Evaluate system response at specific frequency
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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
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Evaluate Discrete-Time Transfer Function
Open Live Script
Create the following discrete-time transfer function.
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:
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:
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 - 0.9672iAlternatively, 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 - 0.9672iInput Arguments
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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-timesys.z = exp(j*w*Ts), for discrete-timesys, whereTsis the sample time.
Output Arguments
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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
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