System library / Control

Inverted Pendulum

Change the plant. Change the controller. Compare what actually happens.

MULTI-SYSTEM LABθ = 0 upright · positive θ leans right · positive force points rightSingle-system learning lab ↗

Systems 1

Open Loop · NonlinearM 1 kg · θ₀ 0.1 rad

✓ Result up to date

System actions

System nameEnable Pendulum AInclude Pendulum A in comparison

Pendulum A

Open Loop

System preset

Plant model

Physical parameters

MCart mass

mPendulum mass

lPendulum length

gGravity

m/s²

bCart friction

N·s/m

Initial conditions

θ₀Initial angle

rad

ω₀Initial angular velocity

rad/s

x₀Initial cart position

v₀Initial cart velocity

m/s

Controller & reference

Controller

Open-loop plant

No actuator feedback is applied. Reference and tracking error remain available for comparison.

Measured θ; error = θ reference − θ. Cart force uses negative controller polarity because positive force initially accelerates θ negatively.

Angle reference

Gain changes mark this system for rerun.

External disturbance & test

External disturbance

Duration

Sample interval

Test conditions

Reference, disturbance, duration and sample interval are shared. Plant parameters and controllers remain independent.

Physical Systems

1 system · 1 visible

View

Selected: Pendulum A

Open LoopSelected

M 1 kg · m 0.2 kg · l 0.5 m

PHYSICAL SYSTEMθ = 0 at upright · schematic scale

Motion follows the computed statest = 0 s

e_\theta=\theta_{ref}-\theta,\qquad u=-C(s)e_\theta

0 / 10 s

Playback speed

Large angle excursion: the pendulum moved more than 0.35 rad from upright. This describes physical motion, not necessarily a numerical error or a failure to recover.

Educational fall threshold exceeded (0.6 rad). Inspect the complete trajectory.

Compare responses

Distinct systems. One view of their computed behavior.

Compare

Pendulum A

Plot

Chart layout

NormalizeShow referenceShow open-loop baseline

1 response trace · scroll to zoom · drag to pan

Measured performance

Metrics belong to the displayed run snapshots. End values are finite-time observations, not guaranteed steady states.

Metric	Pendulum AOpen Loop
Peak output [rad]	6.097
Value at end [rad]	5.751
Settling (2% band) [s]
Error at end [rad]	-5.751
RMS tracking error [rad]	3.776
Integral absolute error [rad·s]	30.69
Integral squared error [rad²·s]	142.6
Time-weighted absolute error [rad·s²]	154.3
Maximum actuator force [N]	0
RMS actuator force [N]	0
Time saturated [fraction]	0
Maximum angle [rad]	6.097
Maximum cart displacement [m]	0.09291
Cart error at end [m]	-0.04625
Time within upright tolerance [s]	0
Stabilization test	Not stabilized

Stabilized means the last full second of a run lasting at least 5 s stays within |θ|≤0.035 rad and |ω|≤0.1 rad/s, with no fall or travel breach. Cascade additionally checks final cart error and speed. It is a result of this simulated test, not a global stability proof.