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Implement second-order filter

Simscape / Electrical / Specialized Power Systems / Control / Filters

Based on the **Filter type** selected in the block menu, the
Second-Order Filter block implements the following transfer
function:

Low-pass filter:

$$H(s)=\frac{{\omega}_{n}^{2}}{{s}^{2}+2\zeta {\omega}_{n}s+{\omega}_{n}^{2}}$$

High-pass filter:

$$H(s)=\frac{{s}^{2}}{{s}^{2}+2\zeta {\omega}_{n}s+{\omega}_{n}^{2}}$$

Band-pass filter:

$$H(s)=\frac{2\zeta {\omega}_{n}s}{{s}^{2}+2\zeta {\omega}_{n}s+{\omega}_{n}^{2}}$$

Band-stop (notch) filter:

$$H(s)=\frac{{s}^{2}+{\omega}_{n}^{2}}{{s}^{2}+2\zeta {\omega}_{n}s+{\omega}_{n}^{2}}$$

$$\begin{array}{c}s=\text{Laplaceoperator}\\ {\omega}_{n}=\text{naturalfrequency;}{\omega}_{n}=2\pi {f}_{n}\\ \zeta =\text{dampingratio}\text{}\text{}\text{(calledZetaintheblockmenu)}\end{array}$$

The key characteristics of the Second-Order Filter block are:

Input accepts a vectorized input of N signals, implementing N filters. This feature is particularly useful for designing controllers in three-phase systems (N = 3).

Filter states can be initialized for specified DC and AC inputs.

It enables you to compute and plot filter response.

**Filter type**Specify the type of filter:

`Lowpass`

,`Highpass`

,`Bandpass`

(default), or`Bandstop (notch)`

.**Natural frequency fn (Hz)**Specify the natural frequency of the filter, in hertz. This value must be a scalar or a vector. Default is

`120`

.**Damping ratio Zeta (Q = 1/(2*Zeta))**Specify the damping ratio of the filter. The damping ratio is typically a value between 0 and 1. Default is

`0.707`

.The damping ratio is related to the filter quality factor Q:

$$Q=\frac{1}{2\zeta}$$

For a bandpass or a bandstop filter, the 3 dB bandwidth is given by

$$BW=\frac{{f}_{n}}{Q}=2\zeta {f}_{n}$$

**Sample time**Specify the sample time of the block, in seconds. Set to 0 to implement a continuous block. Default is

`0`

.**Initialize filter states**When this check box is selected, filter states are initialized according to the

**AC initial input**and**DC initial input**parameters. Default is selected.**AC initial input: [ Mag, Phase (degrees), Freq (Hz) ]**Specify the magnitude of the initial AC component of the input signal, its phase, in degrees, and its frequency, in hertz. Default is

`[0, 0, 60]`

.When the input is vectorized (N signals), specify an N-by-3 matrix, where each row of the matrix corresponds to a particular input.

The

**AC initial input**parameter is visible only when the**Initialize filter states**parameter is selected.**DC initial input**Specify the value of the initial DC component of the input signal. When the input signal is vectorized, specify a 1-by-N vector, where each value corresponds to a particular input. Default is

`0`

.The

**DC initial input**parameter is visible only when the**Initialize filter states**parameter is selected.**Plot filter response**When this check box is selected, the filter step response and its Bode diagram (magnitude and phase of transfer function as a function of frequency) are plotted in a figure. Default is cleared.

**Frequency range (Hz): [Start, End, Inc.]**Specify the frequency range for plotting the filter Bode diagram. Specify a vector containing the starting frequency, the end frequency, and the incremental frequency, in hertz. Default is

`[0, 500, 1]`

.The

**Frequency range**parameter is visible only when the**Plot filter response**parameter is selected.

Direct Feedthrough | Yes |

Sample Time | Specified in the Sample Time parameterContinuous if Sample Time = 0 |

Scalar Expansion | Yes, of the parameters |

States | Two states per filter |

Dimensionalized | Yes |

The `power_SecondOrderFilter`

example
shows the Second-Order Filter block using two **Filter type** parameter
settings (`Lowpass`

and `Bandstop`

).

The model sample time is parameterized with variable Ts (default
value Ts = 50e-6). To simulate continuous filters, specify Ts = 0
in the MATLAB^{®} Command Window before starting the simulation.