Passive attitude stabilization of ionic-wind-powered micro air vehicles

Hengyu ZHANG, Jiaming LENG, Zhiwei LIU, Mingjing QI, Xiaojun YAN

School of Energy and Power Engineering, Beihang University, Beijing 100191, China

KEYWORDS Air dampers;Altitude control;Ionic wind propulsion;Micro air vehicle;Monte Carlo methods;Stability

Abstract The ionic-wind-powered Micro Air Vehicles (MAVs) can achieve a higher thrust-toweight ratio than other MAVs.However, this kind of MAV has not yet achieved controlled flight because of the unstable thrust produced by the ionic wind and the dynamic instability related to the small size.In this paper, a passive attitude stabilization method of the ionic-wind-powered MAV using air dampers is introduced.The key factors that influence the performance of the air dampers,including the layout,position,and area of the air dampers,are theoretically studied.The appropriate optimal position of the air dampers is also obtained by Monte Carlo stochastic simulations.Then the proposed passive attitude stabilization method is applied to the ionic-wind-powered MAVs of different wingspan (2 cm and 6.3 cm).Finally, the experimental results show that using the proposed method,attitude stabilization is achieved for the first time for the ionic-wind-powered MAV.Moreover,the altitude control of an ionic-wind-powered MAV with a wingspan of 6.3 cm is also demonstrated.

1.Introduction

Ionic wind propulsion is a new type of propulsion mechanism for Micro Air Vehicles (MAVs), which needs no mechanical moving parts for thrust generation.1,2Ionic wind propulsion is also called Electrohydrodynamic (EHD)3,4or Electroaerodynamic (EAD)2propulsion in some literature.Compared with the flapping-wing propulsion and the rotatory-wing propulsion,ionic wind propulsion is noiseless,easier to design,lighter in weight, and simpler in structure, which brings the advantage of high thrust-to-weight ratios, and is attractive to MAVs.5,6The thrust,corresponding with the ionic wind,relies on the accelerated neutral air molecules.Ions are generated by the corona discharge between two asymmetric electrodes at high voltage differences.These ions are accelerated by the Coulomb force and collide with the neutral air molecules,increasing the momentum of the neutral air molecules and causing a propulsive force4,7–9.

Currently, the ionic-wind-powered MAV has not yet realized the controlled flight.10–12One of the most important reasons is that ionic-wind-powered MAV is dynamically unstable in flight, quickly tumbling in the absence of attitude stability mechanisms.On the one hand,the ionic wind propulsion operates at a high voltage of several thousand voltages, and the corona discharge has a certain degree of instability, resulting in an unstable thrust.12–16In addition,the flow dynamics characteristics of the ionic wind are susceptible to ambient air disturbance, which aggravate the thrust instability.On the other hand,with the reduction in size,the mass and moment of inertia of the MAV decrease.17The dynamics become faster,increasing the difficulties of active control.The delay and accuracy of sensors and calculations will have a significant impact on the active control of the system18,19.

Passive stabilization is a method of using air dampers to achieve automatic correction of the attitude of the MAV,20which locates the center of air dampers above the center of gravity, generating a self-righting torque to stabilize the upright orientation.This method eliminates the need of sensors and actuators for attitude control of the MAV, thus simplifying the design of the MAV and reducing its mass compared to the active control method.Previous work has used air dampers for hovering the MAVs or improving the attitude stability of the MAVs for active control21–27.

In this paper,inspired by previous work on air dampers for hovering aerial robots,20the passive attitude stabilization of the ionic-wind-powered MAVs is investigated, as shown in Fig.1.By analyzing the root locus of the state-transition matrix, the position of the air dampers is optimized, and the approximate optimal position within a certain range is obtained by Monte Carlo stochastic simulation.Finally, the attitude stability of the ionic-wind-powered MAVs with dampers is tested.The altitude control of an ionic-wind-powered MAV with a 6.3 cm wingspan is achieved for the first time.

2.Principles of operation

2.1.Modeling of MAV with air dampers

The air dampers should provide adequate aerodynamic drag and be placed in the proper position to achieve the passive attitude stabilization of the MAV.The horizontal placement of the dampers will cause a large aerodynamic drag during takeoff and affect the flight near the ground.So, the dampers are placed vertically, and the lateral motion of the dampers can generate the aerodynamic drag needed for the attitude stabilization.

Fig.1 Image of an ionic-wind-powered MAV with dampers on the top and bottom.

The force analysis of the MAV(with dampers)during flight can be simplified to a two-dimensional model because of the approximate symmetry of the MAV body.As shown in Fig.2, the MAV (with dampers) is subjected to the aerodynamic drag F1,F2,Fb,gravity mg,and the thrust FTgenerated by the ionic wind thrusters when moving laterally.Two air dampers are used: Damper 1 and Damper 2, placed above and below the MAV, respectively.In the modeling process,the area of the damper can be set to 0 to represent the situation that this damper is not used.

Due to the small size of the MAV,the small lateral motion velocity and rotation velocity,and the small Reynolds number,the aerodynamic drag is assumed to be proportional to the lateral motion velocity and in an opposite direction:

where b is the aerodynamic damping coefficient related to the area and shape of the damper, which can be approximated as proportional to the area, and v is the relative velocity of the airflow.

The lateral forces of the MAV (with dampers) include the aerodynamic drag F1, F2, Fb, and the horizontal component FTxof the thrust.The relationship between the lateral forces and the acceleration of motion can be expressed as:

where d1, d2, and dbindicate the distance between the aerodynamic drag and the center of gravity of the MAV (with dampers), b1, b2, and bbindicate the aerodynamic damping coefficients.

Assuming that the thrust FTis in the same line as the center of gravity, the MAV (with dampers) is only subjected to the torques generated by the aerodynamic drag:

where J is the rotational inertia of the MAV (with dampers).When considering the passive attitude stabilization of the MAV (with dampers) during flight, it can be assumed that the deflection angle θ is small and the thrust FTis approximately equal to the gravity mg.Then assuming that sin θ ≈θ,cos θ ≈1,FT≈mg,the above kinetic equations can be simplified as:

To facilitate the analysis of attitude stability, based on the above equations,three state variables vx,θ,and ω are defined,and the state vector x = [vx, θ, ω]Tis obtained.The above kinetic equations can be rewritten as:

According to Lyapunov stability theory, the system is asymptotically stable if λmax< 0,critically stable if λmax=0,and unstable if λmax> 0.Therefore, the conditions under which the system is passively stable can be described as:

2.2.Effect of layout and area of air dampers

The performance of the air dampers is affected by serval factors: the layout, the position, the area, etc.To quantitatively investigate the effect of these factors on attitude stability, the root locus method is used.

Adding dampers will change the mass,the center of gravity,and the rotational inertia of the MAV.So,in Eq(7),m,d1,d2,db, and J are needed to be calculated at first.Eq (10) gives in detail how these unknowns are obtained23:

where m0,m1,and m2represent the mass of the MAV(without dampers), Damper 1, and Damper 2.r1and r2represent the distance between the center of dampers (Damper 1 and Damper 2) and the center of gravity of the MAV (without dampers).rcmrepresents the movement of the center of gravity after adding dampers.rbis the distance between the center of the aerodynamic drag of the MAV (without dampers) and the center of gravity (without dampers).J0, J1, and J2correspond to the rotational inertia of the MAV(without dampers),the Damper 1, and the Damper 2.

Table 1 shows some parameters of an ionic-wind-powered MAV (without dampers).Given the aerodynamic damping coefficients,the mass and the rotational inertia of the dampers,and the mounting position, m, d1, d2, db, and J can be calculated from Eq(10).Then the obtained parameters can be substituted into Eq (7) to calculate the eigenvalues.

There are three layouts of the dampers: below the MAV,above the MAV, or both.The effects of the position and area of the dampers on the stability of the system for each layout are analyzed.The aerodynamic damping coefficients used in the simulation are referenced to the value in the literature23and are approximated to be proportional to the area of the dampers.The mass of the dampers is obtained from experimental measurements.Four tracking markers weight 10 mg have been added on Damper 2 to obtain the motion of the MAV using an external motion capture system.Table 2 shows some parameters of the dampers.Besides,the mass of the support structure required to support the dampers is neglected.

For each layout, the center of dampers is set away gradually from the center of gravity of the MAV.And then, a Matlab program is built to solve and plot the eigenvalues of matrix A.Four different sizes of dampers are set.

Fig.3 shows the root locus as r1and r2increase.The range is set to 0.5–20 cm with a step size of 0.1 cm.The red, green,and blue colored points in the figure represent the three eigenvalues of matrix A.The diamonds are the eigenvalues at the initial position.Three cases are considered: (A) the damper is only mounted below the MAV; (B) the damper is only mounted above the MAV; (C) the dampers are mounted both above and below the MAV.

Table 1 Parameters of MAV (without dampers) in simulation.

Table 2 Parameters of dampers in simulation.

In Fig.3(a), the area of Damper 1 is set to 0 cm, and the area of Damper 2 is set to 1 cm × 1 cm, 2 cm × 2 cm,4 cm×4 cm,and 6 cm×6 cm,which means the only damper is mounted below the MAV.The simulation results illustrate that regardless of increasing the distance between the damper and the MAV or increasing the area of the damper,the system always has a positive eigenvalue, and the system will be constantly unstable.This is consistent with the results of previous studies, which show that the system cannot be passively stabilized when the aerodynamic drag center is located below the center of gravity of the system.

In Fig.3(b),the area of the Damper 2 is set to 0 cm,and the area of the Damper 1 is set to 1 cm × 1 cm, 2 cm × 2 cm,4 cm × 4 cm, and 6 cm × 6 cm.In this situation, the aerodynamic drag center is located above the center of gravity of the system.The simulation results illustrate that as the damper moves away from the MAV,the max eigenvalue λmaxincreases at first and then decreases to near 0.Even with an increased area of the damper, the max eigenvalue λmaxis still greater than 0, which means that the system is always unstable within the selected parameter range.This shows that the aerodynamic drag center above the center of gravity is not a sufficient condition for the stability of the system.

In Fig.3(c), the dampers are placed symmetrically above and below the MAV,which means r1=r2.The areas of Damper 1 and Damper 2 are the same, and they are set to 1 cm × 1 cm, 2 cm × 2 cm, 4 cm × 4 cm, and 6 cm × 6 cm.The simulation results illustrate that when the area of the damper is small (1 cm × 1 cm), the dampers cannot generate enough restoring torque to stabilize the system, but it has a smaller λmaxcompared with the results in Fig.3(b).When the damper area is larger (4 cm × 4 cm and 6 cm × 6 cm),the system will quickly reach stable with the increase of the distance between the dampers and the center of gravity of the system.However,after r2increases to a certain value,the stability of the system will decrease.

For a given system, it is easier to be stabilized when the dampers are placed both above and below the MAV.In this layout, the area of the dampers needs to be large enough to provide the restoring torque.Within the selected parameter range, the larger the area of the dampers, the smaller λmaxcan be achieved.Besides, the dampers also have the best mounting position to achieve the minimum λmax.

2.3.Approximate optimal mounting position

In Section 2.2,it can be concluded that there exists an optimal mounting position of the dampers, which achieves the minimum λmax.By traversing the positions of the dampers,the optimal mounting position can be obtained.In addition,the optimal mounting position of the dampers can be asymmetrically placed.Monte Carlo stochastic simulation is used to obtain the mounting position of the dampers that enables the system to reach an approximate optimal steady state.

Fig.3 Root locus of state-transition matrix A as r1 and r2 increase in different layouts and areas of dampers.

For the MAV described in Table 1, with two dampers(6 cm × 6 cm) mounted symmetrically above and below, the root locus as r1and r2increase (range 0.5–20 cm) are shown in Fig.3(c).The calculated minimum λmaxis -2.80 when the distance of the dampers from the center of gravity (without dampers) r1= r2= 3.5 cm.When the mounting positions are asymmetric, the positions (range 0.5–20 cm) are set randomly, and the obtained roots are plotted in Fig.4(a) to find the approximate minimum λmaxand the corresponding position.The approximate optimal positions are r1= 11.9 cm,r2= 8.8 cm, and λmaxis -3.27.Therefore, the dampers with asymmetric mounting positions will have a smaller λmax,which is more beneficial to the passive stability of the MAV.

The MAV will be more difficult to achieve attitude stabilization at smaller scales.For the MAV with a wingspan of 2 cm(Table 3 shows some parameters of the MAV),the range of r1and r2from 0.5 cm to 5 cm are set.When the dampers are mounted symmetrically,the eigenvalues are calculated,and the λmaxgets the minimum value of -1.44 at the farthest distance(r1=r2=5 cm).Fig.4(b)shows the root locus,where the diamond is the starting point.As r1and r2increase, the real part of the max eigenvalue gradually decreases.The imaginary part of the max eigenvalue is not 0,which indicates that the system can reach stability,but will be accompanied by oscillation.The Monte Carlo stochastic simulation results show that the dampers with asymmetric distribution can achieve smaller λmax,and the imaginary part of the max eigenvalue is equal to 0.The roots distribution of all simulations is shown in Fig.4(c).The minimum λmaxis -2.30, and r1= 3.2 cm,r2= 5.0 cm, which shows that the asymmetric placement of the dampers is better than the symmetric placement.

3.Experimental apparatus

3.1.Ionic-wind-powered MAVs

The ionic-wind-powered MAV in this article has one thruster,mainly consisting of needle-shaped emitters, a collector, and supports,as shown in Figs.5(a)-(c).The emitters have a small radius of curvature, and the collector is a mesh with ‘‘large holes”.This ‘‘needle-mesh”configuration is expected todecrease both the aerodynamic drag coefficient and body mass of the MAV.When a high voltage difference is applied between the emitters and the collector,the electric field around the emitters is extremely strong because of their small radius of curvature, which will cause corona discharge at the emitters and produce space charges.These space charges are accelerated by the electric field between the emitters and collector and move to the collector.During the movement, these space charges will collide with neutral air molecules, transferring momentum to the neutral molecules.The neutral air molecules are pushed by the MAV, and the MAV will be subject to a propulsive force, i.e.the thrust of the MAV.

Table 3 Parameters of MAV (wingspan of 2 cm) in simulation.

Fig.5 Components and physical diagram of ionic-windpowered MAVs.

Fig.4 Root distribution of state-transition matrix A in different conditions.

The material used for the emitters and collector is a carbon fiber sheet with a density of 1.8 g/cm3and a thickness of 0.13 mm.The electrodes are cut into the designed shapes by laser cutting technology.The electrode supports are made of glass fiber (density 2.2 g/cm3) with a thickness of 0.16 mm and have a good insulating property.All emitters are connected by carbon fiber or copper wires.The conductive silver paste is applied to enhance the electrical conductivity at joints.The prototypes of the MAVs with a wingspan of 2 cm and a wingspan of 6.3 cm are shown in Fig.5(d) and Fig.5(e),respectively.

3.2.Air dampers

Since the MAV flies in three dimensions, two degrees of freedom, roll, and pitch need to be considered in designing the dampers.The mass of the damper should also be limited to ensure it can be carried by the MAV.In addition, due to the high operating voltage of the ionic wind thruster,the discharge of the dampers should be avoided, which may produce ion wind undesirable for the stability of the system.

The designed damper is shown in Fig.6(a).The damper consists of two interlocking surfaces.The interlocking surface consists of a support frame and a damping membrane.The support frame is used to fix the damping membrane and set the connection.The damping membrane is used to block the flow of air.

The support frame of the damper is made of insulated glass fiber with a thickness of 0.16 mm,and the damping membrane is made of mylar film with a thickness of 1.5 μm to ensure a lighter mass.The support frame and the damping membrane are connected by hot-melt adhesive.After the three parts are cut by the laser cutting machine, they are stacked together and heated to 180 °C under certain pressure conditions for 2 h, and then cooled at room temperature to ensure that the three parts are bonded together.Figs.6(b)-(d) shows parts of the dampers and the physical picture after heating and bonding.

After manufacturing the dampers, the dampers and the MAV are glued together by a glass fiber support.Fig.6(e)shows the MAV(wingspan of 6.3 cm)with dampers.The area of the dampers shown in the figure is 6 cm×4 cm,considering the thrust of the MAV and the mass of the dampers.The position of the dampers can be adjusted according to the simulations by the length of the glass fiber support.

4.Results

4.1.Attitude stability test

Before mounting the dampers on the MAV, the flight of the MAV without dampers was tested.As shown in Fig.7(a),the MAV was quickly tumbling.The flight was dynamically unstable, and the MAV fell to the ground after it flipped 270° in attitude within a short time.

Fig.7(b)shows the flight of the MAV(wingspan of 6.3 cm)with two dampers.According to the model simulation,the attitude would be passively stabilized.It can be seen that from takeoff to landing, the MAV can always recover its attitude and remain approximately upright.

Fig.6 Design and physical diagram of damper mounted on MAV.

Fig.7 Attitude stability test of MAV.

Fig.8 Flight data of micro air vehicle in altitude control.

For a smaller size of the MAV with a wingspan of 2 cm(Fig.1),the dampers were mounted in the proper position predicted by the theoretical simulation to achieve passive stabilization of the attitude.The flight of the MAV is shown in Fig.7(c).

4.2.Altitude control test

A feedback system was designed to achieve altitude control of the MAV(wingspan of 6.3 cm).By using a motion capture system to obtain the altitude data of the MAV and a low voltage control method to control the thrust,12we stabilize the altitude of the MAV with small errors.Fig.8(a) shows the 3D trajectory of the MAV with a target altitude of 0.20 m, and Fig.8(b) shows the altitude variation curve with time.The MAV has lateral drift caused by inherent torque bias due to assembly asymmetry or a random disturbance of the airflow28.

5.Conclusions

(1) The effects of the layouts of the dampers are analyzed on the attitude stability of the MAV.By analyzing the root locus of the state-transition matrix, it can be concluded that it is easier to be stabilized when the dampers are mounted both above and below the MAV.

(2) The area of the dampers needs to be large enough to provide the restoring torque.In a stable system,within a suitable range, the larger the area of the dampers, the more stable the system can be.

(3) The approximate optimal mounting position can be obtained by Monte Carlo stochastic simulations, and this optimization has a greater impact on smaller-sized MAVs.The simulation results show that the passive attitude stabilization of the ionic-wind-powered MAV with a wingspan of 2 cm can be achieved if the dampers are mounted in proper positions.

(4) The passive attitude stabilization of the ionic-windpowered MAVs with a wingspan of 6.3 cm and 2 cm is achieved.This is the first time that an ionic-wind-powered MAV achieved attitude stabilization.

(5) The altitude control of an ionic-wind-powered MAV with a 6.3 cm wingspan is achieved.This is the first controlled altitude flight of ionic-wind-powered MAVs, and will benefit further controlled flights with active control methods.

Declaration of Competing Interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Acknowledgements

This work was supported by the National Natural Science Foundation of China (No.12002017) and the 111 Project,China (No.B08009).