| name | active-vibration-control |
| description | Active vibration control (AVC) — feedforward/feedback architectures, filtered-x LMS, piezoelectric actuators, active mounts, AMD, ANC, stability, hardware, applications. |
| metadata | {"priority":7,"promptSignals":{"phrases":["active vibration control","AVC","active noise control","filtered-x LMS","piezoelectric actuator","active mount","active damping"],"minScore":3}} |
Active Vibration Control — Complete Skill
System Architecture
Feedforward Control
Principle: Reference signal correlated with disturbance → predict and cancel
Application: periodic/tonal disturbances (engine orders, unbalance)
Filtered-x LMS (FxLMS) algorithm:
y(n) = w^T(n) x(n) [actuator signal; w = adaptive filter weights; x = reference]
e(n) = d(n) + y_actual(n) [error = disturbance + control response]
Update: w(n+1) = w(n) - μ × e(n) × x'(n) [gradient descent; μ = step size]
x'(n) = filtered reference through secondary path model G_hat
Secondary path: transfer function from actuator to error sensor
Must be identified (offline or online) for stability
Convergence: stable if μ < 1 / (λ_max × ||G_hat||²)
Feedback Control
Principle: measure vibration → control law → actuate to suppress
Application: broadband disturbances; non-deterministic sources
PID-based:
u(t) = K_p e + K_i ∫e dt + K_d de/dt (e = displacement or acceleration error)
Stability: phase margin ≥ 30°; avoid resonances in open-loop plant
H∞ robust control:
Minimize ||T_zw||∞ (worst-case energy from disturbance w to performance z)
Handles model uncertainty; more complex design
MATLAB: hinfsyn command
Sky-hook damping:
F_control = -c_sky × ẋ_body (virtual damper connected to inertial reference)
Effective for isolation; implemented via inertial sensor (accelerometer + integrator)
Actuator Types
Piezoelectric Actuators
PZT (Lead Zirconate Titanate):
Strain: ε = d₃₃ × E_field = d₃₃ × V/t_pzt
d₃₃ ≈ 400–600 pm/V; typical stroke: 0.1–0.5% strain
Blocking force: F = d₃₃ × E × A_pzt [N]
Bandwidth: DC to 100s of kHz (stiff actuator; high resonance frequency)
Stack actuator: layers of PZT; stroke ∝ n_layers; stiffness ∝ 1/n_layers
Patch actuator: bonded to structure; bending excitation; lower force but distributed
Limitations: high voltage (100–1000V); brittle; low displacement; hysteresis (5–20%)
Hysteresis compensation: feedforward model or charge amplifier drive
Voice Coil (Electromagnetic)
Linear motor: F = B L i (B = flux, L = wire length, i = current)
High bandwidth; mid-range force; limited stroke
Used in: hard drives, vibration isolators, seismic isolators
Magnetostrictive (Terfenol-D)
Strain: ε = d_mag × H (H = applied magnetic field)
Strain levels: up to 0.2% (larger than PZT)
High force; moderate bandwidth; simpler drive circuit (current control)
Active Isolation
Active engine mount:
Piezo or EM actuator in parallel with passive mount
Secondary path from actuator to chassis sensor
FxLMS control for engine order cancellation
Typical: 20–40 dB attenuation at engine orders
Active vibration isolation table (semiconductor):
6-DOF control; pneumatic actuators + voice coils
Achieves < 1 nm RMS in vertical (for lithography tools)
Transmissibility < -60 dB at 10 Hz+
Active Mass Damper (AMD)
Large moving mass driven by actuator (hydraulic, EM) to counteract building motion
AMD reaction: F = m_a × ẍ_a acts on building
Used in: skyscrapers (Taipei 101 pendulum-based; Yokohama Landmark Tower AMD)
Control: feed back building velocity or acceleration; command AMD to generate opposing force
HMD (Hybrid Mass Damper): passive TMD + active actuator → better performance + smaller mass
Active Noise Control (ANC)
1D duct (in-plane): antisound from speaker cancels noise from source
FxLMS; reference from upstream microphone; error at downstream microphone
Headphones (ANC):
Feedforward: microphone outside → cancel before reaching ear
Feedback: internal mic monitors residual → suppress
Combined hybrid: best performance across frequencies
Performance limits:
Sound speed constrains maximum control point separation
Works well below ~500 Hz (wavelength > control geometry)
Causality: control system latency must be less than acoustic propagation time
Stability Considerations
Spillover: control of low modes may excite higher (unmodeled) modes
Spatial filtering helps (distributed sensors/actuators)
Sensor-actuator collocation: if sensors and actuators collocated → passivity → guaranteed stability
Non-collocated: requires careful stability analysis; potential for instability
Hardware
Sensors: accelerometer (piezo; sensitivity 1–1000 mV/g), LVDT (position), laser vibrometer
DAQ: 24-bit ADC; sampling rate ≥ 10× max control frequency
Amplifier: voltage amplifier (PZT); power amplifier (EM, voice coil)
Controller: DSP (TI C28xx, ADSP), FPGA (National Instruments, Speedgoat), dSPACE, Speedgoat
Output
Provide: control architecture (feedforward/feedback), algorithm (FxLMS/PID/H∞), actuator type and specifications (stroke [μm], force [N], bandwidth [Hz]), sensor selection, sampling rate, expected attenuation [dB] at target frequencies, stability margin.
