Evaluate system response at specific frequency

collapse all in page

## Syntax

`frsp = evalfr(sys,x)`

## Description

`evalfr`

is a simplified version of `freqresp`

meant for quick evaluation of the system response at any point in the complex plane. To evaluate system response over a set of frequencies, use freqresp. To obtain the magnitude and phase data as well as plots of the frequency response, use bode.

example

`frsp = evalfr(sys,x)`

evaluates the dynamic system model `sys`

at the point `x`

in the complex *s* plane (for continuous-time `sys`

) or *z* plane (for discrete-time `sys`

).

## Examples

collapse all

### Evaluate Discrete-Time Transfer Function

Open Live Script

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)

### Evaluate Frequency Response of Identified Model at Given Frequency

This example uses:

- System Identification ToolboxSystem Identification Toolbox

Open Live Script

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

### Frequency Response of MIMO State-Space Model

Open Live Script

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:

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

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

collapse all

`sys`

— Dynamic system

dynamic system model | model array

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.

`x`

— Point in complex plane

complex scalar

Point in complex plane at which to evaluate system response, specified as a complex scalar. For continuous-time sys, the point `x`

is in the plane of the continuous-time Laplace variable *s*. For discrete-time `sys`

, `x`

is in the plane of the discrete-time Laplace variable *z*.

To evaluate the response of the system at a particular frequency, specify the frequency in terms of the appropriate Laplace variable. For instance, if you want to evaluate the frequency response of a system `sys`

at a frequency value of `w`

rad/s, then use:

`x = j*w`

, for continuous-time`sys`

.`z = exp(j*w*Ts)`

, for discrete-time`sys`

, where`Ts`

is the sample time.

## Output Arguments

collapse all

`frsp`

— Frequency response

complex scalar | complex array

Frequency response of the system at the point x, returned as a complex scalar (for SISO sys) or a complex array (for MIMO `sys`

). For MIMO systems, the array dimensions correspond to the I/O dimensions of `sys`

.

## Version History

**Introduced before R2006a**

## See Also

bode | freqresp | sigma

## MATLAB Command

You clicked a link that corresponds to this MATLAB command:

Run the command by entering it in the MATLAB Command Window. Web browsers do not support MATLAB commands.

Select a Web Site

Choose a web site to get translated content where available and see local events and offers. Based on your location, we recommend that you select: .

You can also select a web site from the following list:

### Americas

- América Latina (Español)
- Canada (English)
- United States (English)

### Europe

- Belgium (English)
- Denmark (English)
- Deutschland (Deutsch)
- España (Español)
- Finland (English)
- France (Français)
- Ireland (English)
- Italia (Italiano)
- Luxembourg (English)

- Netherlands (English)
- Norway (English)
- Österreich (Deutsch)
- Portugal (English)
- Sweden (English)
- Switzerland
- Deutsch
- English
- Français

- United Kingdom (English)

Contact your local office