Engineering problem

The objective was to design and evaluate a closed recirculating-air system for cooling an aircraft avionics/electronics compartment. The model quantified thermal load, required airflow, duct pressure losses, heat-exchanger performance, fan power, robustness, and off-design behavior while maintaining the compartment-temperature requirement.

System architecture

The avionics-side air recirculates through a fan, duct network, and air-to-air heat exchanger before returning to the compartment. A separate external-air stream removes heat through the cold side of the heat exchanger without mixing with the avionics air.

Sensitivity analysis

The system model was used to evaluate sensitivity to recirculation airflow, external-air temperature, heat-exchanger performance, thermal load, and other design variables. Swipe through the plots below.

Thermal & system sensitivity

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Airflow sensitivity. Increasing recirculation airflow reduced the predicted zone temperature, with diminishing benefit at higher flow rates.

External temperature. Warmer cooling air increased the heat-exchanger performance required to hold the zone-temperature target.

Heat-exchanger performance. UA was one of the strongest controllable variables for maintaining thermal margin.

Thermal load and fan power. Higher avionics load increased airflow demand and fan-power requirement.

Operating envelope. The selected design was evaluated over combinations of avionics thermal load and external cooling-air temperature.

3D CFD validation

The selected duct network was evaluated in SOLIDWORKS Flow Simulation to independently check the one-dimensional pressure-loss model and inspect local velocity and pressure behavior through the bends.

CFD results

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Flow trajectories. Streamlines show the flow path and redistribution through the multi-bend duct network.

Static pressure. The pressure field was used to evaluate the duct-network pressure drop.

Velocity magnitude. Local acceleration and nonuniformity appear through the curved sections.

Centerline cut. The cut plot highlights bend-induced velocity redistribution inside the duct.

Final engineering result

The selected robust design used a 0.200 m duct, 0.18838 kg/s recirculation flow, and 102.22 W/K heat-exchanger conductance. Its conservative fan-sizing requirement was 143.96 Pa at about 56.89 W input. The design predicted 32.40°C nominal zone temperature and 39.21°C under the defined +10% thermal-load / −10% effective-UA stress case, leaving 0.795°C margin to the 40°C limit.

Limitation: Standalone air-to-air cooling is insufficient for representative warm-ground operation; supplemental cooling or an additional heat sink would be required.

Problem and model

The project reconstructed a documented Boeing 747 linear small-perturbation longitudinal model at Mach 0.80 and 40,000 ft and identified the short-period and phugoid modes. A later model-validity audit showed that the original elevator-only long-duration simulations could drive forward-speed departure to about 15.6% of trim. Restoring the documented thrust-control channel and adding a simplified airspeed-hold augmentation reduced the maximum nominal forward-speed departure to 0.227% of trim for PID and 0.194% for LQI.

Open-loop model & validation

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Open-loop pitch response. The uncontrolled aircraft response shows why feedback control is required for practical command tracking.

Model cross-check. MATLAB and Simulink responses were compared to verify that the same longitudinal model was implemented consistently.

Classical controller development

P, PI, and filtered-PID controllers were developed first, then evaluated with a nonlinear elevator actuator using travel and 37°/s rate limits. An unshaped 5° command requested about 185°/s of elevator motion, so a 0.10 s first-order command shaper was introduced. The final reference-shaped PID reduced requested rate to 31.57°/s and achieved 15.33% overshoot with 14.07 s settling time.

P / PI / PID comparison

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Pitch-response comparison. The classical controllers were compared on transient tracking and settling behavior.

Elevator-demand comparison. Control performance was evaluated together with the corresponding elevator command.

Reference-shaped PID. The corrected architecture and command shaping keep requested elevator-rate demand inside the adopted 37°/s actuator limit.

Final PID vs tuned LQI

The final corrected-architecture comparison used the same aircraft, thrust/airspeed augmentation, and nonlinear actuator assumptions for both controllers. The tuned LQI achieved 0.682% nominal overshoot and 5.58 s settling with only 5.32°/s requested elevator rate, versus 15.33%, 14.07 s, and 31.57°/s for the reference-shaped PID.

Final controller comparison

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Final corrected nominal comparison. Tuned LQI provides substantially lower overshoot and faster settling while both controllers converge to the 5° command.

Internal-state comparison. Forward-speed, approximate angle-of-attack, pitch-rate, and pitch-angle responses confirm that LQI's faster tracking is not achieved by larger internal aircraft excursions.

Robustness, uncertainty, and supplementary disturbance testing

Final validation included 20% reduced elevator effectiveness, 2° and 5° step commands, a 5° two-second ramp, internal-state checks, frequency-domain robustness, and 500 reproducible ±10% aerodynamic-model uncertainty trials per controller. All 500 LQI trials satisfied every project criterion. PID remained stable and tracked all 500 cases, with 475/500 satisfying every criterion; the remaining 25 exceeded only the selected 20% overshoot threshold. A +2° control-channel disturbance case was retained as supplementary evidence.

Robustness cases

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20% reduced elevator effectiveness. Both controllers remain stable and pass the adopted transient criteria; LQI retains 1.65% overshoot and 5.49 s settling.

Supplementary +2° disturbance case. The actuator-constrained closed-loop response remains stable during the two-second additive control-channel disturbance.

Final results

The tuned LQI was the highest-performing controller in the final simulation study, while the reference-shaped PID remained a validated lower-complexity benchmark. The values below are from the corrected final architecture in the updated report.

Final comparison: Tuned LQI achieved 0.682% overshoot and 5.58 s settling versus 15.33% and 14.07 s for the reference-shaped PID, with substantially lower actuator-rate demand. LQI assumes full-state feedback; no state estimator was developed.

Validated structural baseline

The 3 mm 6061-T6 aluminum baseline was checked three ways: modal FEA, a simplified analytical cantilever estimate, and mesh refinement. SOLIDWORKS predicted 136.19 Hz for first bending and 381.54 Hz for first torsion; the analytical bending estimate was 108.87 Hz, about 20.06% lower as expected for the simplified beam model. Mesh refinement changed the torsional result by only about 0.005%.

Controlled design trade studies

Thickness, span, material, root-support stiffness, and sweep were varied systematically. Span strongly affected flexibility, while the corrected constant-area sweep study showed that isolated tip-chord offset changed the first two natural frequencies by less than 1%. A first-order bonded-joint stiffness estimate of 1×10¹⁰ N/m produced a 128.64 Hz lowest mode, within about 5.5% of the fully fixed reference. Simplified carbon/epoxy screening gave the best stiffness-to-mass result, but was not treated as a laminate-ready design.

Aerodynamic load screening

The static study used two load levels. The original p = q case was retained only as a conservative unit-coefficient reference for consistent speed and thickness comparisons. At 100 m/s it produced 31.50 MPa maximum stress and 1.716 mm displacement. A more physical finite-wing screening model tied equivalent pressure to angle of attack: the 5° case at 100 m/s used 960 Pa and was validated in SOLIDWORKS at 4.94 MPa maximum stress and 0.269 mm displacement.

Preliminary aeroelastic screening

The baseline bending and torsional modes were separated by a frequency ratio of about 2.80. Reduced-frequency analysis connected those structural modes to flight speed, but no flutter speed is claimed: structural damping, aerodynamic damping, unsteady aerodynamic stiffness, and a coupled flutter eigenvalue solution were outside the study.

Final design result

Among the fully evaluated aluminum thicknesses, the 3 mm fin was retained as the best-balanced configuration. The 4 mm design reduced stress and deflection further but increased mass by 33.3%, while the 2 mm design was substantially more flexible.

Scope limit: The aerodynamic loads remain equivalent-pressure screening models, the baseline root is idealized, and no formal coupled flutter solution or fatigue-life prediction is claimed.