Model & Simulation Parametrization¶
This section presents the WavePiston model parametrization and simulation setup used throughout the competition. All quantities, conventions, and numerical configurations are identical for all participants to ensure a fair and consistent comparison of submitted control strategies.
WavePiston Device Parametrization¶
The WavePiston device dynamics are represented as a single-degree-of-freedom (heave) oscillator, governed by equation (1). The following parameters fully characterize the model accessible to participants.
Variable |
Description |
Value / Units |
|---|---|---|
\(m_w\) |
Sail module mass |
2800 kg |
\(m_\infty\) |
Added mass at infinite frequency |
71795.62 kg |
\(M = m_w + m_\infty\) |
Total effective mass |
74595.62 kg |
\(\mathbf{A_r}\) |
Radiation state matrix |
\(\begin{bmatrix} -2.7078 & 3.1078 & -2.7078 & 2.7078 \\ -1.9403 & 1.5403 & -1.5403 & 1.5403 \\ -1.3122 & 1.3122 & -1.3122 & 5.3560 \\ 2.0435 & -2.0435 & -2.0003 & -2.0435 \end{bmatrix}\) |
\(\mathbf{B_r}\) |
Radiation input matrix |
\(\begin{bmatrix} 2.7078 & 1.5403 & 1.3122 & -2.0435 \end{bmatrix}^T\) |
\(\mathbf{C_r}\) |
Radiation output matrix |
\(\begin{bmatrix} 23214.043986 & 23198.820014 & -44584.0254375 & -141900.8654375 \end{bmatrix}\) |
\(\rho\) |
Water density |
1025 kg/m³ |
\(A_{sail}\) |
Effective sail area |
32.0 m² |
\(C_D\) |
Quadratic viscous drag coefficient |
1.5 |
\(x_{\max}\) |
Maximum allowed displacement |
2.0 m |
\(F_{pto,\max}\) |
Maximum allowed PTO (control) force magnitude |
1.0 MN |
Up-wave measurement location |
Surface elevation probe position |
\(x = -10\) m |
Note
These values are public and identical for all participants. Any additional internal parameters remain undisclosed.
Radiation state-space model matrices are also provided (in full precision) with the WAPPAC simulation platform (see Getting Started with WAPPAC Simulator for details).
Excitation Force Characterization¶
The excitation force acting on the WavePiston sail is defined by the interaction between the incident wave surface elevation and the excitation force kernel of the WavePiston device.
Three predefined sea states, representing realistic conditions at a potential WavePiston deployment site, are used in the competition. These remain undisclosed to participants.
Although the excitation force time series \(F_{ex}(t)\) is not directly provided, participants may estimate or reconstruct it if needed, using the following available information and resources:
Real-time sail motion data: The instantaneous sail position and velocity available within the controller function (see Writing Your Controller for details).
Excitation force kernel: The frequency-domain excitation kernel distributed with the WAPPAC simulation platform (see Getting Started with WAPPAC Simulator for details).
Up-wave surface elevation measurement: The surface elevation probe located 10 m up-wave of the device (\(x = -10\) m), available to participants during the scoring interval via the simulation interface (see Numerical Implementation and Writing Your Controller for details).
Public WavePiston model parametrization: The shared model parameters provided above.
In summary, while direct excitation force data remain undisclosed, participants are equipped with sufficient information to implement observer-based or model-driven estimators as part of their control strategy.
Note: Linear wave theory is used for modeling the wave surface elevation, using the following associated parameters:
Variable |
Description |
Value / Units |
|---|---|---|
\(\rho\) |
Seawater density |
1025 kg/m^3 |
\(d\) |
Seawater depth |
10000 m (~Inf) |
Simulation Parametrization¶
The simulation environment defines the time integration, control update, and transient handling procedures. All control strategies are evaluated under the same deterministic numerical setup.
Variable |
Description |
Value / Units |
|---|---|---|
Integrator |
Time integration method |
4th-order Runge–Kutta (RK4) |
\(\Delta t\) |
Fixed integration time step |
0.05 s |
– |
Controller update interval (ZOH) |
\(\Delta t\) |
\(t_{\text{init}}\) |
Simulation initial time |
0 s |
\(t_{\text{end}}\) |
Simulation end time |
Sea-state dependent |
\(T_{\text{ramp}}\) |
Excitation force ramp-up duration |
20 s |
\(T_0\) |
Scoring interval start time |
30 s |
Initial conditions |
Sail position, velocity, and radiation states |
\(x(0)=0\), \(\dot{x}(0)=0\), \(\mathbf{\xi}(0)=\mathbf{0}\) |