Long-Endurance HAPS Day–Night Cycle

Problem Setup

Can the HAPS Survive 24–72 Hours?

This problem introduces a simplified high-altitude platform system flying at near-constant altitude. The aircraft must maintain lateral station-keeping while experiencing wind disturbance and repeated day–night solar charging cycles.

The aim is not to create a full aircraft model. The aim is to show the systems-level trade-off: a controller that stabilizes the aircraft may consume too much energy, while an energy-saving controller may fail to reject wind.

Core question:
Can the aircraft survive the mission without energy collapse, actuator saturation, or loss of station keeping?

State 1

Lateral deviation from target path

State 2

Lateral velocity

State 3

Controller effort

State 4

Battery energy

State 5

Solar input and consumed power

State 6

Mission survival status

Why HAPS Endurance Is Different

Short-Term Stability Is Not Enough

A normal control simulation may run for 30 seconds or a few minutes. A HAPS endurance mission must survive across many hours or days. That means the aircraft must remain dynamically stable and energetically sustainable.

A controller can look excellent in a short simulation but fail over a long mission because every correction consumes power.

Simplified Flight Dynamics Model

One-Dimensional Lateral Deviation Model

The HAPS is represented using a simple lateral station-keeping model. The state is lateral displacement error $x$ and lateral velocity $\dot{x}$.

$$ \ddot{x} = -c\dot{x} + u + d(t) $$

where $x$ is lateral displacement error, $\dot{x}$ is lateral velocity, $c$ is aerodynamic damping, $u$ is controller command, and $d(t)$ is wind disturbance.

This is intentionally simple, but it keeps the important engineering connection: disturbance produces deviation, control rejects deviation, and control effort consumes energy.

Wind Disturbance Model

Persistent Wind Plus Gusts

The disturbance model combines slow wind variation with gust-like oscillations. Stronger wind requires more controller effort and therefore higher power consumption.

$$ d(t) = W\sin(2\pi f_g t) + 0.35W\sin(2\pi(3f_g)t) $$

The simulator lets you change wind strength and gust frequency to test calm, moderate, and severe conditions.

Controller Model

PD Station-Keeping Controller

The aircraft uses a PD-style controller to reduce displacement and velocity error.

$$ u = -K_p x - K_d\dot{x} $$

Conservative gains use less energy but allow larger deviations. Aggressive gains improve station-keeping but increase control power demand.

Actuator and Control Effort

The Controller Cannot Command Infinite Correction

A real aircraft has actuator limits. The commanded control effort is clipped to a maximum available value.

$$ u_{actual} = clamp(u, -u_{max}, u_{max}) $$

Actuator saturation means the controller may be asking for correction that the hardware cannot deliver.

Battery and Solar Energy Model

Energy Is the Heart of the Problem

The battery changes according to solar input, base aircraft power demand, and additional power used by control effort.

$$ E_{battery}(t+\Delta t) = E_{battery}(t) + P_{solar}\Delta t - P_{base}\Delta t - P_{control}\Delta t $$

Control power is approximated using a quadratic relation:

$$ P_{control} = k_u u^2 $$

This captures the key idea: small control effort is cheap, while aggressive correction becomes expensive.

Day–Night Cycle

Smooth Solar Charging Across Each 24-Hour Cycle

The solar input is represented using a smooth day–night cycle. Solar power rises after sunrise, peaks during the day, and falls to zero at night.

$$ P_{solar} = P_{max}\max\left(0,\sin\left(\frac{2\pi t}{24}\right)\right) $$

The aircraft may survive one cycle but slowly lose energy over several cycles if daytime recharge does not fully recover nighttime drain.

Interactive Mission Simulator

Simulate 24–96 Hours of HAPS Endurance

Use the sliders and scenario buttons to test whether the aircraft survives. The simulation tracks lateral deviation, velocity, controller effort, battery state, solar input, total demand, and failure mode.

Preset Scenarios

Mission and Energy Inputs

Mission Duration: 72 hours

Initial Battery: 80%

Battery Capacity: 120 kWh

Solar Power: 12 kW

Base Power Demand: 4.5 kW

Energy Cost of Control: 1.2

Wind, Controller, and Actuator Inputs

Controller Mode

Wind Strength: 0.08

Wind Gust Frequency: 0.18 cycles/hour

Controller Aggressiveness Kp: 0.18

Damping Gain Kd: 0.85

Actuator Limit: 0.18

Allowable Deviation: 8 km

Aerodynamic Damping c: 0.12

Adjust the mission, wind, controller, actuator, and energy settings to test survival.

Mission status will appear here after simulation.

Battery Margin

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Control Energy

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Station-Keeping Error

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Survival Status

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Actuator Saturation

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Energy Margin

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Compare Controller Strategies

Conservative vs Balanced vs Aggressive Control

Different controllers produce different system-level outcomes. The best controller is not always the one with the smallest deviation over a short time window.

Strategy	Control Behaviour	Energy Behaviour	Risk
Conservative	Low correction effort	Lower control energy	Large station-keeping error
Balanced	Moderate correction effort	Moderate power draw	Usually safest trade-off
Aggressive	Strong correction effort	High control energy	Battery collapse or saturation
Custom	User-defined gains	Depends on tuning	Useful for exploration

Failure Mode Diagnosis

How the Mission Can Fail

This problem is powerful because failure can happen in different ways. A HAPS mission is not only a control problem and not only an energy problem. It is a coupled system.

Failure 1 — Battery Collapse

The aircraft remains controlled but runs out of energy overnight.

Failure 2 — Loss of Station Keeping

The battery survives, but the controller is too weak to fight wind.

Failure 3 — Actuator Saturation

The controller asks for correction, but hardware cannot deliver it.

Failure 4 — Slow Energy Decline

The aircraft survives one day but fails after repeated day–night cycles.

Failure diagnosis will update after the simulation runs.

Engineering Interpretation

Endurance Is a Systems Problem

In long-endurance flight, the controller, actuator, wind environment, solar array, base power demand, and battery capacity all interact. Improving one metric may damage another.

Better station keeping → more control effort → higher power demand → lower battery margin

Lower control effort → better energy margin → larger deviation → possible mission failure

The engineering question is not only: “Is the controller stable?”
The stronger question is: “Can the whole system survive the mission envelope?”

Takeaway

What This Problem Shows

For long-endurance HAPS flight, stability is only one part of success.

control stability + actuator feasibility + wind rejection + positive energy balance = mission survival

The aircraft must remain controllable, stay within actuator limits, survive wind disturbances, and maintain a positive energy balance across repeated day–night cycles.

A controller that looks excellent over 30 seconds may fail over 48 hours because endurance depends on the whole system, not only the control law.