PID Controller
control-systems · 37 views
control-systemsperiodic
What It Is
PID controller tracking a step-changing setpoint. Deterministic, narrowband, strongly correlated.
Interpretation
Standard analysis sees: smooth / autocorrelated; long-range memory (persistent); red spectrum (low-frequency / 1-over-f power); low-complexity (predictable, not noise-like); volatility-clustering (bursty); multifractal; low-dimensional; nonstationary / drifting. The atlas additionally detects Multifractal Spectrum:hurst_estimate.
What standard analysis sees
tail heaviness0.38
asymmetry0.23
occupancy0.68
short-range corr0.98
long-range memory0.99
spectral colour0.11
periodicity0.76
complexity0.06
time-irreversibility0.84
volatility clustering0.98
multifractality0.95
dimensionality0.14
nonstationarity0.89
What the atlas adds
Multifractal Spectrum:hurst_estimate+2.3z
self-affinity H = τ(2)/2 (alternate to Hölder hurst)
Composition
dtypefloat64
range[-1.794, 1.535]
unique values16121 / 16384
mean ± std0.101 ± 0.831
Render Gallery
Native > phase_plotraw
Native > timeseriesraw
Native > triple_latticeraw
Boltzmann > lag_map
Boltzmann > spin_grid
Cayley > default
Chladni > free_plate_nodal
Chladni > plate_bottom
Chladni > plate_top
_(centered)/signed_log_z/PID_Controller.png)
Heisenberg (Nil) (centered) > signed_log_z
_(centered)/xy_path/PID_Controller.png)
Heisenberg (Nil) (centered) > xy_path
Hodge–Laplacian > default
/barcode/PID_Controller.png)
Inflation (Substitution) > barcode
/d_curve/PID_Controller.png)
Inflation (Substitution) > d_curve
Information Theory > default
Julia Set > escape_histogram
Klein Bottle > default
Laplacian > default
Logarithmic Spiral > default
Möbius-S³ > mobius_cylinder
Möbius-S³ > s2_base_map
Ordinal Partition > default
/phi_spectrum/PID_Controller.png)
Penrose (Quasicrystal) > phi_spectrum
Persistent Homology > barcode
Persistent Homology > h1_diagram
Predictability > default
Recurrence Quantification > default
Spectral Analysis > default
Spectral Graph > default
Spirograph > mode_spectrum
Spirograph > phasor_trajectory
Symplectic > flux_grid
Symplectic > phase_space
/default/PID_Controller.png)
Ulam Spiral (Sacks) > default
/default/PID_Controller.png)
Ulam Spiral (Square) > default
Visibility Graph > default
Wavelet Cascade > default
Atlas Position
| Nearest neighbor | Distance | |
|---|---|---|
| Triple Pendulum | 3.24 | cross-origin |
| FPUT N=16 | 3.48 | cross-origin |
| Magnetic Pendulum (3-Magnet) | 3.60 | cross-origin |
Which Geometries Light Up
Catch24 › Catch24:PD_PeriodicityWang_th0_01 | rank 3/307 | 3512.5333 |
Catch24 › Catch24:SB_BinaryStats_diff_longstretch0 | rank 4/307 | 1094.8000 |
H² × ℝ (Thurston) › H² × ℝ (Thurston):hyperbolic_step_dispersion | rank 304/307 | 0.0308 |
Visibility Graph › Visibility Graph:nvg_hvg_reach_divergence | rank 5/307 | 0.9949 |
Wasserstein › Wasserstein:recurrence_distance | rank 1/307 | 0.1077 |
in number-theory
← / → within domain · ⇧← / ⇧→ alphabetical · ⇧← / ⇧→ inside an open render = same view across sources