Design and Implementation of a Depth Control System for a Submersible Vehicle at Various Operating Depths

Water quality monitoring in reservoirs is essential for sustainable water resource management because reservoirs support domestic consumption, irrigation, fisheries, and hydroelectric power generation [1]. Water quality conditions are often non-uniform across different depths due to vertical stratification, which affects parameters such as temperature, pH, dissolved oxygen, and pollutant concentrations [2]. Studies conducted in Saguling Reservoir reported lead (Pb) concentrations exceeding water quality standards at several depth levels, highlighting the importance of monitoring water quality at multiple depths [3]. Furthermore, previous studies have shown that thermal and physicochemical stratification can occur not only in deep waters but also in shallow water bodies with depths of only 1–2 m, resulting in significant variations in water quality characteristics between surface and bottom layers [4]. Vertical profiling measurements have demonstrated that changes in water quality parameters can be observed within depth intervals as small as 10–20 cm, indicating the need for accurate depth-specific measurements to obtain representative water quality data [5].

Conventional water quality monitoring methods generally rely on manual sampling techniques such as spot sampling and Patterson grab samplers, although transporting collected samples to laboratories may alter their physical and chemical characteristics due to temperature changes, contamination, and transit time, thereby reducing measurement accuracy [6]. Other approaches, such as submersible pumps, are primarily designed for sample collection and still require integration with automated sensing systems to enable continuous monitoring [7]. These limitations indicate the need for more efficient and automated water quality monitoring technologies capable of performing in-situ measurements at various depths.

Recent developments have shifted water quality monitoring toward underwater vehicle-based systems. Autonomous underwater vehicles (AUVs) can perform underwater missions without direct human intervention and are widely used in scientific, military, and commercial applications [8]. They are generally classified as thruster-based vehicles using propellers for propulsion and depth control or buoyancy-based vehicles regulating motion through buoyancy variation [9]. Equipped with environmental sensors to enable more efficient and flexible monitoring at multiple depths than conventional sampling methods.

Previous studies have developed buoyancy-engine-based submersible platforms for operation at varying depths. In such systems, depth regulation is achieved by changing the vehicle's buoyancy through a fluid-transfer or variable-volume mechanism. However, the previously developed platform required an additional ballast mass of 3.7 kg to achieve neutral buoyancy, while its layered pipe structure was susceptible to leakage during operation. Furthermore, sensor data could not be monitored in real time and had to be retrieved after the vehicle surfaced, limiting its effectiveness for continuous monitoring applications. These limitations indicate the need for an alternative submersible configuration that can regulate depth through direct propulsion while maintaining a compact and watertight structure. In contrast to the buoyancy-based approach, the proposed vehicle directly generates vertical thrust using electrically driven thrusters rather than relying on buoyancy adjustment.

In this study, three vertical thrusters are employed to control the vehicle's heave motion while maintaining a compact and mechanically simple propulsion system. Two vertical thrusters can generate sufficient net vertical force but provide a less symmetrical force distribution around the vehicle center, whereas four or more thrusters offer additional actuation capability and redundancy at the expense of increased actuator count, power requirements, mechanical complexity, hydrodynamic drag, and space requirements. Therefore, three thrusters positioned symmetrically at 120° intervals were selected as a practical compromise between thrust distribution, stabilization, and system simplicity [10, 11]. This configuration supports accurate and repeatable heave control required to reach and maintain predefined measurement depths for multi-depth monitoring, rather than full multi-axis or six-degree-of-freedom maneuverability.

To address these challenges, this study develops and experimentally evaluates a thruster-based submersible vehicle for automatic depth control within the tested depth range of 1–3.5 m, while its watertight operation is additionally evaluated up to 4 m. The vehicle employs a watertight mechanical structure and three vertically oriented thrusters arranged at 120° intervals to control the heave motion and maintain the desired depth [12]. The thrusters are regulated by electronic speed controllers (ESCs) using pulse width modulation (PWM) signals from a microcontroller [13]. A pressure sensor provides depth feedback for a proportional-integral-derivative (PID) controller that regulates vertical thrust based on the difference between the measured depth and the desired setpoints to assess steady-state error (SSE) and settling time.

To maintain depth stability, a PID controller is implemented as the primary control method. PID control combines proportional, integral, and derivative actions to minimize the error between the measured depth and the desired setpoint [14]. The proportional term responds to current error, the integral term eliminates SSE, and the derivative term reduces overshoot by considering error variation [14]. Compared with more advanced control approaches such as fuzzy PID and linear quadratic regulator, PID offers simpler implementation, easier tuning, and lower computational requirements while maintaining satisfactory steady-state performance [15-17]. Depth feedback is provided by the MS5837-30BA pressure sensor, which supports measurements up to 30 bar with a resolution of 0.02 mbar and communicates through the I²C interface [18]. Depth estimation is obtained from hydrostatic pressure measurements, which are directly related to water depth according to the hydrostatic pressure principle [18]. Since hydrostatic pressure directly affects underwater vehicle operation and structural integrity, accurate depth sensing is essential [19].

The technical contribution of this work is the implementation and experimental evaluation of a compact three-thruster depth-control architecture that directly actuates vertical motion, in contrast to the buoyancy-based depth-regulation approach used in previous work. The system is evaluated through pressure-sensor calibration, PID parameter tuning, multi-depth experiments, and a full-mission test. Performance is assessed using SSE and settling time to evaluate the capability of the system to maintain stable vertical positioning at different depths. The developed depth-control subsystem is intended to provide a foundation for future autonomous multi-depth reservoir monitoring applications.

3.1 Experimental conditions

The experiments were conducted in a controlled swimming pool environment at the SARAGA ITB Diving Pool, Bandung, West Java, Indonesia. The pool has a maximum depth of 4.6 m and was used to evaluate the depth-control performance of the proposed submersible vehicle. The experimental conditions were maintained as consistently as possible for all tests. Before each depth-control experiment, the vehicle was initially positioned at the water surface according to the test procedure. The selected depth setpoints were 1 m, 2 m, 3 m, and 3.5 m. The full-mission experiment consisted of sequential transitions between these depth setpoints. The main experimental conditions are summarized in Table 3.

Table 3. Experimental conditions

3.2 Buoyancy calibration results

Buoyancy calibration was performed by directly adjusting the vehicle mass in the pool. The initial mass of the submersible was 7.2 kg, equivalent to a gravitational force of approximately 70.6 N. Test results showed that the vehicle still experienced positive buoyancy, meaning the buoyancy force was greater than the gravitational force, causing the vehicle to tend to float on the surface. This indicates that the net force on the vehicle was still directed upward.

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Figure 13. Buoyancy calibration result of the submersible

To achieve neutral buoyancy, ballast weights were added gradually through several tests. In the final configuration, 4.25 kg of ballast was added, bringing the total vehicle mass to 11.45 kg, equivalent to a gravitational force of approximately 112.21 N, as shown in Figure 13.

The test results showed that after adding the ballast, the vehicle achieved neutral buoyancy with a slight tendency toward positive buoyancy. This condition was considered optimal because the vehicle slowly ascends when the thrusters are not operating, which facilitates depth control during testing. In addition, the pressure sensor remains submerged even when the vehicle is near the surface, resulting in more stable and consistent water pressure readings. The final buoyancy calibration result is shown in Figure 14.

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Figure 14. Buoyancy results of the submersible

3.3 Pressure sensor calibration results

Depth estimation was obtained from the MS5837-30BA pressure sensor based on the hydrostatic pressure principle, where water depth is proportional to the pressure difference between the measured pressure and atmospheric pressure. The depth was calculated using the equation:

$P_{{water}}=\rho \cdot g \cdot h_{{water}}$           (8)

$h_{{water}}=\frac{P_{{water}}}{\rho \cdot g}$           (9)

$h_{{water}}=\frac{P_{{sensor}}-P_{{atm}}}{\rho \cdot g}$     (10)

where, the variables are defined as follows:

$h_{{water}}$ = water depth (meter/cm)

$P_{{water}}$ = water pressure (mbar)

$P_{{sensor}}$ = pressure measured by the sensor in water (mbar)

$P_{{atm}}$ = atmospheric pressure obtained from the sensor logger application (mbar)

$\rho$ = freshwater density (1000 kg/m³)

$g$ = gravitational acceleration (9.81 m/s²)

The atmospheric pressure value was obtained from a smartphone barometric sensor and recorded as 935.325 mbar during the experiment.

Based on Table 4, the raw pressure-sensor measurements showed deviations from the reference depths, with an average error of 7.29%. Therefore, a calibration procedure was applied to improve the accuracy of the depth measurements.

Table 4. Pressure sensor test results before calibration

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Figure 15. Linear regression model for pressure sensor calibration

A linear regression analysis was performed by comparing the raw sensor measurements with the corresponding ground-truth depth values, as shown in Figure 15. The resulting calibration equation is expressed as:

$y=1.0423 x+0.0517$         (11)

where, x represents the raw depth measurement obtained from the sensor and y represents the reference depth value. The regression model achieved a coefficient of determination (R²) of 0.9991, indicating an excellent linear relationship between the sensor measurements and the reference values.

The corrected measurements are presented in Table 5. When evaluated using a separate post-calibration dataset, the average measurement error decreased to 2.22%. The calibrated depth values were subsequently used as feedback for the PID-based depth-control system.

Table 5. Corrected pressure sensor measurements after calibration

The calibration process reduced the average measurement error from 7.29% to 2.22%, based on a separate set of post-calibration measurements that was not used to determine the regression coefficients. This result indicates that the linear regression model improved the agreement between the MS5837-30BA pressure sensor measurements and the reference depth values when evaluated using separate measurements. Therefore, the regression equation obtained from the calibration dataset was integrated into the depth measurement system to provide more reliable depth feedback for the PID-based depth controller.

3.4 Proportional-integral-derivative parameter tuning results

The PID parameters were determined through a sequential experimental tuning procedure consisting of proportional (P), proportional-integral (PI), and PID stages. All configurations were tested at a fixed depth setpoint of 2 m to provide consistent operating conditions. The controller performance was evaluated using SSE settling time, overshoot, and response stability, with SSE prioritized because accurate depth holding was the primary control objective.

The proportional gain, K_p, initially varied between 200, 350, 500, and 800 while K_i and K_d were set at zero. The results were used to select suitable K_p candidates for the subsequent PI stage. The integral gain was then introduced to reduce the remaining SSE, followed by the derivative gain to improve transient damping and response stability.

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Table 6. Control system with proportional gain (K_p)

Table 7. Control system with proportional-integral (PI) gain (K_p, K_i) variation

Table 8. Control system with PID gains (K_p, K_i, K_d)

Based on the depth response curves shown in Figure 16, all tested K_p values successfully drove the vehicle toward the 2 m setpoint, with oscillations occurring before reaching steady-state conditions. However, proportional control alone was unable to eliminate the SSE because no integral action was applied. Increasing K_p generally reduced the time required to approach the target depth, although the system dynamics were also influenced by overshoot and oscillatory behavior.

The results summarized in Table 6 show that the tested proportional gains produced different trade-offs between steady-state accuracy and settling time. Among the tested configurations, K_p = 500 provided a relatively low SSE, whereas K_p = 800 produced the fastest settling response. Although increasing K_p generally improved the response speed, the relationship was not strictly proportional because the vehicle dynamics were affected by transient overshoot and oscillations.

Based on the overall response characteristics, K_p = 500 and K_p = 800 were selected as candidates for the subsequent PI tuning stage. The selection of these two gains allowed the effect of additional integral action to be evaluated using configurations with different proportional-response characteristics. The K_p = 500 configuration was retained because of its relatively low SSE, whereas K_p = 800 was retained because it provided the fastest settling response among the tested proportional gains.

Based on the depth responses shown in Figure 17, the addition of the integral component significantly improved depth regulation performance compared with proportional control alone. For all tested parameter combinations, the vehicle successfully reached the 2 m setpoint and exhibited considerably smaller SSE, indicating that the integral action effectively compensated for the residual error observed in the proportional-only controller. However, an initial overshoot followed by oscillatory behavior was still observed before the system reached steady-state conditions.

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Transient performance also varied with the integral gain. Increasing K_i from 15 to 30 generally increased the settling time, indicating that excessive integral action could prolong the stabilization process. Therefore, the PI responses demonstrate a trade-off between steady-state accuracy and transient response, where a higher integral gain can reduce the residual error but may increase the settling time.

The results in Table 7 are consistent with the responses shown in Figure 17. The addition of integral action reduced the SSE compared with proportional control alone by compensating for residual errors. However, the different PI configurations exhibited a trade-off between steady-state accuracy and transient response, as higher integral action could prolong the stabilization process. K_p = 500, K_i = 30 configuration provided the lowest SSE, whereas K_p = 800, K_i = 15 produced the fastest settling response. These PI configurations were subsequently evaluated with derivative action.

A derivative gain of K_d = 5 was added to the four PI configurations to investigate its effect on transient damping and response stability. As shown in Figure 18, all tested PID configurations reached the 2 m setpoint and maintained stable depth after the transient phase. The derivative action reduced oscillatory behavior and improved the damping of the response, resulting in smoother convergence toward steady-state conditions.

The performance results are summarized in Table 8. Compared with the PI configurations, the addition of derivative action improved the overall response by reducing the SSE and enhancing transient stability. The different PID configurations still exhibited trade-offs between steady-state accuracy and settling time; therefore, the final controller parameters were selected based on the overall response characteristics rather than a single performance metric.

The derivative action also improved the transient response characteristics. The measured settling times ranged from 8.30 s to 14.20 s, demonstrating that the controller was able to achieve stable operation within a relatively short period. Compared with the PI controller, the addition of the derivative term reduced oscillatory behavior during the transient phase and improved overall system damping, resulting in smoother depth regulation.

Among the tested PID configurations, K_p = 500, K_i = 15, and K_d = 5 achieved the lowest SSE of 0.27 cm while maintaining an acceptable settling time of 14 s. Although the K_p = 800, K_i = 15, K_d = 5 configuration produced a shorter settling time of 8.30 s, its SSE was higher at 1.60 cm. Therefore, K_p = 500, K_i = 15, and K_d = 5 were selected as the final controller parameters because they provided the most favorable balance between steady-state accuracy and transient response among the tested configurations. These parameters were subsequently fixed for the depth-variation and full-mission experiments.

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During the PID tuning process, most parameter configurations were evaluated in a single experimental run. The purpose of this stage was to compare the control response of different parameter combinations and identify a suitable controller configuration rather than to statistically characterize the performance of each configuration. Therefore, the values reported in Tables 6–8 represent the measured response obtained for each tested configuration. The selected PID parameters were subsequently evaluated through depth-variation and full-mission experiments to assess their performance under different operating conditions.

The repeated measurements generally exhibited similar response characteristics under the same tuning condition. Because the number of repetitions was not consistent across all configurations, the tuning results are presented as measured performance values rather than as a statistically balanced comparison. Where repeated measurements were available, their consistency was used as an additional qualitative indication of repeatability. No standard deviation or confidence interval was calculated for configurations with insufficient repeated measurements. The SSE reported in the experimental results represents the average steady-state depth error calculated from the measurement samples within the steady-state interval of each test. It should therefore not be interpreted as an average across repeated experimental runs.

3.5 Final proportional-integral-derivative parameter value testing

After the PID tuning process, the selected controller parameters of K_p = 500, K_i = 15, and K_d = 5 were fixed and evaluated at different depth setpoints. The controller was tested at 1 m, 2 m, 3 m, and 3.5 m without retuning to evaluate whether the parameters selected at the 2 m tuning condition could maintain stable depth regulation across the tested operating range. SSE and settling time were used to assess the consistency of the controller performance.

Overall, the results presented in Figure 19 demonstrate that the PID controller with these parameters successfully maintained stable depth control at setpoints of 1 m, 2 m, 3 m, and 3.5 m. In all experiments, the submersible reached the desired depth after experiencing an initial overshoot and transient oscillations, followed by stable steady-state behavior. As the depth setpoint increased, larger overshoots and slightly longer settling times were observed due to the greater thrust required to overcome increased hydrostatic pressure and hydrodynamic resistance. Nevertheless, once the system reached the settling region, depth fluctuations remained small across all tested setpoints. These results indicate that the selected PID parameters maintained stable depth regulation across the tested depth setpoints without requiring retuning, although the control performance varied with operating depth.

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Importantly, the PID parameters were not retuned between the tested depth setpoints. The increase in SSE at 3 m and 3.5 m indicates that the controller performance was affected by the operating depth; however, the vehicle remained within the predefined depth tolerance at all tested setpoints. Therefore, the selected parameters could be applied across the tested depth range without parameter adjustment, although identical control performance was not obtained at every depth.

Based on the results summarized in Table 9, all measured SSE values remained well below the predefined ±20 cm tolerance limit, indicating that the selected PID parameters maintained the vehicle close to the target depth across all tested setpoints. Although the control performance varied with operating depth, the results demonstrate satisfactory depth-control accuracy. The settling-time results indicate that the system reached steady-state conditions within a practical period after each depth transition and provide a reference for determining the required waiting time before measurements are performed at the target depth.

Table 9. Control system performance at various depth setpoints using final Proportional-Integral-Derivative (PID) parameters

Overall, the experimental results indicate that the PID controller with K_p = 500, K_i = 15, and K_d = 5 maintained stable depth regulation across the tested depth setpoints without requiring retuning. Although the control performance varied with operating depth, all tested setpoints remained within the predefined ±20 cm depth tolerance. Therefore, within the tested pool conditions and depth range, the selected PID parameters were able to regulate the vehicle depth at multiple setpoints.

3.6 Final mission test of the submersible proportional-integral-derivative control system

As a final evaluation stage, a full-mission experiment was conducted to assess the performance of the selected PID controller during sequential depth transitions. The submersible moved from the water surface to setpoints of 1 m, 2 m, 3 m, and 3.5 m before returning to the surface, while maintaining its position for approximately 2 min at each depth. The experiment evaluated the controller's ability to perform sequential transitions, maintain stable depth at each setpoint, and sustain consistent performance throughout the mission. Settling time was also recorded to characterize the time required to reach steady-state conditions after each transition.

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Figure 20. Full mission depth response and PWM signal at sequential setpoints (1 m, 2 m, 3 m, 3.5 m)

Based on the full-mission response shown in Figure 20, the PID controller with that parameter successfully guided the submersible through sequential depth transitions from 1 m to 3.5 m and back to the surface. Several full-mission trials were conducted using the same PID parameters, and the trial showing representative overall depth-control performance was selected for presentation. At each transition, the system exhibited a transient response followed by overshoot and damped oscillations before reaching steady-state conditions. Despite the successive changes in setpoint, the controller maintained stable depth tracking without significant instability.

The settling behavior varied across the successive transitions, as summarized in Table 10. The decreasing settling time during later transitions suggests that the response was influenced by the transition conditions and the depth increment between consecutive setpoints. The PWM response followed the corresponding depth transitions: the control output increased to generate the required thrust and decreased as the vehicle approached the desired depth, requiring only small corrective actions during steady-state operation.

The results summarized in Table 10 show that all SSE values remained well within the predefined ±20 cm tolerance, indicating that the selected PID controller maintained the desired depth throughout the sequential mission. Compared with the single-setpoint experiments, the selected full-mission trial produced lower SSE values, particularly at the deeper setpoints, demonstrating that stable depth regulation was maintained during successive setpoint transitions. The settling-time results also indicate that the system reached stable operating conditions after each transition and provide a practical reference for determining the waiting period before initiating measurements at the target depth.

Table 10. Control system performance during full mission test at sequential depth setpoints

The full-mission results demonstrate that the integration of calibrated pressure feedback and closed-loop PID control enabled stable depth tracking across the tested operating range under controlled pool conditions. The variation in control performance among the setpoints may be associated with vehicle dynamics, including buoyancy, hydrodynamic resistance, inertia, and actuator behavior. Near-surface operation may also be more sensitive to disturbances and actuator dead-zone effects when relatively small corrective thrust is required.

From an engineering perspective, the three-thruster configuration provided sufficient vertical force distribution for controlled ascent, descent, and depth holding. Combined with calibrated pressure feedback, this configuration offers a practical platform for collecting water-quality measurements at predefined depth layers. Nevertheless, the fixed PID parameters were optimized under controlled pool conditions and may not provide the same performance in the presence of currents, waves, battery-voltage variation, or prolonged sensor drift. The present system is also limited to vertical regulation and does not actively compensate for horizontal displacement. Future work should therefore evaluate long-duration operation in natural water bodies and investigate multi-axis, adaptive, or disturbance-aware control strategies.