Drone Height Control Game

A single-file browser-based simulation for teaching manual control, PID control, feedforward compensation, and practical tuning of a simplified drone height-control system.

The app runs entirely in the browser as one HTML file and is suitable for hosting with GitHub Pages. The current public version is available at:

https://bobernhardsson.github.io/dronesimulation/

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Overview

The simulation focuses on vertical motion only. The user can either:

• fly the drone manually by adjusting thrust, or
• tune a PID controller with feedforward to track changing height references.

The interface contains:

• a drone visualization,
• live plots of:
  • height and reference,
  • control signal,
• real-time controller sliders,
• score calculation based on staying within an allowed tracking corridor.

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Dynamic Model

The drone is modeled as:

$$\ddot{x}(t) = k(t)\,u(t) - m(t)\,g$$

where:

• x(t) = height
• u(t) = thrust command
• g = 9.81 m/s²
• k(t) = thrust effectiveness
• m(t) = drone mass

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Plant Variations During Simulation

To make the control problem realistic, the plant changes during flight:

Battery Fade

The gain k(t) slowly decreases over time.

This means the same control signal gives less lift later in the simulation.

Cargo Drop

At 45 seconds, the mass drops by 30%.

This creates a sudden plant change and tests controller robustness.

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Control Modes

1. Manual Control

The user directly controls thrust.

This demonstrates:

• difficulty of manual tracking,
• need for hover thrust,
• effect of changing plant parameters.

Keyboard control is supported.

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2. PID + Feedforward Control

The controller is:

$$u = u_{ff} + u_{PID}$$

with

$$u_{PID} = K\left[ (br-y) + \frac{1}{T_i}\int(r-y)\,dt - T_d \hat{\dot y} \right]$$

where:

• r = reference height
• y = measured height
• b = proportional setpoint weight
• K = controller gain
• Ti = integral time
• Td = derivative time
• ŷdot = low-pass filtered vertical velocity
• u_ff = feedforward hover bias

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Why Use b

The proportional term uses:

$$br - y$$

instead of:

$$r - y$$

This reduces overshoot after step changes.

Typical values:

• b = 1.0 → normal proportional action
• b = 0.5 → softer setpoint response
• b = 0.0 → no proportional response to reference jumps

This is standard setpoint weighting.

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Feedforward Term

The feedforward term supplies most of the thrust needed to hover:

$$u_{ff} \approx \frac{mg}{k}$$

Then PID only corrects:

• transients
• battery fade
• cargo drop
• modeling mismatch

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Derivative Filtering

The derivative part is based on measured motion, not reference error.

This avoids derivative kick when the reference changes suddenly.

A low-pass filter is used:

$$\hat{\dot y} = LPF(\dot y)$$

This gives smoother control signals.

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Anti-Windup

The integral term uses conditional integration anti-windup.

If actuator saturation occurs:

• the integrator is frozen when it would worsen saturation
• it is allowed to move when it helps recover

This prevents runaway integral buildup.

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Tuning Parameters

The player can tune:

• K
• Ti
• Td
• b
• FF

Typical starting values:

• K = 1
• Ti = 1
• Td = 1
• b = 1

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Reference Profiles

Built-in references include:

• Steps
• Sine
• Challenge

The default game mode uses multiple step changes.

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Scoring System

The score no longer penalizes control effort.

Instead, the drone must stay inside a tracking corridor around the reference.

Corridor Width

$$r \pm 0.4$$

Smart Delays

To avoid unfair penalties:

• when reference increases, the lower boundary waits 1.5 seconds
• when reference decreases, the upper boundary waits 1.5 seconds

This rewards practical tracking rather than impossible instant jumps.

Score Meaning

• Stay inside corridor → high score
• Leave corridor → penalty accumulates
• Fast but wild control gives no direct penalty

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Why Overshoot Can Occur

For this drone system (approximately a double integrator), some overshoot after step changes is natural when integral action is used.

This makes the simulator useful for discussing:

• transient design
• damping
• setpoint weighting
• tradeoff between speed and overshoot

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Classroom Use

Useful for teaching:

• manual vs automatic control
• PID tuning
• feedforward vs feedback
• anti-windup
• robustness
• setpoint weighting (b)
• actuator saturation
• double-integrator dynamics

Suggested exercise:

1. Try manual mode
2. Tune hover feedforward
3. Add proportional action
4. Add derivative damping
5. Add integral correction
6. Tune b to reduce overshoot
7. Observe battery fade and cargo drop

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Running Locally

Open index.html in any modern browser.

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GitHub Pages

Host by placing index.html in the repository root and enabling GitHub Pages.

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Possible Future Extensions

• wind disturbances
• measurement noise
• sensor delay
• leaderboard
• saved best scores
• auto-tuning challenge
• 2D drone motion
• Kalman filter mode