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F. Oliviero
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Path performance optimization has proven to be a powerful tool in solving a wide variety of optimal control problems in the aerospace field. However, the numerical complexity of such methodologies often prevents the possibility to optimize the performance of high-fidelity flight mechanics models characterized by coupled, non-linear, and/or high-order dynamic and aero-propulsive models. This research has explored the impact of reduced-order modeling on the optimal path performance obtainable with surrogates of the high-fidelity flight mechanics model. The developed methodology revolves around the creation of different reduced-order models that retain the characteristics of a full-order flight mechanics model to different degrees of fidelity, while being manageable by an optimal control solver. The methodology has been applied to obtain minimum-time landing trajectories for the UNIFIER19 C7A, a hybrid-electric aircraft featuring over-the-wing distributed propulsion, previously developed under the UNIFIER19 project. Results show that the reduced-order models can be used to generate flyable trajectories, as verified by tracking the resulting landing approach paths using the base high-fidelity model. On the other hand, the value of the objective function differs widely depending on the reduced-order model used, indicating that the modeling choice has a significant impact on the optimal performance prediction.
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Path performance optimization has proven to be a powerful tool in solving a wide variety of optimal control problems in the aerospace field. However, the numerical complexity of such methodologies often prevents the possibility to optimize the performance of high-fidelity flight mechanics models characterized by coupled, non-linear, and/or high-order dynamic and aero-propulsive models. This research has explored the impact of reduced-order modeling on the optimal path performance obtainable with surrogates of the high-fidelity flight mechanics model. The developed methodology revolves around the creation of different reduced-order models that retain the characteristics of a full-order flight mechanics model to different degrees of fidelity, while being manageable by an optimal control solver. The methodology has been applied to obtain minimum-time landing trajectories for the UNIFIER19 C7A, a hybrid-electric aircraft featuring over-the-wing distributed propulsion, previously developed under the UNIFIER19 project. Results show that the reduced-order models can be used to generate flyable trajectories, as verified by tracking the resulting landing approach paths using the base high-fidelity model. On the other hand, the value of the objective function differs widely depending on the reduced-order model used, indicating that the modeling choice has a significant impact on the optimal performance prediction.
The present paper shows the main characteristic of a numerical
simulation tool, developed in the framework of the European H2020
project MAHEPA, to estimate optimal flight performance of a generic
aircraft featuring a Hybrid powertrain. The purpose of the study is to
determine optimal flight trajectories together with optimal power
controls when a powertrain with multi-energy or multi-power sources (as
the case of a generic hybrid one) is considered. For this purpose a
complete new software has been developed, which is composed by three
main parts: a mission performance “analyser” where the system dynamics
of the problem is determined and it solves the aircraft Equation of
Motion; a powertrain simulator that determines the operating conditions
of the powertrain components and it ultimately computes the consumption
of each energy source; a numerical algorithm that optimizes the aircraft
control variables to determine both the optimum flight trajectory and
the power management according to a certain objective functions and a
variety of constraints. Different study cases are discussed when two
existing flying hybrid aircraft are considered: a Hybrid-Electric (HE)
Pipistrel Panthera aircraft and a Fuel-Cell hybrid (FCH) Pipistrel HY4.
Results are presented also depending on the capability to simulate the
entire mission as a whole (Single-Phase approach) as well as through the
distinction of different flight segments as in the case of the
Multi-Phase approach. In addition, two different resolution algorithms
are tested in order to evaluate what are the aspects that might dictate
the selection of the most suitable one.
...
The present paper shows the main characteristic of a numerical
simulation tool, developed in the framework of the European H2020
project MAHEPA, to estimate optimal flight performance of a generic
aircraft featuring a Hybrid powertrain. The purpose of the study is to
determine optimal flight trajectories together with optimal power
controls when a powertrain with multi-energy or multi-power sources (as
the case of a generic hybrid one) is considered. For this purpose a
complete new software has been developed, which is composed by three
main parts: a mission performance “analyser” where the system dynamics
of the problem is determined and it solves the aircraft Equation of
Motion; a powertrain simulator that determines the operating conditions
of the powertrain components and it ultimately computes the consumption
of each energy source; a numerical algorithm that optimizes the aircraft
control variables to determine both the optimum flight trajectory and
the power management according to a certain objective functions and a
variety of constraints. Different study cases are discussed when two
existing flying hybrid aircraft are considered: a Hybrid-Electric (HE)
Pipistrel Panthera aircraft and a Fuel-Cell hybrid (FCH) Pipistrel HY4.
Results are presented also depending on the capability to simulate the
entire mission as a whole (Single-Phase approach) as well as through the
distinction of different flight segments as in the case of the
Multi-Phase approach. In addition, two different resolution algorithms
are tested in order to evaluate what are the aspects that might dictate
the selection of the most suitable one.
With the current advances in aircraft design and Lithium-Ion batteries, electric aircraft are expected to serve as a replacement for conventional, short-range aircraft. This paper addresses the main operational challenges for short-range flights operated with electric aircraft: determining the investment needs for a fleet of electric aircraft, and the logistics of charging stations and swap batteries required to support these flights. A mixed-integer linear program with two phases is proposed. In the first phase, a schedule for flight and battery recharge is developed for a fleet of electric aircraft. In the second phase, optimal times for battery charging are determined, together with an optimal sizing of the number of charging stations and swap batteries. We illustrate our model for short-range flights to and from an European airport and for an electric aircraft designed based on the operational characteristics of a conventional, narrow-body aircraft.
...
With the current advances in aircraft design and Lithium-Ion batteries, electric aircraft are expected to serve as a replacement for conventional, short-range aircraft. This paper addresses the main operational challenges for short-range flights operated with electric aircraft: determining the investment needs for a fleet of electric aircraft, and the logistics of charging stations and swap batteries required to support these flights. A mixed-integer linear program with two phases is proposed. In the first phase, a schedule for flight and battery recharge is developed for a fleet of electric aircraft. In the second phase, optimal times for battery charging are determined, together with an optimal sizing of the number of charging stations and swap batteries. We illustrate our model for short-range flights to and from an European airport and for an electric aircraft designed based on the operational characteristics of a conventional, narrow-body aircraft.
The paper focusses on a methodology developed to determine both mission parameters and power management for a generic Hybrid aircraft in such a way its energy consumption and/or flight time can be minimised. In fact the system dynamics of a Hybrid aircraft has generally one or more degree of freedom, when compared to a conventional one, related to the number of energy (or power) sources present on board with the consequences that classic solutions of mission analysis (e.g. climb rate that minimise the burn fuel) can be no longer valid. The approach adopted in this study is to couple mission perfomance analysis to optimal control methods so that the core mathematical problem is reduced to an optimiziation problem that aims at finding optimal values for certain control variables in such a way an arbitrary objective function can be minimized in presence of a certain set of constraints deriving from limitations of both flight envelope and propulsion operating conditions. To fully characterize the problem, the optimal contol algorithms are coupled to a simulator developed in house to model the operating characterisitic of a generic Hybrid powertrain. The simulator, based on Objected Oriented Paradigm, consists of modules that are used to describe the operation conditions (in terms of efficiency map and delivered Power/Energy) of each powertrain component. Subsequently, those modules can be assembled together to model either a Serial or a Parallel architecture, with several possible power sources: batteries, Combustion Engine, Fuel Cell. Two optimal control approaches (Single Phase and Multi-Phase) have been tested on a Hybrid Electric study case considering different objective functions, namely minimum energy, minimum fuel (when a Combustion Engine is considered) and minimum time. Prelimiary results show an agreement of both the Single-Phase and Multi-Phase approaches. In addition, both the power management and the mission profile differ greatly at varying the considered objective function.
...
The paper focusses on a methodology developed to determine both mission parameters and power management for a generic Hybrid aircraft in such a way its energy consumption and/or flight time can be minimised. In fact the system dynamics of a Hybrid aircraft has generally one or more degree of freedom, when compared to a conventional one, related to the number of energy (or power) sources present on board with the consequences that classic solutions of mission analysis (e.g. climb rate that minimise the burn fuel) can be no longer valid. The approach adopted in this study is to couple mission perfomance analysis to optimal control methods so that the core mathematical problem is reduced to an optimiziation problem that aims at finding optimal values for certain control variables in such a way an arbitrary objective function can be minimized in presence of a certain set of constraints deriving from limitations of both flight envelope and propulsion operating conditions. To fully characterize the problem, the optimal contol algorithms are coupled to a simulator developed in house to model the operating characterisitic of a generic Hybrid powertrain. The simulator, based on Objected Oriented Paradigm, consists of modules that are used to describe the operation conditions (in terms of efficiency map and delivered Power/Energy) of each powertrain component. Subsequently, those modules can be assembled together to model either a Serial or a Parallel architecture, with several possible power sources: batteries, Combustion Engine, Fuel Cell. Two optimal control approaches (Single Phase and Multi-Phase) have been tested on a Hybrid Electric study case considering different objective functions, namely minimum energy, minimum fuel (when a Combustion Engine is considered) and minimum time. Prelimiary results show an agreement of both the Single-Phase and Multi-Phase approaches. In addition, both the power management and the mission profile differ greatly at varying the considered objective function.
The study presents a novel methodology for the conceptual design of a Hybrid Aircraft featuring Propulsive devices distributed along the wingspan of the wing. Distributed Propulsions is a solution that can theoretically augment high lift capabilities so that the resulting needed wing loading can be lowered; in addition, electric propulsion can potentially enable the introduction of such solutions with a relatively low penalty in terms of increased structural weight because of the relative lightness and compactness of electric motors. The proposed sizing procedure consists of several intermediate steps: first, the thrust, lift and drag decomposition are modified to take the effect of aerodynamic interaction into account, leading to a set of modified flight performance constraining equations. Subsequently, a hybrid powertrain model, containing information and operating characteristics extrapolated by the components used in the Mahepa project, allows to determine a series of component-power oriented power loading diagrams; in addition, the energy requirements can be calculated on the basis of a certain mission profile and energy/power management assumptions. Finally, class I weight estimation are used to determine the Maximum Take Off Weight of the aircraft through an iterative procedure. A second sizing procedure, that relies on the use of a lifting-line model where propellers are represented by actuator disks. Two study cases are considered: a CS25 regional aircraft and a CS23 commuter. Preliminary results suggest a slight reduction of the payload-range energy efficiency.
...
The study presents a novel methodology for the conceptual design of a Hybrid Aircraft featuring Propulsive devices distributed along the wingspan of the wing. Distributed Propulsions is a solution that can theoretically augment high lift capabilities so that the resulting needed wing loading can be lowered; in addition, electric propulsion can potentially enable the introduction of such solutions with a relatively low penalty in terms of increased structural weight because of the relative lightness and compactness of electric motors. The proposed sizing procedure consists of several intermediate steps: first, the thrust, lift and drag decomposition are modified to take the effect of aerodynamic interaction into account, leading to a set of modified flight performance constraining equations. Subsequently, a hybrid powertrain model, containing information and operating characteristics extrapolated by the components used in the Mahepa project, allows to determine a series of component-power oriented power loading diagrams; in addition, the energy requirements can be calculated on the basis of a certain mission profile and energy/power management assumptions. Finally, class I weight estimation are used to determine the Maximum Take Off Weight of the aircraft through an iterative procedure. A second sizing procedure, that relies on the use of a lifting-line model where propellers are represented by actuator disks. Two study cases are considered: a CS25 regional aircraft and a CS23 commuter. Preliminary results suggest a slight reduction of the payload-range energy efficiency.
A unified approach to aircraft mission performance assessment is presented in this work. It provides a detailed and flexible formulation to simulate a complete commercial aviation mission. Based on optimal control theory, with consistent injection of rules and procedures typical of aeronautical operations, it relies on generalized mathematical and flight mechanics models, thereby being applicable to aircraft with very distinct configurations. It is employed for an extensive evaluation of the performance of a conventional commercial aircraft, and of an unconventional box-wing aircraft, referred to as the PrandtlPlane. The PrandtlPlane features redundant control surfaces, and it is able to employ Direct Lift Control. To demonstrate the versatility of the performance evaluation approach, the mission-level benefits of using Direct Lift Control as an unconventional control technique are assessed. The PrandtlPlane is seen to be competitive in terms of its fuel consumption per passenger per kilometer. However, this beneficial fuel performance comes at the price of slower flight. The benefits of using Direct Lift are present but marginal, both in terms of fuel consumption and flight time. Nonetheless, enabling Direct Lift Control results in a broader range of viable trajectories, such that the aircraft no longer requires cruise-climb for maximum fuel economy.
...
A unified approach to aircraft mission performance assessment is presented in this work. It provides a detailed and flexible formulation to simulate a complete commercial aviation mission. Based on optimal control theory, with consistent injection of rules and procedures typical of aeronautical operations, it relies on generalized mathematical and flight mechanics models, thereby being applicable to aircraft with very distinct configurations. It is employed for an extensive evaluation of the performance of a conventional commercial aircraft, and of an unconventional box-wing aircraft, referred to as the PrandtlPlane. The PrandtlPlane features redundant control surfaces, and it is able to employ Direct Lift Control. To demonstrate the versatility of the performance evaluation approach, the mission-level benefits of using Direct Lift Control as an unconventional control technique are assessed. The PrandtlPlane is seen to be competitive in terms of its fuel consumption per passenger per kilometer. However, this beneficial fuel performance comes at the price of slower flight. The benefits of using Direct Lift are present but marginal, both in terms of fuel consumption and flight time. Nonetheless, enabling Direct Lift Control results in a broader range of viable trajectories, such that the aircraft no longer requires cruise-climb for maximum fuel economy.
HyPsim
A simulation tool for hybrid aircraft performance analysis
This work presents the performance prediction activities carried out by the research team of Pisa University within the Euopean project “HYPSTAIR”, concerning the development and validation of hybrid propulsion system components and sub-systems for electrical aircraft. The first part of the paper discusses the performance analysis of a serial hybrid general aviation airplane for a reference mission profile. In particular, the best flight performance is evaluated varying the relevant mission parameters (e.g. range, cruise altitude, and cruise speed) and the amount of available energy, in terms batteries and fuel. In the second part, a hybrid plane simulator, conceived to implement different mission profiles and to include pilot effects on power management by adopting a human-in-the-loop approach, is presented. Such simulator consists of three main software modules linked to each other in real time: a flight simulator, used to compute the aerodynamic forces and to visualize the airplane in flight, a flight planner, in which the mission profile can be defined, and a performance module, which calculates the instantaneous consumption of energy and provides the endurance prediction.
...
This work presents the performance prediction activities carried out by the research team of Pisa University within the Euopean project “HYPSTAIR”, concerning the development and validation of hybrid propulsion system components and sub-systems for electrical aircraft. The first part of the paper discusses the performance analysis of a serial hybrid general aviation airplane for a reference mission profile. In particular, the best flight performance is evaluated varying the relevant mission parameters (e.g. range, cruise altitude, and cruise speed) and the amount of available energy, in terms batteries and fuel. In the second part, a hybrid plane simulator, conceived to implement different mission profiles and to include pilot effects on power management by adopting a human-in-the-loop approach, is presented. Such simulator consists of three main software modules linked to each other in real time: a flight simulator, used to compute the aerodynamic forces and to visualize the airplane in flight, a flight planner, in which the mission profile can be defined, and a performance module, which calculates the instantaneous consumption of energy and provides the endurance prediction.