System library / Mechanical

Mass–Spring–Damper

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

MULTI-SYSTEM LABb = damping coefficient [N·s/m] · v = velocity [m/s]Single-system learning lab ↗

Systems 1

Open Loopm 2 kg · b 3 N·s/m · k 20 N/m

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System actions

System nameEnable System AInclude System A in comparison

System A

Open Loop

System preset

Physical parameters

mMass

bDamping coefficient

N·s/m

kSpring stiffness

N/m

Initial conditions

x₀Initial displacement

v₀Initial velocity

m/s

Controller & reference

Controller

Open-loop plant

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

Measured x; error e = r − x. Controller output u is actuator force on the mass, separate from external disturbance.

Position reference

Position reference amplitude

Position reference start

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: System A

Open LoopSelected

m 2 kg · b 3 N·s/m · k 20 N/m

PHYSICAL SYSTEMSI units · schematic scale

Positive displacement →t = 0 s

m\ddot{x}+b\dot{x}+kx=F_{external}(t)+u(t)

0 / 10 s

Playback speed

Compare responses

Distinct systems. One view of their computed behavior.

Compare

System 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	System AOpen Loop
Peak output [m]	0.1
Value at end [m]	3.38e-5
10–90% rise time [s]
Settling (2% band) [s]	5.24
Step overshoot [%]
Error at end [m]	0.09997
RMS tracking error [m]	0.1005
Integral absolute error [m·s]	0.985
Integral squared error [m²·s]	0.1011
Time-weighted absolute error [m·s²]	5.008
Maximum actuator force [N]	0
RMS actuator force [N]	0
Time saturated [fraction]	0
Maximum velocity [m/s]	0.2285
Maximum acceleration [m/s²]	1
Damping ratio ζ	0.2372
Natural frequency (rad/s)	3.162
Damped frequency (rad/s)	3.072