![]() ![]() Laub, A.J., " Efficient Multivariable Frequency Response Computations," IEEE Transactions on Automatic Control, AC-26 (1981), pp. response due to jw-axis or unit circle pole.Įvalfr Response at single complex frequency If the system has a pole on the axis (or unit circle in the discrete case) and w happens to contain this frequency point, the gain is infinite, is singular, and bode produces the warning message If the sample time is unspecified, the default value is assumed. Is periodic with period, bode plots the response only up to the Nyquist frequency. The equivalent "continuous-time frequency" is then used as the -axis variable. To facilitate interpretation, the upper-half of the unit circle is parametrized as See for more details on this technique.įor discrete-time systems, the frequency response is obtained by evaluating the transfer function on the unit circle. The reduction to Hessenberg form provides a good compromise between efficiency and reliability. Otherwise, is reduced to upper Hessenberg form and the linear equation is solved at each frequency point, taking advantage of the Hessenberg structure. When numerically safe, is diagonalized for maximum speed. For state-space models, the frequency response is Only positive frequencies are considered. You can also discretize this system using zero-order hold and the sample time second, and compare the continuous and discretized responses by typingįor continuous-time systems, bode computes the frequency response by evaluating the transfer function on the imaginary axis. To plot the response on a wider frequency range, for example, from 0.1 to 100 rad/sec, type You can plot the Bode response of the continuous SISO system The values mag(i,j,k) and phase(i,j,k) then characterize the response of h ij at the frequency w(k). MIMO systems are treated as arrays of SISO systems and the magnitudes and phases are computed for each SISO entry h ij independently ( h ij is the transfer function from input j to output i). The output arguments mag and phase are 3-D arrays with dimensionsįor SISO systems, mag(1,1,k) and phase(1,1,k) give the magnitude and phase of the response at the frequency = w(k). If sys is an FRD model, bode(sys,w), w can only include frequencies in sys.frequency. You can convert the magnitude to decibels by The outputs mag and phase are 3-D arrays with the frequency as the last dimension (see "Arguments" below for details). Return the magnitude and phase (in degrees) of the frequency response at the frequencies w (in rad/sec). Uses red dashed lines for the first system sys1 and green 'x' markers for the second system sys2. This syntax is useful to compare the Bode responses of multiple systems.īode(sys1,'PlotStyle1'.,sysN,'PlotStyleN') specifies which color, linestyle, and/or marker should be used to plot each system. All systems must have the same number of inputs and outputs, but may otherwise be a mix of continuous and discrete systems. All frequencies should be specified in radians/sec.īode(sys1,sys2.,sysN) or bode(sys1,sys2.,sysN,w) plots the Bode responses of several LTI models on a single figure. Use logspace to generate logarithmically spaced frequency vectors. To use particular frequency points, set w to the vector of desired frequencies. To focus on a particular frequency interval, set w =. The frequency range is determined automatically based on the system poles and zeros.īode(sys,w) explicitly specifies the frequency range or frequency points to be used for the plot. In the MIMO case, bode produces an array of Bode plots, each plot showing the Bode response of one particular I/O channel. This model can be continuous or discrete, and SISO or MIMO. Bode plots are used to analyze system properties such as the gain margin, phase margin, DC gain, bandwidth, disturbance rejection, and stability.īode(sys) plots the Bode response of an arbitrary LTI model sys. The decibel calculation for mag is computed as 20log 10, where is the system's frequency response. The magnitude is plotted in decibels (dB), and the phase in degrees. When invoked without left-side arguments, bode produces a Bode plot on the screen. Bode (Function Reference) Function ReferenceĬompute the Bode frequency response of LTI modelsīode(sys1,'PlotStyle1'.,sysN,'PlotStyleN')īode computes the magnitude and phase of the frequency response of LTI models. ![]()
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