Evaluate system response at specific frequency
evalfr is a simplified version of
meant for quick evaluation of the system response at the Laplace variable value of
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
Evaluate Discrete-Time Transfer Function
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)
ans = 0.2308 + 0.1538i
Evaluate Frequency Response of Identified Model at Given Frequency
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
ans = 0.9705 - 0.1961i
Frequency Response of MIMO State-Space Model
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:
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
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
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:
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.
f — Frequency at which to evaluate system response
Frequency at which to evaluate system response, expressed as the Laplace variable
z, specified as a complex scalar. Specify
the frequency in terms of the Laplace variable
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
sysis in continuous-time.
z = ejwT, if
sysis in discrete-time. Here,
Tis the sample time.
Introduced before R2006a