summary of actuation.txt

1) Surge speed limit

- u_min = 0.1 m/s

- u_max = 12 m/s (approximately 0.2 to 23 knots operational range)



2) Sway speed limit

- v_min = -3 m/s

- v_max = +3 m/s (realistic lateral drift bounds)



3) Yaw rate limit

- r_min = -0.15 rad/s

- r_max = +0.15 rad/s (approximately ±8.6 deg/s, realistic for large vessel)



4) Shaft speed limits (both azipods)

- n_min = -80 rpm

- n_max = 160 rpm



5) Azimuth angle limits (both azipods)

- alpha_min = -pi rad

- alpha_max = +pi rad (full rotation capability)



6) Commanded shaft limits (both commands n1_c and n2_c)

- same as shaft state limits: [-80, 160] rpm



Moving (state-dependent) actuation limits that are very important:



1) Azimuth steering rate limit

- alpha_dot is limited to ±0.21 rad/s (approximately 12 deg/s)

- This is a mechanical constraint on how fast the azipod can rotate.

- In the NMPC, this is enforced as: |alpha(k+1) - alpha(k)| <= alpha_rate_max * dt



2) First-step azimuth rate constraint

- The first control step must also respect the rate limit relative to the previous applied control.

- Enforced as: |alpha(1) - alpha_prev| <= alpha_rate_max * dt

- Without this, the NMPC may command azimuth angles that are physically unreachable in one timestep.

- Missing this constraint causes trajectory mismatch and oscillatory behavior (spiral instability).



3) Shaft first-order dynamics

- n_dot = (n_command - n_actual) / Tm

- This means shaft speed cannot jump instantly.



4) Shaft acceleration hard limit

- n_dot is clipped to [-10, +10] rpm/s

- So even if command changes a lot, actual shaft speed changes gradually.



5) Time constant Tm depends on current shaft speed

- Tm = 5.65 / (|n|/60) when |n| > 18 rpm, otherwise Tm = 18.83

- Tm is bounded to [1, 20] seconds for numerical stability.

- This gives slower response at low shaft speeds and faster response at high speeds.



6) Heading kinematics

- psi_dot = r

- So heading change rate is directly limited by yaw-rate feasibility.