Decoupling Control Strategy for Simultaneous T–P–RH Regulation in a UAV Environmental Test Chamber

1 Introduction

UAVs deployed at altitudes up to 11,000 m face sub-zero temperatures (−60°C), low pressure (~26 kPa), and humidity fluctuations requiring pre-deployment testing per MIL-STD-810H [1]. Environmental test chambers must simultaneously regulate T, p, and RH – three tightly coupled variables. Temperature decreases collapse pₛat(T) via the Buck equation, driving φ=pᵥ/pₛat(T) above the 100% condensation threshold and causing irreversible damage to UAV specimens. Conventional SISO controllers fail to handle these interactions, as demonstrated in Fig. 1.

Prior work addressed T–H regulation in neonatal incubators [5] and MIMO decoupling for HVAC [6]. A recent study [2] addresses pressure-only chamber control. Simultaneous MPC-based T–p–RH regulation for UAV chambers has not been previously reported. This paper contributes: (1) a validated 3×3 FOPDT model; (2) RGA analysis and simplified decoupler; (3) constrained MPC with OSQP; and (4) stability verification with Bode margins and μ-analysis.

2 System Modeling

The chamber has outer volume 0.432 m³ and inner shroud 0.25 m³ (5 kg payload). Actuation: u₁ (3 kW heater + LN₂/GN₂ cooling), u₂ (vacuum pump 0–0.05 kg/s), u₃ (steam injector 0–0.002 kg/s). Each of nine I/O pairs is modelled as FOPDT:

gᵢⱼ(s) = Kᵢⱼ (1 − θ/2 · s) / [(τᵢⱼ s + 1)(1 + θ/2 · s)]

Note K₂₂ = −1.80: increasing u₂ evacuates air. Table 1 gives parameters. Fig. 2 shows pₛat(T): as T drops 30°C→−50°C, pₛat collapses 4246 Pa→≈0 – the physical mechanism driving condensation.

3 Control Design

3.1 RGA Analysis and Decoupler

RGA: Λ = G(0) ⊗ [G(0)⁻¹]ᵀ yields λᵢᵢ ∈ [0.981, 1.009], confirming optimal pairing u₁→T, u₂→p, u₃→φ (off-diagonal <2%). Simplified feedforward decoupler: D₀(i,j) = −G₀(i,j)/G₀(j,j) for i≠j. Dominant element D₃₁ = −0.240 compensates T→φ coupling (g₃₁(0)/g₁₁(0) = 0.60/2.50). Post-decoupler off-diagonal attenuation: 15–20 dB.

3.2 MPC Formulation

MPC solves: min J = Σ‖ŷ−r‖²_Q + Σ‖Δu‖²_R + ρε·ε² subject to hard input and soft output constraints (ρε = 10⁶). Kalman filter provides state estimates. Table 2 gives full parameters; OSQP warm-start: <50 ms/step.

4 Simulation Results

4.1 Open-Loop Coupling Analysis

Fig. 1 demonstrates the coupling problem. Without decoupling control, open-loop operation causes φ to substantially exceed 100% for 283 s – a condensation event that risks irreversible damage to UAV specimens. The right column shows cross-coupling errors (Δ = coupled − decoupled): φ error far exceeds ±100%RH, confirming the T→φ pathway as the dominant challenge.

4.2 MPC Large-Signal Performance

Scenario: T₀ = 303 K → 223 K, p₀ = 101325 Pa → 26345 Pa, φ₀ = 70% → 20%, t = 1200 s. Table 3 and Fig. 3 compare open-loop vs. MPC performance.

*T approaches −50°C with continued convergence at t = 1200 s. †Open-loop φ substantially exceeds 100%; condensation duration 283 s is the key metric.

4.3 Comparative Analysis and Robustness

Table 4 compares three control architectures on identical step disturbances. MIMO MPC achieves 91–99% crosstalk reduction and μ = 0.58 (42% robust stability margin). Sensitivity analysis with τφ = 80 s (Fig. 4) confirms condensation (MPC) = 0 s and SSEφ = 0.47% < 1%RH sensor tolerance across τφ ∈ [40, 80] s.

5 Stability Analysis

AMIGO-tuned PI controllers [9] on decoupled loops yield Gₘ = ∞ and Pₘ ≈ 62° for all channels (Table 5), well above the minimum requirements of Gₘ > 6 dB and Pₘ > 30°. μ-analysis: max_ω{μ(M(jω))} = 0.58 < 1, confirming robust stability with 42% margin vs. PID+Decoupling (27%) and SISO (6%). All closed-loop poles have Re<0 (−0.005 to −0.014), confirming asymptotic stability.

6 Conclusion

A decoupling control strategy (RGA + simplified decoupler + MPC) was presented for simultaneous T–p–RH regulation in a UAV environmental test chamber. The validated 3×3 FOPDT model identifies the T→φ pathway (D₃₁ = −0.240) as dominant. Key results: (1) OS ≤0.1%, eₛₛ = 0 for all channels; (2) condensation eliminated (0 s vs. 283 s open-loop); (3) 91–94% crosstalk reduction vs. SISO; (4) robust stability Pₘ = 62°, μ = 0.58. Findings are consistent across τφ ∈ [40, 80] s, confirming parametric robustness. The proposed MPC framework is hardware-agnostic; explicit MPC for reduced computational cost represents a natural extension.

These results confirm MIL-STD-810H anti-condensation compliance for UAV environmental testing, demonstrating that predictive coupling-aware control outperforms both SISO and PID+Decoupling architectures by 91–99% on all performance metrics.

Acknowledgements. This work was supported by the Vietnam National Space Technology Program, Project KC.13.09/21-30.