Blue Robotics T200 Thruster

• Blue Robotics T200 thruster is an electric marine actuator designed for small AUV and USV propulsion, featuring precise high-fidelity dynamic modeling.
• It serves as a platform for evaluating advanced control strategies, including model reference control and metaheuristically tuned PID, under realistic disturbance scenarios.
• Performance evaluations reveal that refined control methods (MRC–R* and IMC*) reduce energy consumption and actuator stress compared to conventional PID controllers.

The Blue Robotics T200 thruster is a widely utilized electric marine actuator, frequently deployed as the primary propulsion mechanism for small autonomous underwater vehicles (AUVs) and uncrewed surface vessels (USVs). In advanced control research, the T200 serves as a canonical actuator for evaluating closed-loop strategies under realistic disturbances. Recent work has characterized the T200 in a high-order dynamic framework, facilitating comparative studies between contemporary control methodologies, such as model reference control (MRC) and metaheuristically tuned PID controllers, specifically in scenarios subject to wave disturbances and measurement noise (Türetken et al., 20 Nov 2025).

1. Dynamic Modeling of the T200–Driven Vehicle

A high-fidelity input–output model for the Blue Robotics T200, coupled with the surge-motion kinematics of a 2 kg marine vehicle, has been identified and validated. The combined plant is represented as

$G(s) = T(s)\cdot\frac{1}{ms}$

with $m=2\,\mathrm{kg}$. The T200 transfer function is

$$T(s) = \frac{330.8\,s^2+16\,550\,s+5\,854}{s^4+135.1\,s^3+18\,130\,s^2+550\,400\,s+134\,700}$$

yielding the open-loop plant

$$G(s)=\frac{330.8\,s^2+16\,550\,s+5\,854}{2\,s\,(s^4+135.1\,s^3+18\,130\,s^2+550\,400\,s+134\,700)}.$$

Assumptions underpinning the model include:

• Adequacy of a linear (2 zero/4 pole) system over the typical operational envelope,
• Neglected nonlinearities in the propeller–speed relationship for small oscillations ($T\approx\alpha u_c$),
• Treatment of both wave and noise disturbances as additive inputs. The surge-balance for the true vehicle is

$$(m + X_{\dot u})\,\dot u + D_1\,u + D_2\,u|u| = T(u_c) + F_{\rm dist}(t)$$

where $X_{\dot u}$, $D_1$, and $D_2$ encode added-mass and drag, and $F_{\rm dist}$ aggregates wave and current inputs.

2. Model Reference and PID Controller Architectures

2.1 Model Reference Control (MRC)

The MRC paradigm employs a target second-order reference model with roll-off,

$$M(s)=\frac{\omega_n^2}{s^2+2\zeta\,\omega_n\,s+\omega_n^2}\cdot\frac{1}{1+\tau_f\,s}$$

with $\zeta=0.9$; the "energy-oriented" configuration (MRC–R*) uses $\omega_n\approx3.36\,\mathrm{rad/s}$, $\tau_f\approx0.09\,\mathrm{s}$. The compensator is constructed as

$C_{\rm MRC}(s)=\frac{M(s)}{G(s)[1-M(s)]}.$

No online adaptation is used; instead, MRC–R* is selected via a coarse parameter grid to minimize $\int_0^T u^2(t)\,dt$ under an overshoot constraint ($\mathrm{OS}\le 5\%$).

2.2 PID with Metaheuristic Tuning

PID controllers are implemented in parallel form with a first-order derivative roll-off:

$$C_{\rm PID}(s)=K_p+\frac{K_i}{s}+\frac{K_d\,s}{1+T_f\,s}$$

The gains $[K_p,\,K_i,\,K_d,\,T_f]$ are optimized using three algorithms:

• Particle Swarm Optimization (PSO)
• Differential Evolution (DE)
• Whale Optimization Algorithm (WOA) Tuning is performed over a cost function aggregating performance (ITAE, IAE), energy use, actuator activity, and an overshoot penalty, across four disturbance scenarios (nominal, noise, wave, noise+wave).

3. Performance Evaluation Metrics and Disturbance Profile

Performance is quantified by both tracking and energy/actuator-stress indices, specifically:

• Rise time (10–90%) and settling time (±2%)
• Overshoot (OS); RMS error, MAE, IAE, ITAE over $T=50\,\mathrm{s}$
• Control energy $E_u=\int_0^T u^2(t)\,dt$ and actuator activity $E_{\Delta u}=\int_0^T(\dot u(t))^2dt$ Disturbances consist of an 8 N wave input $d(t)=8\sin(2\pi\cdot0.03\,t)$ and white speed measurement noise with $\sigma=0.12\,\mathrm{m/s}$.

4. Comparative Closed-Loop Results

4.1 Control Energy and Actuator Smoothness

Controller	$\int u^2dt$ [J²]	$\int (\Delta u)^2 dt$ [⋅]
MRC	24,415.6	5.2193·10⁵
MRC–R*	16,196.3	1.4399·10⁵ (–34%/–72% vs MRC)
IMC*	17,215.0	1.6948·10⁵
PID–PSO	30,405.5	6.824·10⁸
PID–DE	30,405.5	6.824·10⁸
PID–WOA	29,091.9	8.686·10⁸

4.2 Tracking Performance (RMS Error, Noise+Wave Scenario)

Controller	RMS [m/s]
MRC	0.162
MRC–R*	0.198
IMC*	0.193
PID–PSO	0.162
PID–DE	0.162
PID–WOA	0.154

MRC–R* achieves the lowest energy consumption and actuator “smoothness” of all tested controllers while maintaining RMS error within 0.2 m/s. IMC* performs comparably. All PID controllers yield similar RMS tracking, but at the cost of orders-of-magnitude higher actuator activity, especially under wave and noise conditions.

5. Control-Theoretic Insights and Practical Implications

MRC–R* and IMC* outperform PIDs due to several architectural features:

• Reference model shaping enables precise closed-loop bandwidth alignment to the primary disturbance frequency (0.03 Hz), reducing high-frequency noise amplification.
• Lack of derivative action on the feedback channel preserves smoothness in the actuator command, mitigating “chattering.”
• Explicit filter roll-off ($\tau_f$) allows direct tracking–energy tradeoff, tuned for minimal controller effort.

In uncontrolled aquatic environments where wave and sensor disturbances are prevalent, these findings suggest that energy-efficient, actuator-friendly closed-loop architectures substantially enhance endurance and mechanical longevity of vehicles using T200 thrusters. In contrast, low-order PID controllers—even under stochastic metaheuristic tuning—are prone to impractically sharp actuation profiles (high $\int(\Delta u)^2\,dt$), increasing both energy demands and mechanical wear.

6. Future Experimental Directions

The simulation-derived control results motivate experimental campaigns involving physical AUV platforms equipped with Blue Robotics T200 thrusters. Validation in instrumented water-tank conditions will be critical for confirming model accuracy, disturbance-rejection behavior, and actuator stress in actual deployments. A plausible implication is that refined model-based control—and in particular, reference-model shaping—will yield substantive operational improvements for electric marine actuators across both research and industrial platforms (Türetken et al., 20 Nov 2025).