Rattlesnake Vibration Controller

Notation

Accents

• $\mathbf{x}$ (bold, non-italic typeface) Matrix or vector
• $x$ (non-bold, italic typeface) Scalar or array

Variables

• $n_f$ Number of frequency lines
• $n_c$ Number of control channels
• $n_o$ Number of output signals
• $n_s$ Number of samples in a signal
• $n_{o}s$ Number of samples in an oversampled output signal
• ${\mathbf{G}}_{vv}$ CPSD matrix for the output signals
• ${\mathbf{G}}_{xx}$ CPSD matrix for the responses (i.e. the specification)
• ${\mathbf{H}}_{xv}$ Transfer function matrix between the responses and the output signals
• $\mathbf{X}$ Response spectra (FFT)
• $\mathbf{V}$ Output spectra (FFT)
• $\mathbf{T}$ Transformation matrix
• $\mathbf{A}$ State or system matrix for state space equations of motion
• $\mathbf{B}$ Input matrix for state space equations of motion
• $\mathbf{C}$ Output matrix for state space equations of motion
• $\mathbf{D}$ Feedthrough or feedforward matrix for state space equations of motion
• $\mathbf{x}$ State vector for state space equations of motion
• $\mathbf{y}$ Output vector for state space equations of motion
• $\mathbf{u}$ Input vector for state space equations of motion
• $\mathbf{M}$ Mass matrix for 2nd-order differential equations of motion
• $\mathbf{C}$ Damping matrix for 2nd-order differential equations of motion
• $\mathbf{K}$ Stiffness matrix for 2nd-order differential equations of motion

Operations

• ⬚${}^{+}$ Pseudoinverse of a matrix
• ⬚${}^H$ Complex-conjugate transpose of a matrix (hermitian)