Dynamics & Control · Lab
First-Order System Lab
G(s) = K / (τs + 1). Read the same first-order system in the time domain or in the frequency domain: response and metrics, or Bode magnitude and phase with the corner frequency and bandwidth.
The same K/(τs + 1), seen as a response in time or as magnitude and phase against frequency.
System
Equivalent model
- K
- 1
- τ
- 1 s
G(s) = 1 / (s + 1)
The plotted curve is the total response: zero-input decay from y(0) plus the zero-state response to u(t).
Excitation
Characteristics
| Pole | -1 |
|---|---|
| DC gain G(0) | 1 |
| Corner frequency | 1 rad/s |
| Time to 63.2% | 1 s |
| Rise time (10%–90%) | 2.197 s |
| Settling time (2%) | 4 s |
| Settling time (5%) | 3 s |
Continue with this system
The current model travels with the link; nothing is re-entered and nothing opens on its own.
A first-order lag has no second-order continuation: nothing here maps onto ωn and ζ, so none is offered.
Response y(t)
Measured response metrics
| Final value y∞ | 1 |
|---|---|
| Peak value | 0.9991 |
| Peak time | 7 s |
| Percent overshoot | 0 % |
| Settling time (2%) | 3.912 s |
| Settling time (5%) | 3 s |
| Rise time (10%–90%) | 2.197 s |
Pole–zero map
| Root | Re(s) | Im(s) | Multiplicity |
|---|---|---|---|
| Pole × | -1 | 0 | 1 |
What this Lab models
The single-pole lag G(s) = K/(τs + 1): its time response to standard inputs, its pole and corner frequency, and its magnitude/phase against frequency — the same K and τ throughout.