Vertical Profiler Simulator

Overview

This project is a Python-based simulator for testing and tuning vertical profiler control systems.

The goal of this project is to create a practical test bed for tuning vertical profiler controllers before testing on physical hardware. The simulator models approximate mass, volume, buoyancy engine size, actuator range, drag, water density, and mission settings so different profiler designs and control strategies can be compared quickly.

The simulator is designed for early testing, controller tuning, and design comparison. It helps show how a vertical profiler responds to different PID gains, vehicle properties, actuator behavior, and target depths.

This is not meant to perfectly replace real pool testing. It is meant to make the tuning process easier before hardware testing.

Purpose

Vertical profilers are hard to tune because they do not respond instantly. The buoyancy engine changes the vehicle’s displacement, but the profiler still has momentum. This can cause overshoot, oscillation, slow settling, or poor target holding.

This simulator was created to help answer questions such as:

• Why does the profiler overshoot the target depth?
• Why does the profiler oscillate even when the proportional gain is low?
• How much does drag affect stability?
• How much does vehicle mass affect control response?
• How does actuator delay affect PID tuning?
• What happens when the same PID values are used on different profiler designs?
• How does the mission behave when the profiler has limited buoyancy force?
• Would a different controller work better than a basic PID loop?

PID Control

The simulator uses a PID control loop similar to the one used on each vertical profiler to drive the buoyancy engine toward the current target depth.

Actuator Model

The simulator converts actuator microseconds into a normalized command value.

The actuator command is centered around the neutral command:

centered command = actuator command - neutral command

The command is normalized by half of the actuator range:

normalized command = centered command / half range

The command is then clamped between -1 and 1:

-1 ≤ normalized command ≤ 1

A direction value is applied so the simulator can handle different actuator wiring or mechanical directions.

final actuator command = direction × normalized command

This command is used to change the simulated buoyancy force.

Buoyancy Model

The simulator calculates buoyancy force from displaced volume:

buoyancy force = water density × gravity × displaced volume

The neutral buoyancy force is based on the profiler’s neutral volume:

neutral buoyancy force = ρ × g × neutral volume

The buoyancy engine changes the effective displaced volume. In the simulator, the actuator command changes buoyancy around the neutral point:

buoyancy force = neutral buoyancy force + command × maximum buoyancy delta

The maximum buoyancy delta is calculated from the buoyancy engine volume:

maximum buoyancy delta = ρ × g × (buoyancy engine volume / 2)

This means the buoyancy engine can make the profiler more or less buoyant around the neutral condition.

Weight Force

Weight force is calculated from the mass of the profiler:

weight force = mass × gravity

Where:

gravity = 9.81 m/s²

Drag Model

The simulator uses a quadratic drag model:

drag force = -0.5 × ρ × Cd × A × v × |v|

Where:

• ρ is water density
• Cd is drag coefficient
• A is reference area
• v is vertical velocity

The v × |v| term makes drag increase with the square of velocity while keeping the drag force opposite the direction of motion.

This is important because drag helps slow the profiler down and reduces overshoot at higher speeds.

Net Force

The net force is calculated from weight, buoyancy, and drag:

net force = weight force - buoyancy force + drag force

In this simulator, increasing depth is treated as downward motion. The sign convention is based on depth increasing as the profiler moves down.

If net force is positive, the profiler accelerates downward.

If net force is negative, the profiler accelerates upward.

Acceleration

The simulator uses Newton’s second law:

force = mass × acceleration

Solving for acceleration:

acceleration = net force / mass

The simulator updates the profiler’s acceleration every time step based on the current force balance.

Velocity Calculation

Velocity is updated by integrating acceleration over time:

velocity = velocity + acceleration × dt

This is a simple numerical integration step.

The simulator uses this velocity to update depth:

depth = depth + velocity × dt

This allows the profiler to keep moving even after the actuator changes command, which is important for modeling overshoot and oscillation.

Velocity and Buoyancy Proof

The simulator’s motion model is based on a proof I did in the past to calculate the velocity of a vertical profiler. Most of the equations are the same.

The basic force relationship is:

net force = mass × acceleration

Depth Calculation

Depth is updated from velocity:

new depth = old depth + velocity × dt

Because the simulation treats depth as positive downward, positive velocity increases depth and negative velocity decreases depth.

The simulator prevents the profiler from going above the water surface:

if depth < 0:
    depth = 0
    velocity = 0

This keeps the simulated vehicle from moving into negative depth.

Sensor Model

The simulator includes a simple depth measurement model.

The measured depth is calculated by adding random noise to true depth:

measured depth = true depth + noise

The noise is generated from a normal distribution.

This helps show how sensor noise can affect PID control and tolerance checking.

Target Tolerance

The simulator checks whether the profiler is within the target tolerance:

abs(measured depth - target depth) <= tolerance

If the profiler is inside the tolerance band during a hold state, the hold timer starts.

If it leaves the tolerance band, the hold timer resets.

This matches the behavior expected from a real profiler mission where the vehicle must actually stay near the target.

Example Run

Why This Is Useful for PID Tuning

A real profiler can be frustrating to tune because editing code and reflashing can take several minutes. In addition, it can be hard to observe the profiler and collect data in a reasonable amount of time. The vehicle has low available force, and drag changes with velocity. The simulator makes it easier to see how different PID gains affect the profiler.

Running the Simulator

Install the required Python packages:

pip install numpy matplotlib

Run the simulator:

python vp_sim.py

If the file has a different name, run:

python your_file_name.py

Requirements

The simulator currently uses:

numpy
matplotlib