Maximum Thrust Research Articles

Wind tunnel testing and performance modeling of an atmospheric ion thruster

Abstract In this work a complete atmospheric electro–hydro-dynamic (EHD) thruster is tested in a subsonic wind tunnel, with the purpose of evaluating changes in performance due to simulated flight conditions and, for the first time, comparing them with a physical model of the drift region. An aerodynamic frame was designed to accommodate the electrodes inside the wind tunnel. Propulsive force and electrical measurements were conducted to assess performance exploiting dimensionless coefficients derived from one-dimensional theory. The results, on top of validating the theory, show how EHD thrusters can operate with a non-zero bulk velocity and highlight the importance of optimized frames and electrodes to enhance the capabilities of flying demonstrators. The test campaign revealed that the operating voltage envelope extends with increasing bulk velocity, leading to an increase in maximum thrust.

Stacked generalization ensemble learning strategy for multivariate prediction of delamination and maximum thrust force in composite drilling

The complexity of drilling carbon fiber reinforced polymers (CFRP) requires accurate predictive models. This study addresses the challenge using an ensemble machine learning (ML) approach with stacked generalization. The model captures the relationships between key input variables—such as graphene nanoplatelet (GNP) content, ultrasonic assistance, tool type, stacking sequence, and feed rate—and output parameters, specifically thrust force and delamination. A nested feature scoring (NFS) method was employed for importance analysis, revealing tooling type and feed rate as key features for minimizing delamination and reducing thrust force, respectively. The machinability results revealed that ultrasonic drilling lowered thrust force by improving chip evacuation and reducing fiber breakage. HSS tools with cobalt content, alongside symmetrical stacking sequence, helped to further minimize both thrust force and delamination. However, the inclusion of GNPs led to an increase in thrust force and delamination, attributed to the increased strength of the CFRP/GNP composite. The process involved meticulous training, resulting in four optimal-fit models serving as inputs for the stacked meta-model. Iterative enhancements fortified the ensemble robustness, with fine-tuning of hyperparameters through Bayesian optimization. The ensemble superiority over individual models manifested in a remarkable reduction of mean absolute error (MAE) and root mean squared error (RMSE) by up to 97% and 124% for delamination, and 205% and 154% for thrust force, compared to the best base learner. Visual and statistical assessments effectively illuminated the intricate interactions between variables in the drilling process. The methodology resulted in a highly adaptable predictive model with applications across diverse manufacturing contexts.

Optimizing the Landing Stability of Blended-Wing-Body Aircraft with Distributed Electric Boundary-Layer Ingestion Propulsors through a Novel Thrust Control Configuration

The imperative for energy conservation and environmental protection has led to the development of innovative aircraft designs. This study explored a novel thrust control configuration for blended-wing-body (BWB) aircraft with distributed electric boundary-layer ingestion (BLI) propulsors, addressing the issues of sagging and altitude loss during landing. The research focused on a small-scale BWB demonstrator equipped with six BLI fans, each with a 90 mm diameter. Various thrust control configurations were evaluated to achieve significant thrust reduction while maintaining lift, including dual-layer sleeve, separate flap-type, single-stage linkage flap-type, and dual-stage linkage flap-type configurations. The separate flap-type configuration was tested through ground experiments. Control experiments were conducted under three different experimental conditions as follows: deflection of the upper cascades only, deflection of the lower cascades only, and symmetrical deflection of both cascades. For each condition, the deflection angles tested were 0°, 10°, 20°, 30°, 40°, 50°, and 60°. The thrust reductions observed for these three conditions were 0%, 37.5%, and 27.5% of the maximum thrust, respectively, without additional changes in the pitch moment. A combined thrust adjustment method maintaining a zero pitch moment demonstrated a linear thrust reduction to 20% of its initial value. The experiment concluded that the novel thrust control configuration effectively adjusted thrust without altering the BLI fans’ rotation speed, solving the coupled lift–thrust problem and enhancing BWB landing stability.

Effects of coupled platform motions on the aerodynamic performance and wake characteristics of a floating horizontal-axis wind turbine

ABSTRACT The aerodynamics of floating horizontal-axis wind turbines (FHAWTs) are complex due to platform motions in real sea states. The impacts of coupled platform motions on the aerodynamic loads, wake structure, and wake recovery of FHAWTs were investigated through computational fluid dynamics simulations. Results show that the increases in the maximum rotor power of FHAWTs (compared with the fixed-base ones) under sinusoidal pitch-surge motions (3892 kW) were close to the sum of those under pitch (2121 kW) and surge (1622 kW) motions. The wake tilt angles under pitch-surge motions agreed with those under pitch motions, causing similar wake recovery. The increase in wave periods (Tw ) amplified the resonance between waves and platforms under the wind-wave coupling, increasing the maximum rotor power and thrust. Compared with Tw = 16 s, the relative decreases in the averaged wake velocity, which was 7D (where D is the rotor diameter) downwind of the FHAWTs, were 5.93% and 2.64% at Tw = 8 s and 12 s, respectively. Long Tw increased pitch periods, yielding fast wake recovery by enhancing the interaction between blade-tip vortices and hub ones. The output power of a floating wind farm was higher than the fixed-base counterpart due to fast wake recovery.

A Modified Robust Homotopic Method for the Low-Thrust Fuel-Optimal Orbital Control Problem

This study focuses on improving the application of the quadratic penalty smoothing technique for solving the fuel-optimal problem of low-thrust trajectory. Some practical techniques, including the Particle Swarm Optimization algorithm (PSO), the co-state normalization technique, and the single shooting method, are employed. These approaches can enhance convergence to the globally optimal solution. The application of PSO is improved through the introduction of the diversity termination term. Furthermore, a new parameter, the maximum thrust to initial mass ratio (CTm), is introduced and analyzed. The relationships among Lagrange multipliers for different CTm in the energy-optimal auxiliary problem are also derived. These relationships can be used in scenarios with high CTm to reduce the variable search space, leading to a significant decrease in computation time. Nonetheless, few researchers have proposed a well-defined strategy for the homotopic process. We propose a robust iteration strategy, involving the determination of the maximum step size and the distinction of sub-optimal solutions. This iterative strategy could ensure a robust convergence toward the optimal solutions. An interplanetary rendezvous example is provided to demonstrate the effectiveness of the presented techniques and strategy.

On the role of wake-capture and resonance in spanwise-flexible flapping wings in tandem

Numerical simulations of the flow around spanwise-flexible flapping wings in tandem are reported, focusing on a thrust-generating configuration. Wings of aspect ratio 2 and 4 in forward flight undergo heaving and pitching motion following optimal 2D kinematics. The Reynolds number of the simulations is Re=1000. The effect of flexibility is explored by varying the effective stiffness of the wings, while the effective inertia is kept constant. The aerodynamic performance of the tandem system results from a combination of unsteady aerodynamics mechanisms, fluid–structure resonance, vortex–wing interactions (denoted wake capture in this study) and aerodynamic tailoring. It is found that the aerodynamic performance and structural behavior of forewings are dominated by a fluid–structural resonance. The maximum mean thrust for the forewings is obtained when the driving frequency approaches the first natural frequency of the structure, ωn,f/ω≈1, similarly to what is observed in isolated wings undergoing the same kinematics. On the other hand, hindwings show optimal performance in a broad region near ωn,f/ω≈2, and their aerodynamic performance seems to be dominated by wake–capture and aerodynamic–tailoring effects. The aerodynamic performance of the hindwings is dependent on the flexibility of the forewing, which impacts the intensity of the vortices shed into the wake and the resulting effective angle of attack (i.e., wake capture). The timing between the effective angle of attack and the pitching motion of the hindwing controls the generation of thrust (or drag) of each spanwise section of the hindwing (i.e., aerodynamic tayloring). A proof of concept study on the aerodynamic performance of systems made of wings with different flexibility suggests that they could outperform tandem systems with equally flexible wings. Thus, the optimal mixed–flexibility tandem system is composed by a resonant forewing, which maximizes the thrust generation of the forewing and the intensity of the vortices shed into the wake, and a hindwing whose flexibility must be tuned to maximize wake capture effects.

Optimization techniques for the design of crescent-shaped hard sails for wind-assisted ship propulsion

Wind-assisted ship propulsion is one of the most promising technologies to achieve net zero emission in ship operations by 2050 due to its reliance on a fully renewable energy source. Hard sails with crescent profiles have been shown to potentially provide a greater benefit than symmetric sails in recent studies. In order to justify their application, it is necessary to create and adopt a specific design that guarantees a reduction in the engine load over the whole operational range of encounter angles. The current study provides a systematic approach to obtain such a design based on two techniques, one aiming to maximum sail thrust, the other to minimize propeller power. Surrogate models based on validated CFD simulations are adopted for optimization, and the most efficient design is found as an average over all the possible encounter angles. It was shown that the thrust maximized approach increased the average thrust generated by sail up to 12.3%, and the propeller power minimized approach improved the effectiveness of the sails up to 22% in terms of percent power reduction. It was also confirmed that crescent-shaped airfoils generally outperform symmetric airfoils in the considered conditions.

Design and optimization of a high thrust density air-breathing pulsed plasma thruster array

For satellites in Very Low Earth Orbit (VLEO) or the upper atmosphere, Air-Breathing Electric Propulsion (ABEP) can be used to counteract the drag effects of the atmosphere or provide attitude control without the need for onboard propellant storage. The Dense Plasma Focus (DPF) inspired the design of an ABEP Pulsed Plasma Thruster (TAMU PPT) which takes advantage of the simplicity, scalability, and high energy density of the DPF. This work details the design and testing of a PPT for use on satellites in the upper atmosphere. Testing was conducted at a variety of pressures and pulsing energies to determine which conditions provide maximum thrust and thrust to power ratios (TPR). It was found through single pulse experiments that a pressure of 6.3 hPa (corresponding to an altitude of about 35 km) and an energy per pulse of 9 J yield a TPR of 21 mN/kW. High frequency operation at 20 Hz in similar conditions showed a TPR of up to 28 mN/kW with a corresponding thrust of 4.8 mN. High speed imaging of the plasma plume found plasma velocities in excess of 2 km/s and identified metal ejecta with velocities up to 350 m/s. The pinching phenomenon associated with a DPF was also observed and a plasma jet velocity up to 50 km/s was recorded. The TPR of the TAMU PPT demonstrated in this work is comparable to that of other ABEP thrusters, however the TAMU PPT has an advantage when comparing thrust density. The TAMU PPT has a thrust density between 4.8 and 19 mN/cm2 while other ABEP thrusters have thrust densities between 0.019 and 0.36 mN/cm2.

Brayton Cycle Analysis of the Effect of Wake Ingestion on Aircraft Range

The effect of wake ingestion on the propulsive efficiency of turbojet and turbofan engines has been examined to determine the effect of wake ingestion on jet aircraft range. In a new approach, the Brayton turbine cycle was analyzed to show how wake ingestion affects the thrust and specific fuel consumption of jet engines. It is argued that it is not necessary to add an expression for propulsive efficiency to the Breguet range equation, because the thrust-specific fuel consumption is an explicit function of the inlet Mach number. It is concluded that wake ingestion does not increase the aircraft’s maximum range because it reduces the engine’s maximum thrust.

Investigation of Gas-Turbine Afterburner with Aluminized Fuel-Rich Propellant

This paper describes the design and development of a compact afterburner system for a mini gas turbine engine using aluminized fuel-rich propellant. The working principle of the system is analogous to a dual combustor ramjet engine in which the propellant is burnt in the primary chamber. Hot gases from the primary chamber combust further in the secondary chamber with incoming air from the inlet. In this work, fuel-rich gases were injected into the afterburner through radially mounted gas generators. The hot gases mix with the oxygen-rich turbine exhaust and burn further, resulting in high-enthalpy gases. These high-enthalpy gases were expanded in the convergent nozzle to generate higher exit velocity. This study investigated the thrust enhancement capability of the gas turbine afterburner system with fuel-rich propellant grains at different operating conditions. Furthermore, the effect of increasing afterburner length and decreasing nozzle exit diameter on the performance of the system was also examined. An overall static thrust of about 320 and 360 N was obtained for three and four grains, respectively, with maximum unburnt fuel residues of 11% in both the cases, out of which four grain configurations achieved a maximum thrust enhancement of around 180%.

A parametric investigation of Dual-throat nozzle bypass channel configurations for advanced Aviation applications

The Bypass Dual-Throat Nozzle (BDTN) has garnered growing attention due to its remarkable thrust vectoring capabilities. This type of nozzle boasts broad application prospects as it achieves deflection control of the jet stream merely through regulating the opening and closing of bypass channels. Our comprehensive study delves deeply into the intricate parameterization of the bypass channel within the BDTN. Research has demonstrated that utilizing Fluent software in conjunction with the Realizable k-epsilon turbulence model, standard wall functions, and the Sutherland formula for viscosity coefficient approximation can yield a relatively accurate representation of the vector flow field structure within the BDTN. Following the validation of the numerical computation methodology employed in this study, we have investigated the influence of factors such as bypass channel radius, precise valve positioning, and actuation direction on the nozzle's vectoring performance. Key findings indicate that, due to the relatively small proportion of secondary flow, the radius of the bypass channel has minimal impact on the thrust vector angle. The positioning of the valve and its opening direction are critical in determining the thrust vector angle, requiring careful consideration during the design and optimization process. Fully opening the bypass channel does not necessarily yield the maximum thrust vector angle. Moreover, the total pressure, velocity, position, and direction of the secondary flow within the bypass channel exert a more profound influence on the nozzle's vector performance compared to the mere presence of the secondary flow itself. Notably, the forward opening method of the valve emerges as the preferred choice, as it facilitates more precise later vector control.

A Study of an Integrated Analysis Model with Secondary Flow for Assessing the Performance of a Micro Turbojet Engine

The objective of this study is to implement a more realistic integrated analysis model for micro gas turbines by incorporating secondary flow and combustion efficiency into the existing model, which includes main engine components such as the compressor and turbine, and to validate this model by comparing it with test results. The study was based on the JetCat P300-RX, which has a maximum thrust level of 300 N. Simulations were performed using ANSYS CFX, employing the κ-ω SST turbulence model and a mixing plane interface between individual components. The eddy dissipation model (EDM), with a combustion efficiency of 90%, was used as the combustion model. A user subroutine was also applied for the power matching of the compressor and turbine to calculate the fuel flow rate in each iteration. For secondary flow, it was assumed that 3% of the total air flow rate would flow through the secondary path and be applied to the compressor and turbine. Simulations were conducted over a range of 30,000 to 104,000 RPM, with ground conditions evaluated, including altitude-simulated conditions. To validate the analysis model, engine performance metrics such as pressure ratio, air flow rate, fuel flow rate, and exhaust gas temperature (EGT) were compared with test results. The results demonstrated that errors were less than 5% for most engine performance metrics, except for EGT and fuel flow. The discrepancy in EGT was attributed to differences in the sensing methods, while the variation in fuel flow was found to be due to the lubrication system and losses due to the secondary air flow. Consequently, this study confirmed that the integrated simulation model accurately predicts engine performance. The results indicate that the integrated simulation model provides a more realistic prediction of overall engine performance compared to previous studies. Therefore, it can evaluate detailed thermo-fluid properties without the need for component performance maps, enhancing performance evaluation and analysis.

Development of a low-power Hall thruster with permanent magnets and a dual trigger electrode hollow cathode for the Qilu satellite constellation

A low-power Hall effect thruster (LpHet-100) has been installed on the Qilu-3 satellite and has been launched by the Long March 2D rocket in January 2023. The specific features of LpHet-100 are presented in this article. An innovative dual trigger electrode poison-resistant hollow cathode and an effective magnetic shielding configuration with permanent magnets, additive manufacturing gas distributor are designed and experimentally verified. The prominent characteristics of a shorter starting time, lower ignition shock, and self-healing have been shown in tests of the dual trigger electrode hollow cathode. Thrust performance tests proved that LpHet-100 can work stably in the power range of 50–230 W and generate a thrust of 2.9–10.8 mN, with the maximum specific impulse of 1594 s and maximum thrust efficiency of 38 %. Rigorous environmental tests were conducted to verify the thruster design scheme. In addition, Torque measurement of Hall thrusters is incorporated into the ground tests for the first time. A plasma torque of 5.65–9.88 μN·m is obtained when LpHet-100 operated in 132–228 W. It provides a critical guideline for the attitude and orbit control schemes of the Qilu-3 satellite, which is an essential part of space mission planning. Generally, this study proposes new design of the thruster body and hollow cathode, providing an exhaustive reference for the development process and application of low-power Hall thrusters.

Synergetic and Performance Characteristics of A High-Speed Pre-Cooled Propulsion Concept

Abstract Pre-cooled air-breathing cycles are promising candidates to power future high-speed flight as well as Single-Stage-To-Orbit vehicles, due to their increased efficiency over contemporary propulsion systems and launch vehicles. These concepts usually feature complex interactions in the synergy of their thermodynamic cycles. In this study, a performance model of such a cycle is developed for its air-breathing mode of operation. One-dimensional thermodynamic modeling is employed within a component-level approach, to evaluate the performance and operation of the cycle under investigation in the range of 1.35 = ≤ 8 = 5 and conditions of up to 26 kilometers altitude. The model is validated quantitatively and qualitatively for both design and off-design conditions. The specific impulse Isp and specific thrust, as predicted by the model, agree within less than 5% for both design and off-design point conditions, while it captures the trend of Isp for the range modeled. Moreover the maximum gross thrust point is predicted correctly at M∞ = 4. The fundamental operating principles and synergetic characteristics of the engine at design and off-design conditions are investigated and reported. A model which does not feature a bypass duct is created and compared for the same inflow conditions and mission profile. It is found that the engine without the bypass duct exhibits reduced specific impulse up to 32% lower at off-design conditions while the overall trend of engine efficiency cannot be properly captured without modeling of the bypass duct, especially at the region of M∞ < 3.5.

Unsteady CFD simulation of a rotor blade under various wind conditions

Wind and gusts can significantly impact the performance of rotors and turbines. The transient behavior of the rotor should be carefully examined to account for these effects. This paper investigates the unsteady aerodynamic characteristics of a rotor blade under different wind conditions, such as direction, speed, and angle. A 3D transient Computational Fluid Dynamics (CFD) simulation using the dynamic mesh technique is performed to analyze the rotor dynamics. The unsteady Reynolds-averaged Navier–Stokes (URANS) equations with the k-ω SST turbulence model are solved. The rotor blade used for this study is the U15XXL Combo KV29 industrial blade, which has not been numerically analyzed before. The results show that wind in the same direction as the rotation reduces the thrust more than lateral or opposite wind. Lateral wind with a speed lower than 5 m/s decreases the blade performance, but higher speeds increase it. Higher lateral wind speeds also cause two peaks in the torque curve, forming a butterfly wing shape in the polar torque plot and multiple extrema in the torque curve with increasing speed. The maximum thrust shifts slightly to the left with increasing lateral wind speed. The lateral angle does not affect the average thrust produced in one blade revolution but only causes a spatial shift. The thrust production decreases as the angle approaches the opposite direction of rotation. The motion amplitude decreases, and the curve becomes smoother as this angle increases. A nearly straight line similar to no side wind is observed at 60 and 90 degrees, which is attributed to the constant effective angle of attack during the rotation cycle.

Development of a Plate Linear Ultrasonic Motor Using the Power Flow Method.

Linear ultrasonic motors can output large thrust stably in a narrow space. In this paper, a plate linear ultrasonic motor is studied. Firstly, the configuration and operating principle of the Π-type linear ultrasonic motor is illustrated. Then, two slotting schemes are put forward for the stator to enlarge the amplitude of the driving foot and improve the output performance of motor. After that, a novel optimization method based on the power flow method is suggested to describe the energy flow of stator, so as to estimate the slotting schemes. Finally, the prototypes are manufactured and tested. The experimental results show that the output performance of both new motors are excellent. The maximum output thrust of the arc slotted motor is 76 N/94 N, and the corresponding maximum no-load speed is 283 mm/s/213 mm/s, while the maximum output thrust of V-slotted motor reaches 90 N/120 N, and the maximum no-load speed reaches 223 mm/s/368 mm/s.

Effect of curvature variations on the hydrodynamic performance of heaving and pitching foils

AbstractThe use of heaving and pitching fins for underwater propulsion of engineering devices poses an attractive outlook given the efficiency and adaptability of natural fish. However, significant knowledge gaps need to be bridged before biologically inspired propulsion is able to operate at competitive performances in a practical setting. One of these relates to the design of structures that can leverage passive deformation and active morphing in order to achieve optimal hydrodynamic performance. To provide insights into the performance improvements associated with passive and active fin deformations, we provide here a systematic numerical investigation in the thrust, power, and efficiency of 2D heaving and pitching fins with imposed curvature variations. The results show that for a given chordline kinematics, the use of curvature can improve thrust by 70% or efficiency by 35% over a rigid fin. Maximum thrust is achieved when the camber variations are synchronized with the maximum heave velocity, increasing the overall magnitude of the force vector while increasing efficiency as well. Maximum efficiency is achieved when camber is applied during the first half of the stroke, tilting the force vector to create thrust earlier in the cycle than a comparable rigid fin. Overall, our results demonstrate that curving fins are consistently able to significantly outperform rigid fins with the same chord line kinematics on both thrust and hydrodynamic efficiency.

Optimization of swimming mode for elongated undulating fin using multi-agent deep deterministic policy gradient

Optimizing speed and propulsive efficiency are the most crucial survival skills for biomimetic robots. This paper investigates a swimming mode controller inspired by the black Knifefish to govern the fast-swimming gait with high propulsive efficiency for an elongated undulating fin robot. The proposed swimming mode controller is composed of a couple of Hopf oscillator-based central pattern generators (CPG) to generate the moving gait of robotic fish and a novel variant of Reinforcement Learning (RL) known as Multi-Agent Deep Deterministic Policy Gradient (MA-DDPG) for optimizing the propulsive efficiency. The proposed swimming controller facilitates the autonomous optimization of the oscillatory amplitude of the robotic fish to improve its propulsive efficiency. The proposed MA-DDPG demonstrates an aptitude for functioning within mixed cooperative-competitive environments. Furthermore, it effectively mitigates the drawback of zero amplitude in the updating process of conventional reinforcement learning (RL) methodologies. These findings highlight the potential utility of the MA-DDPG in optimizing the performance of multi-agent systems in dynamic, real-world scenarios. The simulation results show that the undulating fin robot reaches a maximum thrust of 0.9 N with a propulsive efficiency of 12.48 %, which is higher than that of traditional reinforcement learning methods.

A centipede-inspired bonded-type ultrasonic actuator with high thrust force density driven by dual-torsional-vibration-induced flexural traveling waves

This paper presents an ultrasonic actuator with high thrust force density driven by dual-torsional-vibration-induced flexural traveling waves. Here, the PZT plates are bonded onto a duralumin vibrating body in a block shape to accomplish a compact configuration and they operate in the 2nd torsional vibrations, whose strong electromechanical coupling effect facilitates the enhancement of the driving force. Interestingly, the operating principle somewhat imitates the movement pattern of the centipede’s feet. To test the validity, first, by using a Mason-equivalent-circuit-based dynamic model, several key dimensions were tuned to increase the driving-force-to-weight ratio. Meanwhile, the driving feet’s configurations are adjusted based on a kinetic model to make the elliptical motion shape close to a circle. Then, an actuator prototype with the size of 48 × 47 × 6 mm3 and the weight of 29 g was fabricated and the moving/loading/positioning performance was evaluated. When the actuator adopts a continuous operation, its maximal sliding speed reached 630 mm/s at the frequency of 24.95 kHz. Moreover, it yielded the maximal thrust force and the maximal output power of 4.38 N and 527.8 mW, corresponding to the thrust force density and the power density of 151.2 N/kg and 18.2 W/kg, respectively. In a stepping operation, the minimal step displacement was 0.91 μm. These results demonstrate that the dual-torsional-vibrations-induced traveling wave allows the actuator to produce the high thrust force density and provides a new actuating principle to design powerful ultrasonic actuators.

Dual-Loop μ-Synthesis Direct Thrust Control for Turbofan Engines

As the power unit of an aircraft, the engine’s primary task is to provide the demanded thrust, making research on direct thrust control crucial. However, being a complicated multivariable system, effective multivariable direct thrust control methods are currently lacking. The main content of this paper is threefold. First, it presents a dual-loop multivariable μ-synthesis direct thrust control scheme for mixed-exhaust low-bypass turbofan engines, which is a typical rotationally symmetric machine. The scheme adjusts fuel flow for thrust control and nozzle area to control the turbine pressure ratio, ensuring thrust tracking while maintaining the engine’s key parameters within safe limits. Second, a fast, accurate thrust estimation algorithm based on aerodynamic thermodynamics and component characteristics is introduced. At last, considering the model uncertainties between off-design and design points, a weight function frequency shaping μ-synthesis control design method is proposed to address internal loop coupling and external disturbance suppression. Nonlinear simulations within the flight envelope show that μ-synthesis direct thrust control achieves robust servo tracking and disturbance rejection, with a maximum steady-state thrust error of no more than 0.1%, and the key parameters are not over their safety boundaries.