*Article* **In-flight Lift and Drag Estimation of an Unmanned Propeller-Driven Aircraft**

**Dominique Paul Bergmann 1,\*, Jan Denzel 1, Ole Pfeifle 2, Stefan Notter 2, Walter Fichter <sup>2</sup> and Andreas Strohmayer <sup>1</sup>**


**Abstract:** The high-power density and good scaling properties of electric motors enable new propulsion arrangements and aircraft configurations. This results in distributed propulsion systems allowing to make use of aerodynamic interaction effects between individual propellers and the wing of the aircraft, improving flight performance and thus reducing in-flight emissions. In order to systematically analyze these effects, an unmanned research platform was designed and built at the University of Stuttgart. As the aircraft is being used as a testbed for various flight performance studies in the field of distributed electric propulsion, a methodology for precise identification of its performance characteristics is required. One of the main challenges is the determination of the total drag of the aircraft to be able to identify an exact drag and lift polar in flight. For this purpose, an on-board measurement system was developed which allows for precise determination of the thrust of the aircraft which equals the total aerodynamic drag in steady, horizontal flight. The system has been tested and validated in flight using the unmanned free-flight test platform. The article provides an overview of the measuring system installed, discusses its functionality and shows results of the flight tests carried out.

**Keywords:** unmanned aircraft; thrust determination; flight testing; e-Genius-Mod; free-flight wind tunnel

#### **1. Introduction**

While investigating the flight performance of new aircraft configurations or technologies, knowledge about aerodynamic and flight mechanical parameters is required to understand their impact on the aircraft. From the perspective of aircraft design, one main focus is the impact on flight performance when investigating for example the effects of new propulsion technologies or aircraft configurations. To investigate and assess the flight performance, the determination of lift and drag is of major importance. Especially the determination of drag from flight tests with an unmanned propeller aircraft is a challenging task.

Flight tests with unmanned aircraft systems (UAS) have become increasingly important in recent years. Scaled platforms are not only used as payload carriers, but also for the analysis of novel aircraft configurations or for the assessment of unconventional propulsion systems.

The lower costs as well as the reduction of risks especially in the area of unconventional configurations militate in favor of using unmanned systems. Typical examples for demonstrators used to study flight dynamic effects are the AlbatrossONE [1] of Airbus and the platform of the project FLEXOP (flutter free flight envelope expansion for economical performance improvement) [2]. In the case of the AlbatrossONE, gust loads are minimized

**Citation:** Bergmann, D.P.; Denzel, J.; Pfeifle, O.; Notter, S.; Fichter, W.; Strohmayer, A. In-flight Lift and Drag Estimation of an Unmanned Propeller-Driven Aircraft. *Aerospace* **2021**, *8*, 43. https://doi.org/10.3390/ aerospace8020043

Academic Editor: Roberto Sabatini Received: 14 December 2020 Accepted: 1 February 2021 Published: 6 February 2021

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**Copyright:** © 2021 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/).

by structural interventions in the area of the wing tip, while aeroelastic effects on the wing are observed with the help of the carrier platform FLEXOP. To investigate the impact on flight performance of new technology on an aircraft configuration, a direct comparison between base line configuration and modified aircraft is of interest, as demonstrated by NASA with its Area-I Prototype Technology Evaluation and Research Aircraft (PTERA) [3]. In the research, the PTERA platform was modified to investigate for example combined circulation control [4] and a spanwise adaptive wing [5].

Unmanned aircraft are an important tool to investigate new aircraft configurations and novel aviation technologies at University of Stuttgart, [6]. New technologies or concepts can be flight-tested with little effort, low costs and manageable project risks after initial theoretical investigation. This way, research concepts can reach a much higher feasibility, of particular interest to industry, to close the gap between upstream research and industrial exploitation. This can build a bridge, demonstrating technologies at a higher technology readiness level (TRL). Innovative ideas can be demonstrated and validated in a relevant environment which corresponds to a TRL 5/6. However, there are limitations due to the degree of scaling of the technologies under consideration.

A disadvantage for the investigation of flight performance with scaled unmanned aircraft is the limited data available for the different aircraft system components. When investigating the flight performance, propeller characteristics and efficiency of the individual components of the propulsion system are of specific interest.

The Institute of Aircraft Design (IFB) at the University of Stuttgart has developed the "e-Genius-Mod" test platform based on this background. The platform is modelled on a scale of 33.3% of the electrically powered "e-Genius" aircraft [7], which is also designed, manufactured and operated by the institute. In this particular case, the UAS was realized as Froude-scaled version [6].

Due to the modular design of the testbed, different configurations can be easily realized, which allows an adaptation to different applications. Furthermore, the geometry of the fuselage offers ideal conditions for accommodating various payloads.

For the purpose of identifying the aircraft and measuring flight performance, it is essential to map the aerodynamic parameters of the system. The most important parameters are the aircraft drag and the lift polar. From the correlation of the coefficients for lift and drag of the aircraft, a direct statement about the performance and energy consumption can be derived. The gliding characteristics, the required power installed and the potential range are important parameters that are required to compare different propulsion concepts and identify their impact for a prospective aircraft design.

In order to obtain reliable drag and lift polar, manned test aircraft often would carry out comparative flights with calibrated systems. Especially in the field of gliding, where a precisely identified system is very important, such survey flights are still state of the art today.

In the unmanned area, such survey flights are difficult to carry out. For UAS, a method for a glider model is described by Edwards [8]. Due to the induced drag of the propeller system, this method is not useful for the proposed identification of propeller-driven UAS. A method to identify drag of a propeller aircraft was developed by Norris and Bauer [9]. Alternatively, if available, a model for the propeller wind-milling drag or thrust could be used to apply this method. For the e-Genius-Mod testbed, a different approach was taken. In order to record the performance data, a measurement system was developed that is capable of recording the thrust values required during the flight. Such systems have not yet been installed in large UAS, but have only been used sporadically on manned aircraft. For the aerodynamic characterization of smaller UAS, on-board thrust measurements have been performed in the past, such as presented by M. Bronz and G. Hattenberger [10]. However, for the identification of the flight performance and to show the feasibility of novel technologies in aviation the measurement of drag is essential.

Although the thrust values for the operation of a propeller-driven system can be measured without any problems when stationary, the thrust values during flight are not comparable due to the induced flow to the propeller without prior identification of the propeller via wind tunnel experiments. The efficiency of the drive also changes significantly under different flow conditions. Therefore, a direct, mechanical thrust measurement in flight is of significant advantage.

#### *1.1. Challenge of Current Research Using Unmanned Aircraft as Free-Flight Test Platform*

A current research topic at the University of Stuttgart is how to use unmanned propeller-driven aircraft as a test platform to determine their flight performance without knowing specific data of propeller and powertrain. This ability is for example required to compare different propulsion configurations like Wing Tip Propellers (WTP) to a basic configuration in flight. Based on the collected flight data, the estimated benefits of this technology in flight should be validated and demonstrated. For this purpose, the basic in-flight measurement system of the test platform is extended with a system to measure the thrust of the propeller in-flight.

For this, the assumption was made that in steady horizontal flight the thrust performed by the propeller corresponds to the aerodynamic drag acting on the aircraft.

#### *1.2. The Modular Test Platform e-Genius-Mod*

The free-flight platform e-Genius-Mod (Figure 1) is established as a technology test bed to demonstrate new technologies for future aircraft design in a relevant environment. The UAS test platform [6] is used for academic and innovative research projects to investigate scaling similarities of free flight models and to demonstrate new technologies up to TRL 6. The modular design of the test bed is ideally suited for the investigation of new aircraft configuration solutions for distributed electric propulsion systems. The size of the aircraft with a wingspan of 5.62 m, maximum take-off weight of 40 kg and a payload capacity of more than 10 kg [6] is suited to perform prospective investigations. The maximum possible flight time is up to 100 min, depending on the particular battery capacity and the payload weight. An overview of the technical data of the e-Genius-Mod is summarized in Table 1.

**Figure 1.** Free-flight test platform e-Genius-Mod.


**Table 1.** Technical data of the e-Genius-Mod [6].

\* flight test characteristic.

The test bed e-Genius-Mod is an extension of the full-scale aircraft for further investigation of electric flight and new aviation technologies. For this reason, the test platform is equipped as a free flight wind tunnel. In order to perform measurements in steady, horizontal flight, an autopilot is used to steer the aircraft along a predefined path of constant altitude and velocity, as described in [11]. The measurement system ensures the synchronous logging of all relevant variables (Table 2), as further detailed in Section 3.

**Table 2.** Basic measurement equipment of the free-flight wind-tunnel.


The basic free flight measurement equipment can be easily expanded by connecting additional sensors to the dedicated bus system used solely for measurement data.

Electric propulsion systems allow for new design alternatives in terms of propulsion integration and aircraft design. To investigate and demonstrate new concepts, a modular testbed like the unmanned scale model is a very useful and flexible tool. The demonstration of innovative concepts like distributed propulsion on a manned aircraft would be expensive and time intensive and not useful for research with open-ended findings at this early stage. With its modular airframe design, the e-Genius-Mod is the basis for an efficient and systematic research of the various effects of distributed propulsion.

Onboard thrust measurements on a UAS pose a particular challenge. On the one hand, it must be possible to carry out reliable, calibrated measurements, and on the other hand, the sensor systems are subject to narrow limits in terms of dimensions and weight. For this purpose, sensor systems specifically designed for the e-Genius Mod were developed, calibrated and tested in wind tunnel experiments before installation.

The thrust values are in many respects informative for the evaluation of the flight controller itself, as well as for the assessment of the efficiency of an engine. In general, they establish a direct relationship to aerodynamic quality and, in case the electrical power consumption is known, allow a direct statement about the overall efficiency of the

corresponding powertrain. Especially when considering several distributed engines, it is possible to make a reliable statement about the overall energy balance onboard the platform.

The aim of the thrust measurements is to prove the expected positive effects of the distributed engines in terms of quality, and, in further steps, to make statements about where on the aircraft they can be used most efficiently. Furthermore, previously performed simulations are to be validated with these measured values.

#### **2. Research Objective**

To assess and validate the impact of a novel configuration or technology in flight, knowledge of the flight performance is of vital importance. Required basic information in aircraft design are the aerodynamic coefficients for lift (*CL*) and drag (*CD*) of an aircraft with respect to the angle of attack (*AoA*). Therefore, the objective of this research is the identification of the *CL* − *CD*, *CL* − *AoA* and *CD* − *AoA* polars in-flight. For the investigation of these coefficients in-flight the following well-known approach is proposed as a starting point.

While the investigations are carried out under cruise conditions, it is assumed as a basis for the investigations that the measurements are carried out in a non-accelerated (steady) horizontal flight. This allows to establish the balance of forces in flight direction and perpendicular to it respectively:

$$\text{DRAG} \left( \text{D} \right) = \text{TRRUST} \left( \text{T} \right) \tag{1}$$

$$\text{LIFT}\left(\text{L}\right) = \text{WEIGHT}\left(\text{W}\right) \tag{2}$$

Thrust will be directly measured between engine and engine mount. The measured force corresponds to the force acting on the aircraft caused by the propeller thrust. With

$$T \approx D = \frac{\rho}{2} \ast v^2 \ast \mathbb{C}\_D \ast \mathbb{S} \tag{3}$$

and the knowledge about the true air speed (*v*) and air density (*ρ*), we can directly determine the drag coefficient (*CD*) of the aircraft by assuming drag (*D*) and thrust (*T*) as balanced. *S* describes the reference wing area of the test platform. True air speed and air density will be measured with the air data boom installed in the nose of the aircraft (Table 2). A small deviation has to be considered by the frictional forces of linear bearings in the thrust measurement unit which can be eliminated by a calibration.

The lift coefficient (*CL*) can be determined by the following equation:

$$\mathcal{W} = \ L = \frac{\rho}{2} \ast \upsilon^2 \ast \mathbb{C}\_L \ast \mathcal{S} \tag{4}$$

Since the aircraft is electrically powered by a battery system, the weight is constant throughout the flight. To identify the corresponding angle of attack, the air data boom is used. Angle of attack and angle of sideslip are measured with a five-hole probe. As the measured values of the different sensors are synchronised, the coefficients of lift and drag can be described directly in relation to the *AoA*. The measured *AoA* has only to be corrected by its installation position in relation to the wing. In this way, the direct connection between *AoA* and the corresponding lift and drag values should be representative in flight. Larger values of lift and drag are to be expected with an increasing of the *AoA*.

#### **3. Approach for the Flight Test Scenario**

The approach for the flight test scenario is based on the assumptions made in Section 2 to investigate the flight performance under the condition of a steady horizontal flight and with a zero-wind condition for the atmosphere.

However, considering the reality of free-flight tests, perfect atmospheric conditions will never be achieved. To meet these requirements to some degree, the flight tests are carried out in the early morning on days with calm atmosphere. The impact of atmospheric

disturbances was estimated in [12]. To realize a statistical accuracy of the data measured in flight, the data for a single measurement point is collected over a minimum of four legs with two different flight directions.

To determine the thrust during flight, a measuring system is installed between the electric engine and the engine mount to measure the tensile forces. The occurring tensile forces correspond to the thrust generated by the propulsion system.

The thrust measurement is particularly relevant due to its direct correlation with the aerodynamic drag. The investigations are carried out under cruise conditions, i.e., steady, horizontal flight. For the investigation, a flight track is chosen which allows the longest possible horizontal legs. The limiting factor for the tests is the current regulatory framework, which specifies a maximum flight envelope for the tests in the permitted airspace.

The measurement flights are performed with an autopilot in control to achieve steady, horizontal flight and high repeatability. For the test flight a circuit with maximized straight segments (legs) in-between is chosen. Given the airspace restrictions, the leg on which the measurements can be made is nearly 1000 m long. Figure 2 represents the flight path of a measurement flight at 300 m altitude.

**Figure 2.** Flight track—sections of measurement (**green**); level off sections (**orange**).

The legs are divided into two segments. The first segment is the "level off section". After the turn, airspeed, altitude and attitude are stabilized in this section. Data in this section will not be considered. In the section of measurement, a stabilized flight attitude is expected and the data will be used for the analysis of lift and drag. As there will be no perfect steady horizontal flight with constant altitude and airspeed, limits for the deviation in roll angle, airspeed and altitude are set, to assign a confidence rating to the single leg that is considered in the evaluation. To optimize the steady horizontal flight, the autopilot controls a constant velocity and altitude.

#### **4. Measurement Unit**

The thrust measurement unit consists of two parts. The sensor unit which contains the sensor itself for direct measurement of the thrust and a self-developed data acquisition unit that contains the amplifier module and the interfaces to connect further sensors. The data acquisition unit is also the interface to the data storage.

Recorded values at the propulsion system during flight:


Besides collecting the data with high precision, the complete measurement system is required to feature a lightweight design for use on the UAS. This ensures that the use of the testbed for further studies is not limited by the weight of the measurement unit.

#### *4.1. Sensor Unit*

The sensor unit is based on a standard tension/pressure sensor (HBM U9C 100N). For the sensor unit to be used on the unmanned test platform, the main focus is on a robust and compact lightweight design. The unit is designed to allow for the sensor to be installed without torque and bending moments introduced by the engine.

An engine connection unit is being developed for this purpose. This consists of an engine connection plate, a force introduction bolt and linear guide pins to absorb torsion and bending loads. These loads are directed from the linear guiding pins into the linear bearings installed in the load transmission frame. For the inflight thrust measurement, the sensor unit is installed directly between the engine mount and the engine (Figure 3).

**Figure 3.** Integrated thrust measurement sensor unit; 1—Sensor Unit; 2—Engine Mount; 3—Electric Engine.

Due to its design, the sensor unit allows two separate load paths (Figure 4). Loads will be introduced in the sensor unit via the engine connection plate. The plate is linearly mounted and transmits the force induced by the propeller thrust as tension force directly to the sensor. The torque and the bending loads resulting from the angular and linear acceleration and vibrations of the engine are derived via the linear bearings into the structure of the sensor unit (housing and frames). This way the thrust can directly be derived from the measured tensile force.

tension rod (traction stop) friction bearing tension sensor connecting frame housing force introduction bolt engine connection plate load transmission frame linear guide pins linear bearing

**Figure 4.** Sensor Unit (sectional view).

#### *4.2. Data Acquisition Unit*

The task of the data acquisition unit (Figure 5) is the acquisition and processing of data from the propulsion system and the transmission of the data to the board computer for synchronous logging. An STM32 microprocessor is used to convert analog signals, to encode and time stamp the data and to handle transmission to the central board computer via an RS485 bus (Figure 6). While this is sufficient to handle the sensor input from magnetic rpm measurements and current and voltage sensors, the force sensor outputs need to be amplified first. This is done using a miniaturized amplifier module (GSV-6CPU) installed on the Data Acquisition Unit. Additional interfaces on the data acquisition board allow to connect further sensors that might be required by future studies using the e-Genius-Mod test platform. With a weight of only 28 g, the data acquisition unit (board without cable) is perfectly suited for use in UAS without restricting the payload capacity.

**Figure 5.** Data Acquisition Unit.

**Figure 6.** Information flow of the Data Acquisition Unit.

#### **5. Test Flight Analysis**

In order to obtain repeatable measurement flights, the flights are automatically guided along a previously planned flight path. The autopilot system [11] adjusts the flight condition to different, constant flight speeds at an altitude above mean sea level of 650 m. This results in stable conditions in stationary horizontal flight, during which the corresponding input variables of the drive system are recorded. The available endurance of 85 min for one test flight allows for more than 68 measuring sections, which are segmented into phases with different flight velocities. With this, all measurements required for a characterization of the aerodynamic parameters of a configuration can be carried out in one single flight Figure 7 provides a synopsis of the legs and Table 3 presents the commanded velocities to identify the coefficients for lift and drag in flight.

**Figure 7.** Section of the flight path from a single measurement flight.


**Table 3.** Mean standard deviation of velocity and altitude.

#### *Analysis of Static Horizontal Flight*

In order for the evaluation to be considered valid using the mean value method, the "section of measurement" must be carried out at a velocity and an altitude as constant as possible. The evaluation of the individual legs shows that both velocity and altitude are measured with only a very small standard deviation (Table 3) depending on the flight speed.

As expected, high fluctuations were detected in the recorded propeller speed, which is also reflected in the measured thrust values. This is a result of controlling the airspeed by using the thrust. The resulting control action can be seen in the resulting fluctuations in measured thrust values (Figure 8). They do not mainly represent a scattering in the aerodynamic drag, but moreover the necessary control action to keep the airspeed constant. This is particularly the case during the two turns.

**Figure 8.** Example: Basic measurements on one single leg (with TAS 28 m/s).

The standard deviations caused by this must be taken into account accordingly in the evaluation and interpretation of the measured values. Nevertheless, the measured values on average give a good picture of the expected results and provide an excellent indication of the performance and aerodynamic quality of the aircraft.

For a first estimation and interpretation of the flight results, the values for thrust, angle of attack, lift and power are approximated as a function of 2nd order in dependence of the velocity as expected from the theoretical consideration. The assumption is based on the approximate relationship, that the lift increases linearly in relation to the AoA and the drag increases quadratic to the lift. Even if this procedure involves a degree of uncertainty in the interpretation of the results, it allows for an initial analysis of the aircraft characteristics, to provide input data for the aircraft design process.

#### **6. Results**

This section presents the results of the test flight presented in the previous section. Considering that the UAS should be used as a tool in aircraft design, the analysis focuses on the most interesting aspects for a design engineer. Figures 9 and 10 show the coefficients of lift and drag obtained from the measurement flights and the approximated resulting polar curve. As expected, due to the rpm variation described above, a significantly increased variation of the identified drag coefficient can be seen in Figure 10. Nevertheless, the values can be used for first design calculations.

**Figure 9.** Lift polar.

**Figure 10.** Drag polar.

Even if only a certain regime of the drag polar and the thrust to velocity curve is available, design points of interest (Table 4) can be estimated with the available identification. The points of maximum range and maximum endurance can directly be identified.

**Table 4.** Estimated points of max. range and max. endurance.


The point of maximum range is given by the maximum of the glide ratio (*CL*/*CD*) and can be determined directly from Figures 10 and 11. The point of maximum endurance can be determined as point of minimum required thrust (min drag) in Figure 12.

**Figure 11.** Glide ratio (*CL*/*CD*) to velocity.

**Figure 12.** Thrust to velocity.

With the knowledge of the electrical power and the power output of the propeller in terms of thrust, the overall efficiency of the test platform can be determined (Figure 13).

**Figure 13.** Performance and Efficiency of the free-flight test platform for different velocities.

#### **7. Discussion**

The measurements obtained from the flight tests provided the expected results with regard to the thrust curves and the resulting polar. As a first comparison between flight test results and a simulation of the wing airfoil, the gradient of lift coefficient versus the angle of attack was assessed. A comparison with the lift of the airfoil simulated in XFoil [13] shows a very good agreement with reality (Figure 14). The slight deviation of the slope of the two curves results from the influence of the lift distribution on the real wing caused by the boundary vortices.

**Figure 14.** Comparison of XFoil airfoil simulation, semi empirical method and flight test data.

The amount of the deviation depends on the aspect ratio (*AR*) of the wing and can be calculated approximately [14] as follows with *b* describing the wing span and *S* the reference wing area:

$$\frac{d\mathbb{C}\_L}{dAoA} = \frac{AR}{(2+AR)} \ast 2\pi \text{ with } AR = \frac{b^2}{S} \tag{5}$$

The angle of attack for zero lift is found as −3.8◦ from interpolation of the measured values from real flight, which gives a good agreement with the value expected from the simulation. The corresponding installation position of the air data probe in relation to the wing's angle of attack is thus correctly recorded.

An additional validation method was performed, calculating the wing's lift curve slope with a semi-empirical formula [15], applicable for subsonic design.

$$C\_{L\_{AoA}} = \frac{2\pi AR}{2 + \sqrt{4 + \frac{AR^2\beta^2}{\eta^2} \left(1 + \frac{\left(\tan AR\_{max\_l}\right)^2}{\beta^2}\right)}} \left(\frac{S\_{exp}}{S}\right)F\tag{6}$$

Within formula (6) *η* describes the so-called efficiency of the airfoil and is approximately 0.95 according to [15]. *β*<sup>2</sup> considers the flight velocity respectively the Mach number (M).

$$
\beta^2 = 1 - M^2 \tag{7}
$$

The wing geometry and the influence of the wing are considered in Equation (7) with *ARmaxt* , *Sexp* and *F*: *ARmaxt* is the aspect ratio of the wing section with the thickest airfoil chord location. The wing area exposed by the fuselage is considered with *Sexp* and the lift generated by the wing is approximated with *F* estimated via the diameter *d* of the fuselage tube under the wing. According to Raymer [15], these can be calculated as follows.

$$F = 1.07 \left( 1 + \frac{d}{b} \right)^2 \tag{8}$$

To consider also the effects of the winglet the effective aspect ratio of the wing is estimated according to [14] taking into account the height of the winglets *h* in relation to the wing span.

$$AR\_{eff} = AR\left(1 + 1.9\frac{h}{b}\right) \tag{9}$$

The polar of the calculated lift curve slope (*CLAoA* = 0.0764) is plotted in Figure 14 and the zero crossing is shifted by the estimated = 0.33. In a direct comparison of the part of the lift polar which can be considered as nearly linear between the semi-empirical and the measured lift curve slope with *CLAoA measured* = 0.0787 *for* (0◦ < *AOA* < 5◦) a good match is achieved with only 3.01% deviation of the curve slope.

In the simplified approach used in this paper, the possible error in the results must also be considered. A relatively small error can be assumed for the lift coefficient. This error is made up of the accuracy of the air data probe (measurement error flow angle: <1.0◦, velocities: <1.0 m/s) and a possible installation error which is corrected in the post processing. The drag measurement must be viewed with greater caution. The accuracy of the measuring system has been demonstrated under laboratory conditions, the variation of the measured thrust values due to the fluctuating speed controller (see Section 5) leads to a high standard deviation (mean 26.56%).

Nevertheless, the thrust measuring system generated usable data, which, however, are subject to fluctuations due to controlling thrust values. This must be considered in the evaluation. For further flight tests, control authority for the airspeed control should be reduced in order to ensure that the measured thrust values are smoother and there is less scattering. The proper functioning of the measuring system was verified in laboratory tests before and after the flight tests.

The measurement of the thrust finally gives information about the total drag, which is necessary to establish the drag polar and aerodynamic parameters of interest. From the illustrations in the "results" section the corresponding statements regarding the aerodynamic performance of the system can be derived. The values are within the predicted range. As expected, the scaling of the aircraft brings the optima for best range and flight duration very close together. By measuring the thrust during flight while simultaneously

observing the electrical power consumption, a direct statement can also be made about the overall efficiency of the drive train. It can be seen from Figure 13 that the optimum efficiency is found in the range of the speed at which the system is operated in the glide ratio of best range. This is an important step to assess the impact of future design changes to the e-Genius Mod.

#### **8. Conclusions**

The measurement flights with the unmanned e-Genius-Mod test platform have shown that on-board thrust measurement provide a direct method to characterize the aircraft. The expectations to draw direct conclusions about the aerodynamic performance could be met. With the presented novel measurement system for direct, in-flight thrust measurements, the unmanned platform represents a useful tool in aircraft design as a "flying wind tunnel". It allows an identification of the flight performance and allows to evaluate the effects of new technologies and configurations. This is of particular interest for new configurations that use distributed electric propulsion to increase efficiency and to enable a future cleaner and greener aviation.

To improve the quality of the flight test results in the future and to allow for drag estimation from non-steady flight conditions, the aircraft dynamics will be included in the drag estimation through acceleration measurements from an inertial measurement unit. Using the thrust measurement system, the characterization of the aircraft could be completed to such an extent that further flight tests with modified settings and distributed propulsion systems can follow. Due to the performance measurements on the baseline configuration it will be possible in the future to draw direct comparisons to flight tests with modified configurations. The measurement system used has been verified and can now also be used for further configurations utilizing distributed propulsion. For this, the sensor unit will be miniaturized to be able to measure the thrust of each propulsion unit in flight. The additional measuring technology installed to record the aerodynamically relevant input variables perfectly complements the thrust measurement of the main propulsor. Therefore, the basic configuration of the e-Genius-Mod is now available for more extensive flight tests and offers ideal conditions for scaled flight tests of all kinds.

**Author Contributions:** Conceptualization, D.P.B.; methodology, D.P.B., J.D., and O.P.; investigation, D.P.B., J.D., and O.P.; writing—original draft preparation, D.P.B., and J.D.; writing—review and editing, D.P.B., J.D., O.P., S.N., and A.S.; supervision, W.F., and A.S.; project administration, D.P.B.; funding acquisition, D.P.B., S.N., W.F., and A.S. All authors have read and agreed to the published version of the manuscript.

**Funding:** This research was supported by Federal Ministry for Economic Affairs and Energy on the basis of a decision by the German Bundestag. Project: ELFLEAN—Electric wing tip propulsion system for the development of energy-efficient and noise reduced airplanes (20E1706).

**Institutional Review Board Statement:** Not applicable.

**Informed Consent Statement:** Not applicable.

**Data Availability Statement:** Data not yet available public.

**Conflicts of Interest:** The authors declare no conflict of interest.

#### **References**


### *Article* **Modeling and Control of a Modular Iron Bird**

**Luciano Blasi 1, Mauro Borrelli 2, Egidio D'Amato 3,\*, Luigi Emanuel di Grazia 1, Massimiliano Mattei <sup>4</sup> and Immacolata Notaro <sup>1</sup>**


**Abstract:** This paper describes the control architecture and the control laws of a new concept of Modular Iron Bird aimed at reproducing flight loads to test mobile aerodynamic control surface actuators for small and medium size aircraft and Unmanned Aerial Vehicles. The iron bird control system must guarantee the actuation of counteracting forces. On one side, a hydraulic actuator simulates the hinge moments acting on the mobile surface due to aerodynamic and inertial effects during flight; on the other side, the actuator to be tested applies an active hinge moment to control the angular position of the same surface. Reference aerodynamic and inertial loads are generated by a flight simulation module to reproduce more realistic conditions arising during operations. The design of the control action is based on a dynamic model of the hydraulic plant used to generate loads. This system is controlled using a Proportional Integral Derivative control algorithm tuned with an optimization algorithm taking into account the closed loop dynamics of the actuator under testing, uncertainties and disturbances in the controlled plant. Numerical simulations are presented to show the effectiveness of the proposed architecture and control laws.

**Keywords:** iron bird; hydraulic system; flight simulator; force control; PID control

#### **1. Introduction**

An iron bird is often defined as an "aircraft which does not fly", used to validate the design and verify performance and stability [1] of aircraft components and systems. It is a mechanical representation of aircraft systems, including actuators, arranged on a frame instead of being inside the fuselage or the wings, completely visible, to test the integration of components as the integration of the actuation systems for aerodynamic surfaces and landing gears into the airframe, and their links to the power supplies and the flight control system.

Since the beginning of aviation, giants steps have been made on actuator technology. Currently, fly-by-wire aircraft use hydraulically supplied actuators in order to control mobile surfaces, but the birth of the All (or More) Electric Aircraft philosophy is changing this paradigm towards increasing the use of electrically supplied actuation systems that is usually called power-by-wire (PBW) actuation.

The advantages in using electrical versus hydraulic power on aircraft are well described in [2–5]. Good power density at the level of power network, more efficiency, more options and ease of command, dynamic reconfiguration of power paths are some of them. However, the technology maturity level of PBW is still low in terms of returns of operational experience. Moreover, some technological issues as poor local exchange of heat generated by energy losses have to be studied to increase their diffusion.

**Citation:** Blasi, L.; Borrelli, M.; D'Amato, E., di Grazia, L.E.; Mattei, M.; Notaro, I. Modeling and Control of a Modular Iron Bird. *Aerospace* **2021**, *8*, 39. https://doi.org/10.3390/ aerospace8020039

Academic Editor: Andreas Strohmayer Received: 15 December 2020 Accepted: 29 January 2021 Published: 2 February 2021

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Electro-Mechanical Actuators (EMAs) represent a very good alternative also for small commercial aicraft and UAVs, because of the lower cost and the general lower maintenance effort needed with respect to Electro-Hydraulic Actuators (EHAs).

One of the earliest studies on EMA is [6], where the researches completed by Boeing and Rockwell in the eighties are summarized. Boeing concluded that their baseline aircraft would remain roughly the same mass when switched to EMAs, Rockwell predicted an increase in mass, but in both cases, when EMAs were introduced, the mass of the aircraft secondary power systems decreased.

In [7], a review of EMAs is presented, starting from a brief history on the use of this type of actuators on aircraft. It also explains the main ways to test an EMA, from tests in a room temperature situation, to tests in a thermal vacuum environment, to tests on an iron bird. Generally speaking, the iron bird testing is intended to validate also the linkages of the EMAs with other systems, e.g., the power system and the Flight Control System (FCS).

Iron birds are useful in both industrial and scientific worlds. In the literature, although several authors use iron birds to prove the effectiveness of their solution about flight control algorithms, without focusing on its design, their works represent useful examples and the state of the art about this topic. In [8], Airbus explains how the electrical flight control system used on its aircraft is validated through iron bird testing. In [9], the power plant system of a tilt rotor UAV was verified by means of iron bird ground tests. In [10], a modular iron bird was designed to test new concepts in the flight control area, however, the modules are used for a specific aircraft. In [11], a new methodology for Prognostic Health Management systems of electro-mechanical flight control validation using an iron bird is proposed. The MIB (Modular Iron Bird), which is currently in the construction phase at PROTOM, developed in collaboration with the University of Campania "L.Vanvitelli", is a new concept of geometrically simplified and modular iron bird to perform verification tests of equipment developed for FCSs of small/medium aircraft belonging to the general aviation and unmanned aerial vehicles. It is mainly designed to test the control and actuation system moving the aerodynamic control surfaces and their integration in the flight control system. On the other hand, the test objective is quite extensive, ranging from the analysis of the actuator dynamic response, stability, and accuracy, to the efficiency and power capability, to the response to fault.

Usually, iron birds are custom ground-based test device used for prototyping and integrating aircraft systems (e.g., actuators) during the development of new aircraft designs. Systems are installed into the iron bird so their functions can be tested both individually and in correlation with other systems. They are expensive and often not reusable, being economically inaccessible for many small companies. However, the growth of unmanned aircraft market and the lowering of costs in the design of small aircraft and their actuators, makes attractive the use of a network of affordable facilities able to test systems with limited costs. The MIB architecture tries to give an answer to this increasing need.

The paper is organized as follows. Section 2 deals with the MIB control system architecture description. The mathematical model of the plant to design and validate the proposed control laws is described in Section 3, whereas in Section 4 the force control law is presented together with the algorithm used to tune the control gains. Finally Section 5 illustrates some numerical simulation results.

#### **2. The MIB Testing Facility**

The basic elements composing MIB are:

	- **–** the Real-Time Process Controller (RTPC) implementing the so called Process Control Algorithms for the tracking of desired loads on the aerodynamic surfaces and the actuator unit under test reference positions;
	- **–** a loading hydraulic actuator linked to a rigid mobile surface;
	- **–** a set of pressure, position and load sensors, needed for control purposes and to acquire and archive test data;
	- **–** the EMA Unit Under Testing (UUT) which is mechanically loaded by the hydraulic actuator;

The modularity of the proposed Iron Bird is based on the presence of several TS that can adapt to different actuators and layouts; actuators can be tested in parallel or one at a time. Also the hydraulic actuator simulating the aerodynamic and inertial loads can be chosen in function of the loads requested by the test. At the moment, a single rod actuator is adopted to mount a double load sensor, but in future a different actuator can be mounted. Moreover the flexibility offered by the automation system allows to plan different tests including those simulating the aircraft flight and related maneuvers.

#### *2.1. The Process and Automation Control System*

As shown in Figure 2, the MIB Process Control System implements the following subsystems:


**Figure 2.** MIB Automation and Control System Architecture.

Red, dark red and yellow blocks are replicated for each TS active.

The MIB Test Planner (TP) manages the test setup procedure implementing the UI, and it is able to generate the input signals for the real time simulator and the reference signals to be passed to the RTPC.

The Automation Function block implements the functions to monitor the overall system health. These functions are implemented with a time step of 0.1 s.

The MIB Aircraft Real Time Simulator (ARTS) is a flight simulator, implementing the equations of the rigid body aircraft dynamics with moving surfaces, including the equations to compute hinge moments on mobile surfaces because these are needed to calculate the flight loads on EMA actuators. The use of simulators in the aircraft design and testing phase is well recognized by the scientific community [12].

The ARTS is also connected with a simulator of the flight control laws. Its inputs are the mobile surface positions, measured by sensors if the related stand is active, otherwise the desired position from the flight control laws is used. In this case the reference commands to the flight controller are produced by the TP with a time step of 0.1 s. The ARTS outputs are the loads to be actuated on the mobile surface, and hence to be passed to the Force Control block as reference signals. Gravity effects due to the aerodynamic surface installation are taken into account and compensated before generating reference loads.

Although this can be easily replaced, the standard flight control law module has a classical structure for fixed wing aircraft, and is based on three nested loops (see Figure 3, namely: a Stability Augmentation System (SAS), a Control Augmentation System (CAS), and an outer Autopilot. These loops can be activated by the User.

SAS control action implements a pitch, roll and yaw damper. CAS implements both a pitch and roll rate control. Finally the autopilot can control altitude, true air speed, and heading.

Due to the use of Matlab/Simulink simulation blocks, both the rigid six degrees of freedom (DoF) aircraft model with moving surfaces and the flight control law implemented can be readily replaced with a more detailed model including flexibility or other phenomena (e.g., ground effects during landing and take-off), and more complex control laws.

The Force Estimation and Control block implements the algorithm to estimate and control the load on the mobile surface and hence on UUT. The input to this block are the reference force to be actuated, the measurements from load cells and pressure sensors, and the position of the aerodynamic surface. The output is the command to the servo-valve controlling the flow-rates to the hydraulic actuator. Two force measurements are available at the top and the bottom of the hydraulic cylinder. On the basis of these measurements, pressure measurements into the cylinder chambers, and a position measurements to correct for geometrical effects, a more reliable estimation is obtained via Kalman Filtering.

Similarly, the Surface Position Estimator block can estimate the position of the mobile surfaces on the basis of the position measurement coming from two LVDTs and a speed measurement produced by a digital encoder. LVDTs are the position sensors shown in Figure 1 from which is possible to calculate the angular position of the mobile surfaces. This estimation block is divided from the Position Control block for flexibility purposes. In fact it may happen that the UUT is already equipped with a position control. In this case the MIB Position Control is disabled but a position estimation is still needed to drive the aircraft simulation.

#### *2.2. The Test Planner*

The Test Planner is a software module for the test preparation. It implements a GUI (Graphical User Interface) to set test parameters and runs on the host PC, in order to supply test parameters to the RTPC. During the test, variables are monitored with a refresh rate of 0.1 s.

Different kind of tests can be performed on MIB depending on the control modes foreseen for the EMA and for the hydraulic system, and on the use of the ARTS. EMA can be controlled in two different ways:


Hydraulic actuators can be controlled in two different ways:


Finally, the ARTS can be operated in two different ways:


The TP also provides initial conditions for the flight simulation if the ARTS is enabled. This is obtained via a suite of tools implemented in the TP module, including trim and linearization.

#### **3. Control Oriented Plant Mathematical Modeling**

Hydraulic systems are typically adopted in iron birds to generate loads for their compactness and performance. However, they also present some modeling and controllability issues, due to uncertainties and hard nonlinear dynamic behaviours. Non-linearities are mainly due to flow rates through servo-valves. Uncertainties and disturbances can derive from pressure fluctuation across the pumps or from fluid physical characteristics, such as the bulk modulus, but also from the deformation of the chambers and piston walls, and other effects related volume uncertainties.

Several modeling approaches can be found in the literature. In [1], modeling is based on Newton equation for UUT piston and for load actuator movement. In [13,14], the model is obtained directly in the Laplace domain for the load actuator. In [15,16], the mathematical model is based on Newton equation for the electro-hydraulic piston movements, and a mass balance is used for servo-valve modeling, controlled with input flow rate. In [17,18], the Newton equation is used for piston displacement: Coulomb friction model is adopted taking into account some model uncertainties. Friction, that is a relevant aspect in this field, is also modeled in [19–21]. Relevant works can be found in [22–26].

The objective of the following preliminary modeling is not to precisely describe the physical phenomenon behind the hydraulic system, but to formulate a sufficiently rich, though simple, parametric model, to be tuned with experimental data collected on the plant, on which a first validation of the controller structure and tuning of the controller gains can be done.

An important source of uncertainty in the modeling of the overall system is the actuator UUT which will change from test to test although, for the validation of the plant control system, a specific and known actuator will be used.

With the above premises, the following main modeling simplifications are made:


One single TS is assumed to describe the mathematical modeling in more details. The hydraulic load generation system, schematically shown in Figure 4, is composed of four main elements: an open reservoir, an HPU, an electro-hydraulic servo-valve, and a cylinder connected to the movable surface on which the load is applied. The first two components are common to all the TSs.

**Figure 4.** Schematic of the Hydraulic Load Generation System.

The HPU pump converts mechanical into hydraulic power, injecting fluid in the supply line. An accumulator is included in the power unit. This is a pressure storage reservoir in which a relatively small quantity of fluid is held under a pressure which is regulated by the system to a given value. The accumulator allows to react quickly to a transient flow rate demand, to smooth out possible pulsations, and avoid significant pressure losses. On the other hand the pump guarantees the mass flow rate needed by the hydraulic cylinder to actuate significant forces in short time.

The servo-valve modulates the flow rate into the two cylinder chambers moving the piston that generates the force on the UUT.

Other standard hydraulic and electric components, needed for a correct and safe operation of the plant, are not modeled and described, as not strictly related to process control validation and design. First of all, compressibility of the oil in the hydraulic circuit has to be taken into account because of the high pressure. In fact the fluid density *ρ<sup>r</sup>* depends, assuming the definition of isothermal bulk modulus, on the fluid pressure *Pr*:

$$\rho\_r = \rho\_0 \cdot \varepsilon x p \left( (P\_r - P\_0) / \beta \right) \tag{1}$$

where *ρ*<sup>0</sup> is the density at the atmospheric pressure *P*0, and *β* is the fluid bulk modulus.

Due to the presence of the trapped air in the plant, the bulk modulus cannot be assumed constant, and consequently it is modeled as a nonlinear function of the hydraulic pressure:

$$\beta = \beta\_0 \frac{1 + \alpha (\frac{P\_0}{P})^{1/\gamma}}{1 + \alpha \frac{P\_0^{1/\gamma}}{\gamma P^{\frac{\gamma + 1}{\gamma}}} \beta\_0} \tag{2}$$

where *β*<sup>0</sup> is the fluid bulk modulus at *P*0, *α* is the trapped air volume ratio at *P*0, *P* is the fluid pressure, *γ* is the air specific heat ratio.

Hydraulic systems need a finite volume of recirculating liquid to work. A reservoir permits to accumulate the fluid getting rid of the trapped air. The reservoir has a breather to maintain the pressure constant at the atmospheric value. The dynamic equations relating volume, pressure and flow rates are the following:

$$
\dot{V}\_r = q\_{r,in} - q\_{r,out} \tag{3}
$$

$$P\_r = \rho\_r g h$$

where *Vr* is the liquid volume in the reservoir, *qr*,*in* and *qr*,*out* are the input and output volumetric flow rates, respectively, *Pr* is the pressure at the bottom of the reservoir, *g* is the gravity acceleration, *h* = *Vr*/*Ar* is the height of fluid column, with *Vr* and *Ar* volume and cross section area of the cylindrical reservoir, respectively.

The hydraulic pump is a device used to convert mechanical power into hydraulic power. Modern HPUs can adapt fluid flow rate to keep a fairly constant pressure in an accumulator downstream the pump.

This accumulator is used to store a limited amount of fluid to smooth out pressure oscillations and to make the downstream components dynamic response less sensitive to the upstream conditions.

The whole HPU is modeled with the following uncertain first order system:

$$
\dot{P}\_p = \mathcal{K}\_H (q\_p - q\_v) \tag{5}
$$

$$q\_p = k\_p(P\_{p,ref} - P\_p) + k\_I \int (P\_{p,ref} - P\_p)d\tau \tag{6}$$

where *Pp* is the pressure in the accumulator. The maximum pressure delivered by the pump is 200 bar. *qp* and *qv* are the flow rate provided by the hydraulic pump, and the flow rate across the servo-valve, *KH* is a constant obtained from the linearization of the system behavior around its operating conditions and is assumed to be uncertain. *Pp*,*ref* is the reference pressure in the accumulator controlled by the HPU local pressure control system.

The force control is obtained with a servo-valve converting electrical command signals into a spool valve command to control the flow rate. Under simplifying assumptions and the absence of leakages, the servo-valve dynamics can be approximated as a first order dynamics:

$$\dot{X}\_{\rm sv} = -\frac{1}{\tau\_{\rm sv}} X\_{\rm sv} + \frac{u\_{\rm sv}}{\tau\_{\rm sv}} \tag{7}$$

$$X\_{\text{sv},\text{win}} < = X\_{\text{sv}} < = X\_{\text{sv},\text{max}} \tag{8}$$

where *Xsv* is the servo-valve spool displacement, *τsv* is the time constant, and *usv* is the control action computed on the basis of error between desired force acting on the cylinder and the estimated one, *Xsv*,*min* and *Xsv*,*max* are the limits on the servo-valve opening variable. The flow rate through the servo-valve is

$$q\_{sv} = \mathcal{C}\_d w X\_{sv} \sqrt{\frac{2\left(P\_{\rm l} - P\_{\rm d}\right)}{\rho\_{sv}}} \tag{9}$$

where *Cd* is the servo-valve discharge coefficient, *w* = *Asv*/*Xsv*,*max* is the servo-valve area gradient, *Asv* is the servo-valve port area, *ρsv* is the fluid density, *Pu* is the pressure upstream the servo-valve, and *Pd* is the pressure downstream the servo-valve.

Assuming that *Pi* (*i* = 1, 2) is the pressure in chamber *i* with *i* = 1, 2, *Pu* and *Pd* are identified on the basis of the servo-valve position. If *Xsv* ≥ 0, chamber #1 is connected to the fluid supply line, then *Pu* = *Php*, *Pd* = *P*1; if *Xsv* < 0, chamber #1 is connected with the return line, then *Pu* = *P*1, *Pd* is equal to the pressure of the return line that can be assumed as the pressure *Pr* in the reservoir. *ρsv*,*<sup>s</sup>* and *ρsv*,*<sup>r</sup>* being the servo-valve densities in the supply and return lines, respectively, the flow rates in the hydraulic actuator chambers are the following:

$$q\_{sv,1} = \begin{cases} \mathbb{C}\_d w X\_{sv} \sqrt{2(P\_{hp} - P\_1)/\rho\_{sv,s}} & X\_{sv} \ge 0\\ \mathbb{C}\_d w X\_{sv} \sqrt{2(P\_1 - P\_r)/\rho\_{sv,r}} & X\_{sv} < 0 \end{cases} \tag{10}$$

$$q\_{sv,2} = \begin{cases} \mathbb{C}\_d w X\_{sv} \sqrt{2(P\_2 - P\_r)/\rho\_{sv,r}} & X\_{sv} \ge 0\\ \mathbb{C}\_d w X\_{sv} \sqrt{2(P\_{hp} - P\_2)/\rho\_{sv,s}} & X\_{sv} < 0 \end{cases} \tag{11}$$

Hysteretic effects due to static friction, and deadband, as reported by the servo-valve manufacturer are also included in the dynamic modeling used to validate the control law.

In the hydraulic actuator, the piston is forced by the pressure difference between two chambers. Volume variation in chamber *i* is *V*˙ *<sup>i</sup>* = (−1)*<sup>i</sup> XA*˙ *<sup>i</sup>*, *i* = 1, 2. The chamber volume variation is related to pressure variations as follows:

$$\mathcal{P}\_i = (q\_i - \mathcal{V}\_i) \frac{\mathcal{B}}{V\_i} \qquad i = 1, 2 \tag{12}$$

$$\ddot{X}\_p = \left( \left( P\_1 A\_1 - P\_2 A\_2 \right) - b\_p \dot{X}\_p - k\_p X\_p - m\_{\text{fl}} \text{g} \cos(X\_p / l\_{\text{fl}}) + R \right) / \left( m\_p + l\_{\text{fl}} / l\_p^2 + l\_{\text{EMA}} / l\_p^2 \right) \tag{13}$$

where *Xp* is the piston position with respect to the center of the cylinder, *Ai* the i-th chamber cross section, *Pi* the chamber pressure, *qi* the i-th chamber input volumetric flow rate, *bp* the damping coefficient, *kp* the elastic coefficient, *mac* is the movable surface mass, *lac* the distance between the surface center of mass and the hinge axis, *mp* the piston mass, *lp* the distance between the piston and the hinge axis, *Jac* and *JEMA* the inertia moments of the surface and the EMA, respectively, with respect to the hinge axis, and *R* the force generated by EMA. The mechanical linkages are supposed rigid, however backlashes are introduced in the numerical simulations to evaluate their uncertain effects of control laws.

#### *3.1. EMA Actuator under Testing*

Special attention must be paid to the modeling of the EMA actuator UUT moving the mobile aerodynamic surface. In fact, being the object of the test, its model depends on the particular test itself. For the control system architecture validation and testing a specific EMA is used. This is modeled with a first order dynamic system

$$\dot{R} = -\frac{1}{\tau\_{EMA}}R + \frac{u\_{EMA}}{\tau\_{EMA}}\tag{14}$$

where *R* is the generated force, *τEMA* is the EMA time constant, *uEMA* is the control action generated by the position controller. In addition a rate limiter and a saturation is added for the force controller performance assessment.

In case the UUT comes as a black box to be tested, a procedure to identify the EMA dynamic model including non-linearities, based on the use of Neural Networks and Nonlinear AutoRegressive eXogenous (NARX) dynamic models [27–30], has been formulated and validated with numerical simulations.

#### **4. Force Control Algorithm**

An interesting problem to be taken into account for the Process Controller, is that force control has to counteract the reaction of a position controller implemented on the UUT actuator side.

For this reason, the Force Control Algorithm must satisfy very tight requirements on the closed loop speed of response and the capability to counteract disturbances induced by the position control of the UUT.

In fact, both the hydraulic and EMA actuators are mechanically linked to the movable surface and each controller becomes a source of disturbance for the other. Looking at force control, the piston speed induced by position control, causes a variation of the volume of the two cylinder chambers, namely *Vi*, *i* = 1, 2. Therefore, since the pressure rate in each chamber *P*˙ *<sup>i</sup>*, *i* = 1, 2 depends on the volume derivative *V*˙ *<sup>i</sup>* according to (12), if this effect is not properly compensated by dumping the necessary amount of fluid from one chamber to the other, strong overshoots of the controlled force occurs.

In the scientific literature, this problem has been dealt with in [1], where a Proportional-Integral (PI) controller with feed-forward compensation is adopted to counteract UUT speed disturbances on force control. This control approach, called *traditional*, suffers from synchronization accuracy issues. In [31] structured guidelines for the synthesis of dynamic force simulators that are required for the testing of high speed aerospace actuators are developed. Realistic and proven solutions at both test bench hardware and control

design levels are provided. In [13], asynchronous controller is used to to regulate the loading actuator operating velocity synchronously with UUT actuator so as its actuator motion disturbance can be decoupled. In [32], the traditional control is achieved with an adaptive control approach based on the relationship between speed and current in electro-mechanical actuators.

In [15], it is shown that the closed loop poles of the UUT, controlled in position, are zeroes of the force driven open loop transfer function for load actuation. This leads to a performance limitation when a PID control is used for force control. A Quantitative Feedback Theory (QFT) based control technique is proposed to overcome this problem. QFT is used also in [16,33,34], a force controller is designed with a loop shaping technique.

In [35], several techniques are analysed: feedback force control with force direct measurement using a PI action, combinations of state feedback control schemes with state observers and velocity feedforward compensation actions. In [36], a PID controller is used and disturbances due to UUT speed are compensated with a signal proportional to a model based estimation of UUT acceleration.

A PID controller is proposed in [37], where three tuning methodologies are presented: optimal time tuning PID, optimal frequency tuning, and multi-objective PID. Also in [38], a PID is used for both load actuation and for rejecting UUT velocity disturbances. This controller is also used in [39] for servo-valve pressure control.

In [40], a feedforward controller and a feedforward inverse control with disturbance observer are used for load actuation. The former is used to reject disturbances due to UUT movements, the latter is used for the other disturbances. In [17,41] adaptive reference controls are presented. In [42], a fuzzy logic MIMO controller is proposed. Fuzzy logic is also used in [19,43] to tune a PID, in order to increase robustness. Fuzzy logic is also used in [44]. In [45], a Minimal Control Synthesis with integral action is used with adaptive gains, while in [20], a back-stepping based controller is adopted. Other works are based on *H*∞ control [46], nonlinear adaptive optimal control strategies [47], sliding mode in [48] and an adaptive decoupling synchronous controller in [49].

In [50], a Model Predictive Controller is proposed by the authors dealing with loads generated by fast moving EMAs. The proposed controller uses a simplified model of hydraulic plant, achieved by neglecting the faster dynamics of pump, reservoir, pipes and accumulator. However, the computational burden of the predictive approach does not yet allow an online implementation with low-cost hardware solution.

The present work is focused on a preliminary classical PID control, tuned on the mathematical model of the plant, in view of a model calibration, controller parameters re-tuning, and first closed loop tests.

In fact force control is based on a Proportional-Integral-Derivative (PID) scheme, which computes the input to the servo-valve in order to act on the input/output flow rate in the two chambers of the hydraulic actuator to control pressure. The closed loop actuator control system has to be tuned to have a dynamic response which is significantly faster than the EMA position control time response. In this way the design of force control can be reasonably decoupled from the position controller dynamics.

Therefore, by taking into account the frequency separation between the two controllers, the force control gains have been optimized to guarantee a certain degree of robustness and given performance.

In practice the following quantities are defined:

	- **–** Bulk modulus *β*<sup>0</sup>
	- **–** air trapped volume ratio *α*,
	- **–** Servo-valve time constant *τsv*.
	- **–** Discharge coefficient and servo-valve area product *CdAsv*,
	- **–** EMA time constant *τEMA*.

A family of *Nu* plant models, implementing the above uncertainties, is defined:

$$
\dot{x}\_{\dot{j}} = f\_{\dot{j}}(x\_{\dot{j}}, u) \tag{15}
$$

$$y\_j = h\_j(\mathbf{x}\_j, \mathbf{u}) \tag{16}$$

(*j* = 1, ..., *Nu*), where *xj*, *yj*, and *u* are the state vector, the controlled output (force on the aerodynamic surface) and control input (servo-valve command), respectively;

• a set of *NS* operating scenarios to evaluate the robust performance of the controller over the *Nu* models by means of the following cost function:

$$J(e\_j^k(\cdot), \mu(\cdot), \mathbf{x}\_{0j}, t\_{0\prime}t\_{f\prime}w), \quad k = 1, \ldots, N\_{\mathbb{S}} \tag{17}$$

with *y<sup>k</sup> ref* − *<sup>y</sup><sup>k</sup> <sup>j</sup>* the output tracking error, *yref* ,*<sup>k</sup>* being the force reference signal, *x*0*<sup>j</sup>* the initial state at time *t*0, *tf* a finite time for the cost function evaluation, and *w* a suitable vector of weights;

• a parametric structure for the force controller:

$$u(t) = u\_{\mathbb{C}L}(p, e\_{[t\_0, t]}(\cdot), t) \tag{18}$$

with *e* = *yref* − *y*. In our case, the vector *p* represents the gains of a PID control action to be optimized.

Therefore, the following optimization problem was solved:

$$\min\_{\begin{array}{c}p\\k=1,\ldots,N\_{\text{u}}\\k=1,\ldots,N\_{\text{S}}\end{array}} \int (e\_{\text{f}}^{k}, u\_{\text{CL},\prime}, \mathbf{x}\_{0\text{\hat{\phantom{x}}}}, t\_{0\text{\hat{\phantom{x}}}}, w) \tag{19}$$

subject to

$$\dot{\mathbf{x}}\_{j} = f\_{j}(\mathbf{x}\_{j}, \boldsymbol{\mu}(p, e\_{j}^{k}(t), t)) \quad \text{ , } \mathbf{x}\_{j}(t\_{0}) = \mathbf{x}\_{0j} \tag{20a}$$

$$y\_j = h\_j(x\_{j'} \, u(p, e\_j^k(t), t))\tag{20b}$$

$$
\underline{u} \le u(t) \le \overline{u} \tag{20c}
$$

$$
\underline{\mathbf{x}} \le \mathbf{x}\_{\dot{f}}(t) \le \overline{\mathbf{x}} \tag{20d}
$$

The above optimization Problem, defined by (19) and (20), was solved in the discrete time using a Genetic Algorithm [51,52].

#### **5. Numerical Result**

Table 1 reports the main plant parameters used for numerical simulations. A single TS control implementing ailerons tests is considered.

The servo-valve is an adirectional control valve, direct operated, with integrated digital axis controller (IAC Multi Ethernet), Rexroth type 4WRPDH. The servo-valve opening variable in plots is a normalized servo-valve opening.

To optimize the controller gains, the following scenarios were considered:

	- **–** force multi step (with increasing amplitude 100, 500 and 1000 N), constant pump pressure (15 MPa);
	- **–** force multi step with constant pump pressure (80% of the nominal 15 MPa);
	- **–** force multi step with constant pump pressure (120% of the nominal 15 MPa);
	- **–** force multi step with sinusoidal pump pressure (15 MPa+ 0.15 sin(*ω* ∗ *t*) MPa).
	- **–** Aileron doublet (2.5 deg deflection for 9 s followed by −2.5 deg deflection for 9 s);
	- **–** Aileron step (2.5 deg deflection).

In addition, the following model uncertainties were taken into account:


**Table 1.** Plant parameters.


To test the performance of the force controller, a campaign of simulations was performed. In each simulation, the above uncertainties were considered. In addition the following disturbances or additional phenomena were considered: hysterical effects of the servo-valve and mechanical links, servo-valve dead zone, piston end-stroke.

To evaluate the controller performance, responses to small step inputs (100 N for force and 0.1 cm for position) are considered in the presence of perturbed models. In Table 2, mean values of control performance indexes are shown. In particular, the mean quadratic error (MQE), the overshoot and the settling time (ST) are reported for the worst case. For the settling time the worst case is assumed to be the maximum for force control and the minimum for position control.

**Table 2.** Controllers performance: Mean Quadratic Error (MQE), Overshoot, Settling Time (ST).


In the proposed Simulation #1, pre-programmed reference force and position signals were considered, as shown in Figures 5 and 6, respectively.

In Figure 7 the normalized servo-valve position time history is shown. Figure 8 shows the pressure provided by the pump including the sinusoidal disturbance. Lastly, in Figures 9 and 10 both cylinder chambers pressure are shown. It is worth noticing that the controlled force results is able to reject the disturbance represented by the piston movement. This is an important characteristic to be sure to evaluate the EMA in a wellemulated scenario.

Simulation #2, carried out with the same reference signals as Simulation #1, demonstrates the robustness of the controllers to measurement white gaussian noise on position and force measurements. The same quantities shown for Simulation #1 are shown in Figures 11–16. The controlled force is able to reject the disturbance represented by the piston movement also in presence of model uncertainties and measurement noise.

**Figure 5.** Simulation #1: Actuated force compared to the reference force.

**Figure 6.** Simulation #1: Piston Position compared to the reference position.

**Figure 7.** Simulation #1: Servo-valve opening command.

**Figure 8.** Simulation #1: Accumulator Pressure.

**Figure 9.** Simulation #1: Chamber #1 Pressure.

**Figure 10.** Simulation #1: Chamber #2 Pressure.

**Figure 11.** Simulation #2: Force actuated by the Hydraulic cylinder compared to the reference signal.

**Figure 12.** Simulation #2: Piston Position compared to the reference signal.

**Figure 13.** Simulation #2: Servo-valve opening command.

**Figure 14.** Simulation #2: Accumulator Pressure.

**Figure 15.** Simulation #2: Chamber #1 Pressure.

**Figure 16.** Simulation #2: Chamber #2 Pressure.

#### *5.1. Numerical Results with the Flight Simulator in the Loop*

An innovative feature of MIB is the capability of reproducing loads provided by a real time flight simulator including control laws.

Several tests involving the ARTS were carried out. In particular the following conditions, implying an aileron deflections, were simulated:

	- **–** a 0.044 rad step on ailerons deflection;
	- **–** a ±0.044 rad doublet on ailerons deflection;
	- **–** a 0.044 rad step on ailerons deflection;
	- **–** a ±0.044 rad doublet on ailerons deflection;
	- **–** an impulse (1.05 rad/s) on roll rate command;
	- **–** a doublet (±1.05 rad/s) on roll rate command;
	- **–** a step (0.088 rad) on the heading angle reference;
	- **–** a ramp (0.26 rad/s) on heading angle reference;

The Cessna 172 was assumed as reference aircraft, whose main parameters are reported in Figure 17.

In the following Simulation #3, ARTS was used in "self-consistent mode" without flight control laws, and driven by a doublet input signal to the ailerons shown in Figure 18. The resulting force is shown in Figure 19. The reference force and position signals compared to the actual one in the presence of uncertainties are shown in Figures 20 and 21.

Figures 22 and 23 give an idea of the simulated maneuver, which is a sort of turn. Roll angle and roll angular speed are shown. It can be noted that reference signals produced by the ARTS are like smoothed by the aircraft dynamics. Therefore, force controller provides better results with respect to sharp reference signals.

**Figure 17.** Simulated Aircraft-Cessna 172.

**Figure 18.** Simulation #3: Surface Deflection Reference.

**Figure 19.** Simulation #3: Actuated Force Reference.

**Figure 20.** Simulation #3: Actuated Force compared to the reference signal.

**Figure 21.** Simulation #3: Surface Deflection compared to the reference signal.

**Figure 22.** Simulation #3: Roll Angle from the Aircraft Simulator.

**Figure 23.** Simulation #3: Roll Rate from the Aircraft Simulator.

#### **6. Conclusions**

This paper describes the control architecture of the Modular Iron Bird which makes use of several test stands to increase flexibility and reduce costs for small commercial aircraft or unmanned aerial vehicles. This iron bird can reproduce preprogrammed loads to test single or multiple actuators, or realistic "in flight" load conditions thanks to the presence of a real time aircraft simulation module.

The design and tuning of the control law needs particular attention because of the concurrent action of both a force controller to guarantee the testing loads and a position controller to control the aerodynamic surface position. This required the use of high quality components, and suggested the use of a dynamic model of the plant during the design phase, to make a robust tuning of the force controller driving the hydraulic actuator.

In the plant design phase, a classical control approach has been adopted. Indeed, the force control algorithm is based on a PID, whose gains have been optimized to ensure robust performance in the presence of parametric uncertainties, and a closed loop response faster (∼0.01 s response time) than the EMA position controller (∼0.1 s response time). Results proved that the proposed solution works well in the presence of uncertainties and noise and hard nonlinearities neglected in the design of the control law such as hysteresis and dead zones. In particular, both the dynamic and static precision, is quite insensitive to the uncertainties and to the different scenarios considered to include possible tests on different kinds of aircraft.

**Author Contributions:** Conceptualization, methodology, formal analysis, investigation, writing, E.D., L.E.d.G., I.N., L.B., M.M. Data curation, visualization, software development, E.D., L.E.d.G., I.N. Funding acquisition, supervision M.B., M.M., L.B. All authors have read and agreed to the published version of the manuscript.

**Funding:** This research was partially funded by REGIONE CAMPANIA, M.I.B. (Modular Iron Bird) project, CUP B43D18000130007, FESR Campania 2014-2020.

**Institutional Review Board Statement:** Not applicable.

**Informed Consent Statement:** Not applicable.

**Data Availability Statement:** Data available on request due to restrictions. The data presented in this study are available on request from the corresponding author. The data are not publicly available due to NDA between Protom Group and university.

**Conflicts of Interest:** The authors declare no other conflict of interest.

#### **References**

