Evaluate system response at specific frequency
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:
Generalized or uncertain state-space models such as
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
Point in complex plane at which to evaluate system response, specified as a complex
scalar. For continuous-time
sys, the point
is in the plane of the continuous-time Laplace variable s. For
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
w rad/s, then use:
x = j*w, for continuous-time
z = exp(j*w*Ts), for discrete-time
Tsis the sample time.
Introduced before R2006a