Discrete-time notch filter with varying coefficients
Control System Toolbox / Linear Parameter Varying
The block implements the Tustin discretization of a continuous-time notch filter with varying coefficients. Feed the continuous-time values of the notch frequency, minimum gain, and damping ratio to the freq, gmin, and damp input ports, respectively. These parameters control the notch depth and frequency of the continuous-time notch frequency as shown in the following illustration. The damping ratio damp controls the notch width Δ; larger damp means larger Δ.
Use this block and the other blocks in the Linear Parameter Varying library to implement common control elements with variable parameters or coefficients. For more information, see Model Gain-Scheduled Control Systems in Simulink.
u— Filter input
Notch filter input signal
freq— Notch frequency
Continuous-time value of the notch frequency, specified in rad/s.
gmin— Gain at notch frequency
Continuous-time value of the gain at notch frequency, in absolute units. This value controls the notch depth. The notch filter has unit gain at low and high frequency. The gain is lowest at the notch frequency.
damp— Damping ratio of the filter poles
Continuous-time value of the damping ratio, specified as a positive scalar value. The damping ratio controls the notch width; the closer to 0, the steeper the notch.
y— Filter output
Notch filter output signal.
Pre-warping frequency w0 (rad/s)— Pre-warping frequency
Pre-warping frequency, specified as a positive scalar. Discretization of
the continuous-time notch-filter transfer function can shift the notch
frequency when it is close to the Nyquist frequency. To ensure that the
continuous and discrete filters have matching frequency response near a
w0, set this parameter to
w0. The default value
w0 = 0
corresponds to the bilinear (Tustin) transformation without pre-warp:
where Ts is the block sample time, specified with the Sample time Ts parameter.
Sample time Ts— Sample time
Block sample time, specified as a positive scalar. This block does not support inherited sample time, because it requires a specified sample time to compute the discretization of the notch filter.