LSU‑05 NG — Longitudinal Dynamics

The LAPAN Surveillance Aircraft (LSU)‑05 NG is a UAV for observation and research. This page mirrors the ELV layout: quick start, math model, derivatives, and API.

• Quick start

  Launch the environment or the model within minutes.

  See example

• Model API

  Python class documentation for the LSU‑05 longitudinal dynamics.

  Go to API

• Gymnasium environment

  Ready environment for RL agents.

  Explore

• Theory

  State equations and numerical parameters.

  Learn more

Control object structure

\[\dot{x} = A x + B u, \quad y = C x + D u\]

\[ x = \begin{bmatrix} u & w & q & \theta \end{bmatrix}^{\top}, \quad u_{in} = \eta \]

The plant is modeled in the state space, consistent with other systems in the library. The state-space matrices are taken from the reference below. Because the system lacks internal disturbance processes, the output \(y\) is not used during simulation (\(C\) is diagonal, \(D\) is zero).

Mathematical model

\[ \dot{x} = A x + B u, \qquad y = C x + D u \]

\[ \begin{bmatrix} \dot{u} \\ \dot{w} \\ \dot{q} \\ \dot{\theta} \end{bmatrix} = \begin{bmatrix} -0.00271615 & 0.248462 & 0 & -9.81 \\ -0.257616 & -11.3097 & 68.9497 & 0\\ 0.0576336 & -7.23232 & -11.3237 & 0 \\ 0 & 0 & 1 & 0 \end{bmatrix} \begin{bmatrix} u \\ w \\ q \\ \theta \end{bmatrix} + \begin{bmatrix} 1.959083 \\ -73.99448 \\ -188.4752 \\ 0.0 \end{bmatrix} \eta \]

Derivatives (numerical values)

• Matrix A (derivatives):

Coefficient	Value
x_u	-0.00271615
x_w	0.248462
x_q	0
x_θ	-9.81
z_u	-0.257616
z_w	-11.3097
z_q	68.9497
z_θ	0
m_u	0.0576336
m_w	-7.23232
m_q	-11.3237
m_θ	0

• Input η (column B):

Coefficient	Value
x_η	1.959083
z_η	-73.99448
m_η	-188.4752

where

• \(u\) — longitudinal speed [m/s]
• \(w\) — normal speed [m/s]
• \(q\) — pitch rate [deg/s]
• \(\theta\) — pitch angle [deg]
• \(\eta\) — stabilizer deflection angle [deg]
• \(x_u\) — partial derivative of longitudinal force with respect to longitudinal speed
• \(x_w\) — partial derivative of longitudinal force with respect to normal speed
• \(x_q\) — partial derivative of longitudinal force with respect to pitch rate
• \(x_{\theta}\) — partial derivative of longitudinal force with respect to pitch angle
• \(z_u\) — partial derivative of vertical force with respect to longitudinal speed
• \(z_w\) — partial derivative of vertical force with respect to normal speed
• \(z_q\) — partial derivative of vertical force with respect to pitch rate
• \(z_{\theta}\) — partial derivative of vertical force with respect to pitch angle
• \(m_u\) — partial derivative of pitch moment with respect to longitudinal speed
• \(m_w\) — partial derivative of pitch moment with respect to normal speed
• \(m_q\) — partial derivative of pitch moment with respect to pitch rate
• \(m_{\theta}\) — partial derivative of pitch moment with respect to pitch angle

Sources

1. 1. Lembaga, D.O., Antariksa, P.D., Septiyana, A., Hidayat, K., Rizaldi, A., Suseno, P.A., Jayanti, E.B., Atmasari, N., Ramadiansyah, M.L., Ramadhan, R.A., Suryo, V.N., Grüter, B., Diepolder, J., Holzapfel, F., Wijaya, Y.G., Dewan, S., Jurnal, P., Dirgantara, T., Wibowo, H., Panas, P., Septanto, H., Harno, A., Syah, N.A., Angkasa, R., Satelit, M.D., Irwanto, H.Y., Avionik, M.E., Hakim, A.N., Utama, A.B., Wahyudi, A.H., Kurniawati, F., Putro, I.E., & Astuti, R.A. STABILITY AND CONTROLLABILITY ANALYSIS ON LINEARIZED DYNAMIC SYSTEM EQUATION OF MOTION OF LSU 05-NG USING KALMAN RANK CONDITION METHOD. - Jurnal Teknologi Dirgantara Vol. 18 No. 2 Desember 2020 : hal 81 – 92 – 2020

Reward

The default reward function returns the negative absolute tracking error for the pitch angle:

\[r_t = -|\theta(t) - \theta_{\text{ref}}(t)|\]

Higher reward (closer to 0) indicates better tracking performance. A custom reward function can be passed via the reward_func parameter.

Quick start

```python

import gymnasium as gym import numpy as np from tqdm import tqdm

from tensoraerospace.envs import LinearLongitudinalLAPAN from tensoraerospace.utils import generate_time_period, convert_tp_to_sec_tp from tensoraerospace.signals.standard import unit_step

dt = 0.01 tp = generate_time_period(tn=20, dt=dt) tps = convert_tp_to_sec_tp(tp, dt=dt) number_time_steps = len(tp) reference_signals = np.reshape(unit_step(degree=5, tp=tp, time_step=10, output_rad=True), [1, -1])

env = gym.make( 'LinearLongitudinalLAPAN-v0', number_time_steps=number_time_steps, initial_state=[[0],[0],[0],[0]], reference_signal=reference_signals, ) state, info = env.reset() for _ in range(200): action = np.array([[0.1]]) state, reward, terminated, truncated, info = env.step(action) if terminated or truncated: break

Python API

ModelGymnasium environment

LAPAN(x0, number_time_steps, selected_state_output=None, t0=0, dt=0.01)

Bases: ModelBase

LAPAN Surveillance Aircraft (LSU)-05 NG in longitudinal control channel.

Parameters:

Name	Type	Description	Default
x0	ndarray | list[float]	Initial state of the control object.	required
number_time_steps	int	Number of time steps.	required
selected_state_output	optional	Selected states of the control object. Defaults to None.	None
t0	int	Initial time. Defaults to 0.	0
dt	float	Discretization frequency. Defaults to 0.01.	0.01

Action space

ele: elevator [rad]

State space

u: Longitudinal aircraft velocity [m/s] w: Normal aircraft velocity [m/s] q: Pitch angular velocity [rad/s] theta: Pitch [rad]

Output space

u: Longitudinal aircraft velocity [m/s] w: Normal aircraft velocity [m/s] q: Pitch angular velocity [rad/s] theta: Pitch [rad]

Initialize LAPAN instance.

Parameters:

Name	Type	Description	Default
x0	ndarray | list[float]	Initial state of the control object.	required
number_time_steps	int	Number of time steps.	required
selected_state_output	list[str] | None	Selected states of the control object. Defaults to None.	None
t0	float	Initial time. Defaults to 0.	0
dt	float	Discretization frequency. Defaults to 0.01.	0.01

import_linear_system()

Load (set) stored linearized system matrices.

initialise_system(x0, number_time_steps)

Initialize the system and allocate history buffers.

Parameters:

Name	Type	Description	Default
x0	ndarray | list[float]	Initial state.	required
number_time_steps	int	Number of simulation steps.	required

run_step(ut_0)

Run one discrete-time simulation step.

Parameters:

Name	Type	Description	Default
ut_0	ndarray	Control vector.	required

Returns:

Type	Description
ndarray	np.ndarray: Next state at time t+1.

update_system_attributes()

Update time-dependent attributes after each simulation step.

get_state(state_name, to_deg=False, to_rad=False)

Return the time history of a state.

Parameters:

Name	Type	Description	Default
state_name	str	State name.	required
to_deg	bool	Convert radians to degrees.	False
to_rad	bool	Convert degrees to radians.	False

Returns:

Type	Description
ndarray	np.ndarray: State history array.

get_control(control_name, to_deg=False, to_rad=False)

Return the time history of a control input.

Parameters:

Name	Type	Description	Default
control_name	str	Control signal name.	required
to_deg	bool	Convert radians to degrees.	False
to_rad	bool	Convert degrees to radians.	False

Returns:

Type	Description
ndarray	np.ndarray: Control history array.

get_output(state_name, to_deg=False, to_rad=False)

Return the time history of an output signal.

Parameters:

Name	Type	Description	Default
state_name	str	Output name.	required
to_deg	bool	Convert radians to degrees.	False
to_rad	bool	Convert degrees to radians.	False

Returns:

Type	Description
ndarray	np.ndarray: Output history array.

plot_output(output_name, time, lang='rus', to_deg=False, to_rad=False, figsize=(10, 10))

Plot an output signal over time.

Parameters:

Name	Type	Description	Default
output_name	str	Output name.	required
time	ndarray	Time vector.	required
lang	str	Axis label language ('rus' or 'eng').	'rus'
to_deg	bool	Convert radians to degrees.	False
to_rad	bool	Convert degrees to radians.	False
figsize	tuple	Figure size.	(10, 10)

Returns:

Type	Description
Figure	matplotlib.figure.Figure: Figure object.

LinearLongitudinalLAPAN(initial_state, reference_signal, number_time_steps, tracking_states=None, state_space=None, control_space=None, output_space=None, reward_func=None)

Bases: Env

Legacy LAPAN longitudinal-control environment.

Parameters:

Name	Type	Description	Default
initial_state	ndarray	Initial state vector.	required
reference_signal	ndarray	Reference (target) signal array.	required
number_time_steps	int	Number of simulation steps.	required
tracking_states	list[str] | None	Names of tracked states used for reward computation.	None
state_space	list[str] | None	Names of state variables exposed in observations.	None
control_space	list[str] | None	Names of control inputs.	None
output_space	list[str] | None	Names of model outputs returned by the plant.	None
reward_func	Callable[[ndarray, ndarray, int], float] | None	Optional custom reward function.	None

Initialize legacy LAPAN longitudinal environment.

reward(state, ref_signal, ts) staticmethod

Compute tracking reward for the current step.

Parameters:

Name	Type	Description	Default
state	ndarray	Current tracked state vector.	required
ref_signal	ndarray	Reference signal array.	required
ts	int	Current time step index.	required

Returns:

Name	Type	Description
float	float	Reward value (lower is better in the legacy formulation).

step(action)

Run one simulation step.

Parameters:

Name	Type	Description	Default
action	ndarray	Control input(s).	required

Returns:

Name	Type	Description
tuple	ndarray	(observation, reward, terminated, truncated, info) in the
	float	Gymnasium API format.

reset(seed=None, options=None)

Reset environment state to the initial conditions.

Parameters:

Name	Type	Description	Default
seed	int | None	Random seed (Gymnasium).	None
options	dict | None	Optional reset options (unused).	None

Returns:

Name	Type	Description
tuple	tuple[ndarray, dict[str, float]]	(observation, info).

render()

Render the environment (not implemented).

Raises:

Type	Description
NotImplementedError	Rendering is not available.