# evalfr

Evaluate system response at specific frequency

## Syntax

``frsp = evalfr(sys,f)``

## Description

`evalfr` is a simplified version of `freqresp` meant for quick evaluation of the system response at the Laplace variable value of `s` or `z` for a single, specific frequency. Use `freqresp` to evaluate the system response over a set of frequencies. To obtain the magnitude and phase data as well as plots of the frequency response, use `bode` instead.

example

````frsp = evalfr(sys,f)` evaluates the continuous-time or discrete-time model `sys` at the specified frequency `f`.```

## Examples

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Create the following discrete-time transfer function.

`$H\left(z\right)=\frac{z-1}{{z}^{2}+z+1}$`

`H = tf([1 -1],[1 1 1],-1);`

Evaluate the transfer function at `z = 1+j`.

```z = 1+j; evalfr(H,z)```
```ans = 0.2308 + 0.1538i ```

Create the following continuous-time transfer function model:

`$H\left(s\right)=\frac{1}{{s}^{2}+2s+1}$`

`sys = idtf(1,[1 2 1]);`

Evaluate the transfer function at frequency 0.1 rad/second.

```w = 0.1; s = j*w; evalfr(sys,s)```
```ans = 0.9705 - 0.1961i ```

Alternatively, use the `freqresp` command.

`freqresp(sys,w)`
```ans = 0.9705 - 0.1961i ```

For this example, consider a cube rotating about its corner with inertia tensor `J` and a damping force `F` of 0.2 magnitude. The input to the system is the driving torque while the angular velocities are the outputs. The state-space matrices for the cube are:

`$\begin{array}{l}A=-{J}^{-1}F,\phantom{\rule{0.2777777777777778em}{0ex}}\phantom{\rule{0.2777777777777778em}{0ex}}\phantom{\rule{0.2777777777777778em}{0ex}}B={J}^{-1},\phantom{\rule{0.2777777777777778em}{0ex}}\phantom{\rule{0.2777777777777778em}{0ex}}\phantom{\rule{0.2777777777777778em}{0ex}}C=I,\phantom{\rule{0.2777777777777778em}{0ex}}\phantom{\rule{0.2777777777777778em}{0ex}}\phantom{\rule{0.2777777777777778em}{0ex}}D=0,\\ where,\phantom{\rule{0.2777777777777778em}{0ex}}J=\left[\begin{array}{ccc}8& -3& -3\\ -3& 8& -3\\ -3& -3& 8\end{array}\right]\phantom{\rule{0.2777777777777778em}{0ex}}and\phantom{\rule{0.2777777777777778em}{0ex}}F=\left[\begin{array}{ccc}0.2& 0& 0\\ 0& 0.2& 0\\ 0& 0& 0.2\end{array}\right]\end{array}$`

Specify the `A`, `B`, `C` and `D` matrices, and create the continuous-time state-space model.

```J = [8 -3 -3; -3 8 -3; -3 -3 8]; F = 0.2*eye(3); A = -J\F; B = inv(J); C = eye(3); D = 0; sys = ss(A,B,C,D); size(sys)```
```State-space model with 3 outputs, 3 inputs, and 3 states. ```

Compute the frequency response of the system at 0.2 rad/second. Since `sys` is a continuous-time model, express the frequency in terms of the Laplace variable `s`.

```w = 0.2; s = j*w; frsp = evalfr(sys,s)```
```frsp = 3×3 complex 0.3607 - 0.9672i 0.3197 - 0.5164i 0.3197 - 0.5164i 0.3197 - 0.5164i 0.3607 - 0.9672i 0.3197 - 0.5164i 0.3197 - 0.5164i 0.3197 - 0.5164i 0.3607 - 0.9672i ```

Alternatively, you can use the `freqresp` command to evaluate the frequency response using the scalar value of the frequency directly.

`H = freqresp(sys,w)`
```H = 3×3 complex 0.3607 - 0.9672i 0.3197 - 0.5164i 0.3197 - 0.5164i 0.3197 - 0.5164i 0.3607 - 0.9672i 0.3197 - 0.5164i 0.3197 - 0.5164i 0.3197 - 0.5164i 0.3607 - 0.9672i ```

## Input Arguments

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Dynamic system, specified as a SISO or MIMO dynamic system model or array of dynamic system models. Dynamic systems that you can use include:

• LTI models such as `ss`, `tf`, and `zpk` models.

• Sparse state-space models, such as `sparss` or `mechss` models.

• Generalized or uncertain state-space models such as `genss` or `uss` (Robust Control Toolbox) models. (Using uncertain models requires Robust Control Toolbox™ software.)

• For tunable control design blocks, the function evaluates the model at its current value to evaluate the frequency response.

• For uncertain control design blocks, the function evaluates the frequency response at the nominal value and random samples of the model.

• Identified state-space models, such as `idss` (System Identification Toolbox) models. (Using identified models requires System Identification Toolbox™ software.)

For a complete list of models, see Dynamic System Models.

Frequency at which to evaluate system response, expressed as the Laplace variable `s` or `z`, specified as a complex scalar. Specify the frequency in terms of the Laplace variable `s` or `z` based on whether `sys` is a continuous-time or discrete-time model, respectively. For instance, if you want to evaluate the frequency response of a system `sys` at a frequency value of `w` rad/s, then specify `f` in terms of

• `s = jw`, if `sys` is in continuous-time.

• `z = ejwT`, if `sys` is in discrete-time. Here, `T` is the sample time.

## Output Arguments

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Frequency response of the system at `f`, returned as a complex scalar.

## Version History

Introduced before R2006a