pid_controlled_plant

PID-controlled plant with actuator saturation.

pid_controlled_plant(kp=6.0, ki=2.0, kd=1.0, stiffness=3.0, damping=0.6, setpoint_amp=2.0, setpoint_freq=1.0, u_min=-1.0, u_max=1.0, initial_state=None)

Create a PID-controlled second-order plant with saturation.

The state is [position, velocity, integral_error]. The controller tracks a sinusoidal setpoint and saturates the control input, yielding hybrid locations.

Parameters:

Name	Type	Description	Default
kp	float	Proportional gain.	6.0
ki	float	Integral gain.	2.0
kd	float	Derivative gain.	1.0
stiffness	float	Plant stiffness.	3.0
damping	float	Plant damping.	0.6
setpoint_amp	float	Setpoint amplitude.	2.0
setpoint_freq	float	Setpoint frequency.	1.0
u_min	float	Minimum control input.	-1.0
u_max	float	Maximum control input.	1.0
initial_state	ndarray | None	Optional initial state.	None

Returns:

Type	Description
HybridSystem	HybridSystem configured for PID control with saturation.

Source code in src/flowcean/hybrid/benchmarks/pid_controlled_plant.py

def pid_controlled_plant(
    kp: float = 6.0,
    ki: float = 2.0,
    kd: float = 1.0,
    stiffness: float = 3.0,
    damping: float = 0.6,
    setpoint_amp: float = 2.0,
    setpoint_freq: float = 1.0,
    u_min: float = -1.0,
    u_max: float = 1.0,
    initial_state: np.ndarray | None = None,
) -> HybridSystem:
    """Create a PID-controlled second-order plant with saturation.

    The state is [position, velocity, integral_error]. The controller tracks a
    sinusoidal setpoint and saturates the control input, yielding hybrid
    locations.

    Args:
        kp: Proportional gain.
        ki: Integral gain.
        kd: Derivative gain.
        stiffness: Plant stiffness.
        damping: Plant damping.
        setpoint_amp: Setpoint amplitude.
        setpoint_freq: Setpoint frequency.
        u_min: Minimum control input.
        u_max: Maximum control input.
        initial_state: Optional initial state.

    Returns:
        HybridSystem configured for PID control with saturation.
    """
    linear_dynamics = ContinuousDynamics(_flow_linear, label="linear")
    sat_high_dynamics = ContinuousDynamics(
        _flow_sat_high,
        label="sat_high",
    )
    sat_low_dynamics = ContinuousDynamics(
        _flow_sat_low,
        label="sat_low",
    )
    linear = Location(linear_dynamics, label="linear")
    sat_high = Location(sat_high_dynamics, label="sat_high")
    sat_low = Location(sat_low_dynamics, label="sat_low")

    transitions = [
        Transition(
            source=linear,
            target=sat_high,
            event=EventSurface(
                _event_surface_high,
                direction=CrossingDirection.RISING,
                label="hit_high",
            ),
        ),
        Transition(
            source=linear,
            target=sat_low,
            event=EventSurface(
                _event_surface_low,
                direction=CrossingDirection.FALLING,
                label="hit_low",
            ),
        ),
        Transition(
            source=sat_high,
            target=linear,
            event=EventSurface(
                _event_surface_high,
                direction=CrossingDirection.FALLING,
                label="leave_high",
            ),
        ),
        Transition(
            source=sat_low,
            target=linear,
            event=EventSurface(
                _event_surface_low,
                direction=CrossingDirection.RISING,
                label="leave_low",
            ),
        ),
    ]

    if initial_state is None:
        initial_state = np.array([0.0, 0.0, 0.0], dtype=float)

    return HybridSystem(
        locations=[linear, sat_high, sat_low],
        transitions=transitions,
        initial_location=linear,
        initial_state=initial_state,
        parameters={
            "kp": kp,
            "ki": ki,
            "kd": kd,
            "stiffness": stiffness,
            "damping": damping,
            "setpoint_amp": setpoint_amp,
            "setpoint_freq": setpoint_freq,
            "u_min": u_min,
            "u_max": u_max,
        },
    )