Frequency Response & Polar Diagrams

freqresp - Evaluate system response over a grid of frequencies Use freqresp to evaluate the system response over a grid of frequencies. Syntax [H,wout] = freqresp(sys) H = freqresp(sys,w) H = freqresp(sys,w,units) [H,wout,covH] = freqresp(sys,___) Input Arguments sys - Dynamic system dynamic system model | model array w - Frequencies vector units - Units of the values in the input frequency vector rad/TimeUnit (default) | 'cycles/TimeUnit' | 'rad/s' | ... Output Arguments H - Frequency response values array wout - Output frequencies corresponding to the frequency response vector covH - Covariance of the frequency response array Examples Frequency Response of SISO System Compute Frequency Response of System Compute Frequency Response on Specified Frequency Grid Compute Frequency Response and Associated Covariance See also evalfr, bode, nyquist, nichols, sigma, interp, spectrum (System Identification Toolbox) Introduced in Control System Toolbox before R2006a Documentation for freqresp Other uses of freqresp

nyquist - Nyquist response of dynamic system This MATLAB function returns the real and imaginary parts of the frequency response at each frequency in the vector wout. Syntax [re,im,wout] = nyquist(sys) [re,im,wout] = nyquist(sys,w) [re,im,wout,sdre,sdim] = nyquist(sys,w) nyquist(___) Input Arguments sys - Dynamic system dynamic system model | model array w - Frequencies {wmin,wmax} | vector | [] Output Arguments re - Real part of system response 3-D array im - Imaginary part of system response 3-D array wout - Frequencies vector sdre - Standard deviation of real part 3-D array | [] sdim - Standard deviation of imaginary part 3-D array | [] Examples Nyquist Plot of Dynamic System Nyquist Plot at Specified Frequencies Nyquist Plot of Several Dynamic Systems Nyquist Plot with Specified Line Attributes Obtain Real and Imaginary Parts of Frequency Response Nyquist Plot of MIMO System Create Nyquist Plot of Identified Model with Response Uncertainty Nyquist Plot of Model with Complex Coefficients See also nichols, sigma, bode, nyquistplot Introduced in Control System Toolbox before R2006a Documentation for nyquist Other uses of nyquist

bode - Bode frequency response of dynamic system This MATLAB function computes the frequency response of dynamic system model sys and returns the magnitude and phase of the response at each frequency in the vector wout. Syntax [mag,phase,wout] = bode(sys) [mag,phase,wout] = bode(sys,w) [mag,phase,wout,sdmag,sdphase] = bode(sys,w) bode(___) Input Arguments sys - Dynamic system dynamic system model | model array w - Frequencies {wmin,wmax} | vector | [] Output Arguments mag - Magnitude of system response 3-D array phase - Phase of system response 3-D array wout - Frequencies vector sdmag - Standard deviation of magnitude 3-D array | [] sdphase - Standard deviation of phase 3-D array | [] Examples Bode Plot of Dynamic System Bode Plot at Specified Frequencies Compare Bode Plots of Several Dynamic Systems Bode Plot with Specified Line Attributes Obtain Magnitude and Phase Data Magnitude and Phase of MIMO System Bode Plot of Identified Model Obtain Magnitude and Phase Standard Deviation Data of Identified Model Bode Plot of Model with Complex Coefficients See also bodeplot, freqresp, nichols, nyquist, step Introduced in Control System Toolbox before R2006a Documentation for bode Other uses of bode

drawBodediagrams( ) Plotting Bode diagrams of the frequency response (asymptotic and actual superimposed diagrams) of continuous-time transfer functions. INPUT variables: Gs: transfer function, described as TF object; MANDATORY variable omega_values: angular frequency values used to draw the graphs (OPTIONAL - if not present, a suitable frequency range is estimated on the basis of zeros and poles. An appropriate number of values for the angular pulsation in the newly determined range is then chosen). asBode_color: colour of asymptotic graphs (array: three values between 0 and 1) - OPTIONAL Default value: [1, 0, 0] <--> red asBode_line_width: line thickness for asymptotic graphs - OPTIONAL Default value: 2 asBode_line_style: line style for asymptotic diagrams (see 'LineStyle' in plot( ) ) - OPTIONAL Default value: '-' bode_color: colour of actual graphs (array: three values between 0 and 1) - OPTIONAL Default value: [0, 0, 1] <--> blue bode_line_width: line thickness for actual graphs - OPTIONAL Default value: 1.5 bode_line_style: line style for actual diagrams (see 'LineStyle' in plot( ) ) - OPTIONAL Default value: '-' fig_handler: The figure handler of a figure already in use, where Bode diagrams are drawn. If it does not exist, a new figure is created. comp_asympt_vs_actual_ph_diagrsFLAG: a logic flag indicating whether the 360-degree jump between the asymptotic phase diagram and the actual phase diagram should be compensated (if present). Default value: true ---------- OUTPUT variables (optional): the handlers of the couple of axes corresponding to the two subplots.

drawPolarDiagramFreqResp( ) Plotting polar diagrams of the frequency response of continuous-time transfer functions. INPUT variables: Gs: transfer function, described as TF object; MANDATORY variable omega_values: angular frequency values used to draw the graphs (OPTIONAL - if not present, a suitable frequency range is estimated). polar_color: colour of actual graphs (array: three values between 0 and 1) - OPTIONAL Default value: [0, 0, 1] <--> blue polar_line_width: line thickness for actual graphs - OPTIONAL Default value: 2.0 polar_line_style: line style for actual diagrams (see 'LineStyle' in plot( ) ) - OPTIONAL Default value: '-' markerSize: is the size (in pt.) of the circular markers used to put in evidence the points in the polar draw corresponding to null angular frequency and frequency going to infinity. If empty or zero, no markers will be drawn at all. - OPTIONAL Default value: 6 om_selected: some angular frequency values at which you want to place a circular marker (black) in the graph. - OPTIONAL Default value: empty array fig_handler: The figure handler of a figure already in use, where the polar diagram has to be drawn. If it does not exist, a new figure is created. legendFLAG: a logical flag; if true an automatic legend will be inserted in the plot; otherwise, no legend will appear. ---------- OUTPUT variable (optional): the handler of the axes corresponding to the plot.