bode

Arguments

sl

A siso or simo linear dynamical system, in state space, transfer function or zpk representations, in continuous or discrete time.

fmin,fmax

real (frequency bounds (in Hz))

step

real (logarithmic step.)

frq

row vector or matrix (frequencies (in Hz) ) (one row for each SISO subsystem).

db

row vector or matrix ( magnitudes (in Db)). (one row for each SISO subsystem).

phi

row vector or matrix ( phases (in degree)) (one row for each SISO subsystem).

repf

row vector or matrix of complex numbers (complex frequency response).

Captions

vector of character strings (captions).

"rad"

as last optional argument: displays the Bode plot versus Angular frequencies in rad/s, instead of versus frequencies in Hz.

Description

Bode plot, i.e magnitude and phase of the frequency response of the linear dynamical system sl.

sl can be a continuous-time or discrete-time SIMO system given by its state space, rational transfer function (see syslin) or zpk representation. In case of multi-output the outputs are plotted with different colors.

The frequencies are given by the bounds fmin,fmax (in Hz) or by a row-vector (or a matrix for multi-output) frq.

step is the ( logarithmic ) discretization step. (see calfrq for the choice of default value).

db,phi are the matrices of modulus (in Db) and phases (in degrees). (One row for each response).

repf matrix of complex numbers. One row for each response.

Default values for fmin and fmax are 1.d-3, 1.d+3 if sl is continuous-time or 1.d-3, 0.5/sl.dt (nyquist frequency) if sl is discrete-time. Automatic discretization of frequencies is made by calfrq.

The datatips tool may be used to display data along the phase and modulus curves.

Examples

s = poly(0, 's');
h = syslin('c', (s^2+2*0.9*10*s+100)/(s^2+2*0.3*10.1*s+102.01));

clf(); bode(h, 0.01, 100);

s = poly(0, 's');
h1 = syslin('c', (s^2+2*0.9*10*s+100)/(s^2+2*0.3*10.1*s+102.01));
num = 22801+4406.18*s+382.37*s^2+21.02*s^3+s^4;
den = 22952.25+4117.77*s+490.63*s^2+33.06*s^3+s^4;
h2 = syslin('c', num/den);

clf(); bode([h1; h2], 0.01, 100, ['h1'; 'h2']);

s = %s;
G = (10*(s+3))/(s*(s+2)*(s^2+s+2)); // A rational matrix
sys = syslin('c', G); // A continuous-time linear system in transfer matrix representation.
f_min = .0001; f_max = 15; // Frequencies in Hz

clf(); bode(sys, f_min, f_max, "rad"); // Converts Hz to rad/s

See also

• bode_asymp — asymptote de diagramme de Bode
• black — Black-Nichols diagram of a linear dynamical system
• nyquist — nyquist plot
• gainplot — magnitude plot
• repfreq — frequency response
• g_margin — gain margin and associated crossover frequency
• p_margin — phase margin and associated crossover frequency
• calfrq — frequency response discretization
• phasemag — phase and magnitude computation
• datatips — Tool for placing and editing tips along the plotted curves

History