envelope protection limits, and / or scheduling parameters may be provided directly to the slow actuation allocation module 512 to determine limits for the slow actuator commands 514. According to various embodiments, the actuator states, safe operating envelope protection limits, and / or scheduling parameters may be provided directly to the fast actuation allocation module 518 to determine limits for the fast actuator commands 524. Other inputs, such as interpolated aerodynamic parameters and / or battery states, may also be provided directly to modules 512 and 518 to shape the objective functions solved in the respective modules.

[0086] The low frequency force and moment commands 510 are provided to a slow actuation allocation module 512, which may be configured similarly to the optimization module 434 of Figure 4, which determines a set of actuator commands by minimizing an objective function, as described above with respect to the control allocation module 402. A set of slow actuator commands 514 is output from the slow actuation allocation module 512 for controlling the slow actuators.

[0087] The slow actuation allocation module 512 may also output a set of fast actuator commands 516, which may be provided to a fast actuation allocation module 518. The fast actuation allocation module 518 also provides high frequency force and moment commands 520. The high frequency force and moment commands 520 may be provided to the fast actuation allocation module 518 by subtracting from the force and moment commands 504 the forces and moments 522 that the slow actuation allocation module 512 determines to be achieved from the slow actuation commands 514 and the fast actuation commands 516 determined by the slow actuation allocation module 512.

[0088] The fast actuation allocation module 518 determines a set of actuator commands by minimizing an objective function, similar to the slow actuation allocation module 512, as described above with respect to the control allocation module 402. The fast actuation allocation module 518 outputs only fast actuator commands 524 for controlling the fast actuators. Thus, the slow actuators are controlled based on the slow actuator commands 514 from the slow actuation allocation module 512, and the fast actuators are controlled based on the fast actuator commands 524 from the fast actuation allocation module 518.

[0089] According to various embodiments, when the force and moment commands 504 are at a higher frequency than the slow actuators alone can handle, the slow actuation allocation module 512 shall output slow actuator commands 514 that approach but do not exceed the hardware limits of the slow actuators. The unfulfilled portions of the force and moment commands 504 may then be subsequently fulfilled by the fast actuators via the fast actuation allocation module 518. Although the multi-stage optimization with frequency division of the system 500 may be more computationally intensive than a single-step optimization control allocation, it allows for the simultaneous utilization of both slow and fast actuators.

[0090] 6 illustrates an example computing system 600 according to some embodiments that may be used for one or more of the components of system 400 of FIG. 1 and / or system 500 of FIG. 5, such as control allocation module 402 of system 400, slow actuation allocation module 512 of system 500, and / or fast actuation allocation module 518 of system 500. System 600 may be any suitable type of processor-based system. System 600 may include, for example, one or more of an input device 620, an output device 630, one or more processors 610, a storage device 640, and a communication device 660.

[0091] The input devices 620 may be any suitable devices that allow for user input, such as user input from a pilot, such as one or more buttons, levers and / or switches, one or more touch screens, etc. The output devices 630 may be or include any suitable devices that provide output, such as a display, a touch screen, a haptic device, a virtual / augmented reality display or a speaker.

[0092] The storage device 640 may be any suitable device that provides storage, such as an electrical, magnetic or optical memory, including RAM, cache memory, a hard drive, a removable storage disk or other non-transitory computer-readable medium. The communication device 660 may include any suitable device or combination of devices capable of sending and receiving signals from one or more other computing systems or modules. The components of the computing system 600 may be connected in any suitable manner, such as via a physical bus or wirelessly.

[0093] The processor 610 may be any suitable processor or combination of processors, including a central processing unit (CPU), a graphics processing unit (GPU), a field programmable gate array (FPGA), and / or an application specific integrated circuit (ASIC). The software 650 that may be stored in the memory 640 and executed by the one or more processors 610 may include, for example, programming that embodies functionality or portions of functionality of the present disclosure (e.g., as embodied in a device such as those described above). For example, the software 650 may include one or more programs for execution by the one or more processors 610 to perform one or more steps of the methods described herein, such as one or more steps of the method 300 of FIG. 3.

[0094] The software 650 may also be stored and / or transferred in any non-transitory computer-readable storage medium for use by or in connection with an instruction execution system, apparatus, or device, such as those described above, that can fetch and execute instructions associated with the software from the instruction execution system, apparatus, or device. In the context of the present disclosure, a computer-readable storage medium may be any medium, such as storage device 640, that contains or can store a program for use by or in connection with an instruction execution system, apparatus, or device.

[0095] The software 650 may also be propagated in any transfer medium for use by or in connection with an instruction execution system, apparatus or device, such as those described above, that can fetch instructions associated with the software from the instruction execution system, apparatus or device and execute the instructions. In the context of this disclosure, a transfer medium may be any medium that can communicate, propagate or transfer a program for use by or in connection with an instruction execution system, apparatus or device. Transfer computer readable media may include, but are not limited to, electronic, magnetic, optical, electromagnetic or infrared wired or wireless propagation media. The system 600 may implement any suitable operating system and may be written in any suitable programming language.

[0096] The foregoing description has been described with reference to specific embodiments for purposes of illustration. However, the above exemplary discussion is not intended to be exhaustive or to limit the invention to the precise forms disclosed. Many modifications and variations are possible in light of the above teachings. The embodiments have been chosen and described in order to best explain the principles of the technology and their practical applications, thereby enabling those skilled in the art to best utilize the technology and various embodiments with various modifications as suited to the particular use contemplated.

[0097] Although the present disclosure and examples have been fully described with reference to the accompanying drawings, it should be noted that various changes and improvements will become apparent to those skilled in the art. Such changes and improvements should be understood to be included within the scope of the present disclosure and examples as defined by the claims. Finally, the entire disclosures of the patents and publications mentioned in this application are incorporated herein by reference.

Claims

1. 1. A method of controlling an electric aircraft having a plurality of actuators including a plurality of electric propulsion units and a plurality of battery packs powering the plurality of electric propulsion units, the method comprising: receiving desired force and moment commands for the electric aircraft; monitoring an energy state of the plurality of battery packs, wherein at least a first battery pack of the plurality of battery packs is electrically isolated from at least a second battery pack of the plurality of battery packs; determining a set of control commands for the plurality of actuators based on the desired force and moment commands by solving an optimization problem to determine the set of control commands, wherein solving the optimization problem comprises: or minimizing an objective function including energy balance terms for balancing energy draw of the electric propulsion unit from the plurality of battery packs according to the monitored energy states of the plurality of battery packs, the energy balance terms representing a set of penalties on energy usage balance that increase with increasing deviation from a set of preferred operating conditions of the plurality of electric propulsion units; or maximizing an objective function including energy balance terms for balancing energy draw of the electric propulsion unit from the plurality of battery packs according to the monitored energy states of the plurality of battery packs, the energy balance terms representing a set of penalties on balancing energy usage that decrease with increasing deviation from a set of preferred operating conditions of the plurality of electric propulsion units; controlling the plurality of actuators according to the determined control commands to satisfy the desired force and moment commands for the electric aircraft; Including, the objective function includes a main term that determines a set of control commands that satisfies the desired force and moment commands; The method, wherein the main term includes weightings that define the relative priority of execution of force and moment commands in different axes.

2. 2. The method of claim 1, wherein the first battery pack has a lower remaining energy than the second battery pack, and a first electric propulsion unit powered by the first battery pack operates at a lower power than a second electric propulsion unit powered by the second battery pack.

3. The method of claim 2 , wherein the first battery pack and the second battery pack have the same energy capacity.

4. The method of claim 3 , wherein the first electric propulsion unit and the second electric propulsion unit have the same power rating.

5. 2. The method of claim 1, wherein the preferred operating conditions for an electric propulsion unit powered by a battery pack having a lower remaining energy are lower than the preferred operating conditions for an electric propulsion unit powered by a battery pack having a higher remaining energy.

6. 10. The method of claim 1, wherein a penalty for an electric propulsion unit connected to a lower energy battery pack is higher than a penalty for an electric propulsion unit connected to a higher energy battery pack.

7. The method of claim 1 , wherein the optimization problem includes a noise minimization term for minimizing noise generated by the electric propulsion unit.

8. 8. The method of claim 1, wherein the electric aircraft is a vertical take-off and landing aircraft.

9. 8. The method of claim 1, wherein the electric aircraft is manned.

10. 8. The method of claim 1, wherein one or more of the electric propulsion units are configured to provide vertical lift.

11. 8. The method of claim 1, wherein at least one of the electric propulsion units is configured to tilt from a lift configuration to provide vertical lift to a propulsion configuration to provide forward thrust.

12. 8. The method of claim 1, wherein the electric aircraft comprises a plurality of electric propulsion units on either side of a fuselage of the electric aircraft.

13. 1. A system for controlling an electric aircraft having a plurality of actuators including a plurality of electric propulsion units, the system comprising: one or more processors; Memory, One or more programs stored in the memory, the one or more processors being configured to: receiving desired force and moment commands for the electric aircraft; monitoring an energy state of a plurality of battery packs, at least a first battery pack of the plurality of battery packs being electrically isolated from at least a second battery pack of the plurality of battery packs; determining a set of control commands for the plurality of actuators based on the desired force and moment commands by solving an optimization problem to determine the set of control commands, wherein solving the optimization problem comprises: or minimizing an objective function including energy balance terms for balancing energy draw of the electric propulsion unit from the plurality of battery packs according to the monitored energy states of the plurality of battery packs, the energy balance terms representing a set of penalties on energy usage balance that increase with increasing deviation from a set of preferred operating conditions of the plurality of electric propulsion units; or maximizing an objective function including energy balance terms for balancing energy draw of the electric propulsion unit from the plurality of battery packs according to the monitored energy states of the plurality of battery packs, the energy balance terms representing a set of penalties on balancing energy usage that decrease with increasing deviation from a set of preferred operating conditions of the plurality of electric propulsion units; controlling the plurality of actuators according to the determined control commands to satisfy the desired force and moment commands for the electric aircraft; and a program for executing the the objective function includes a main term that determines a set of control commands that satisfies the desired force and moment commands; The main term includes weightings that define the relative priority of execution of force and moment commands in different axes.

14. 14. The system of claim 13, wherein the first battery pack has a lower remaining energy than the second battery pack, and a first electric propulsion unit powered by the first battery pack operates at a lower power than a second electric propulsion unit powered by the second battery pack.

15. 15. The system of claim 14, wherein the first battery pack and the second battery pack have the same energy capacity.

16. The system of claim 15 , wherein the first electric propulsion unit and the second electric propulsion unit have the same power rating.

17. 14. The system of claim 13, wherein the preferred operating conditions for an electric propulsion unit powered by a battery pack having a lower remaining energy are lower than the preferred operating conditions for an electric propulsion unit powered by a battery pack having a higher remaining energy.

18. 14. The system of claim 13, wherein the penalty for an electric propulsion unit connected to a lower energy battery pack is higher than the penalty for an electric propulsion unit connected to a higher energy battery pack.

19. 14. The system of claim 13, wherein the optimization problem includes a noise minimization term for minimizing noise generated by the electric propulsion unit.

20. 20. The system of claim 13, wherein the electric aircraft is a vertical take-off and landing aircraft.

21. 20. The system of claim 13, wherein the electric aircraft is manned.

22. 20. The system of any one of claims 13 to 19, wherein one or more of the electric propulsion units are configured to provide vertical lift.

23. 20. The system of claim 13, wherein at least one of the electric propulsion units is configured to tilt from a lift configuration to provide vertical lift to a propulsion configuration to provide forward thrust.

24. 20. The system of claim 13, wherein the electric aircraft comprises a plurality of electric propulsion units on either side of a fuselage of the electric aircraft.

25. 1. An electric aircraft, comprising: A plurality of actuators including a plurality of electric propulsion units; 20. A system according to any one of claims 13 to 19 for controlling the electric aircraft via the plurality of actuators; An electric aircraft comprising:

26. 26. The electric aircraft of claim 25, wherein the electric aircraft is a vertical take-off and landing aircraft or is manned.

27. 26. The electric aircraft of claim 25, wherein one or more of the electric propulsion units are configured to provide vertical lift.

28. 26. The electric aircraft of claim 25, wherein at least one of the electric propulsion units is configured to tilt from a lift configuration for providing vertical lift to a propulsion configuration for providing forward thrust.

29. 26. The electric aircraft of claim 25, wherein the electric aircraft comprises a plurality of electric propulsion units on either side of a fuselage of the electric aircraft.

Images