Categories &

Functions List

Function Reference: impulse

Function File: impulse (sys)
Function File: impulse (sys1, sys2, …, sysN)
Function File: impulse (sys1, ’style1’, …, sysN, ’styleN’)
Function File: impulse (sys1, …, t)
Function File: impulse (sys1, …, tfinal)
Function File: impulse (sys1, …, tfinal, dt)
Function File: [y, t, x] = impulse (sys)
Function File: [y, t, x] = impulse (sys, t)
Function File: [y, t, x] = impulse (sys, tfinal)
Function File: [y, t, x] = impulse (sys, tfinal, dt)

Impulse response of LTI system. If no output arguments are given, the response is printed on the screen.

Inputs

sys
LTI model.
t
Time vector. Should be evenly spaced. If not specified, it is calculated by the poles of the system to reflect adequately the response transients.
tfinal
Optional simulation horizon. If not specified, it is calculated by the poles of the system to reflect adequately the response transients.
dt
Optional sampling time. Be sure to choose it small enough to capture transient phenomena. If not specified, it is calculated by the poles of the system.
’style’
Line style and color, e.g. ’r’ for a solid red line or ’-.k’ for a dash-dotted black line. See help plot for details.

Outputs

y
Output response array. Has as many rows as time samples (length of t) and as many columns as outputs.
t
Time row vector.
x
State trajectories array. Has length (t) rows and as many columns as states.

Remark

For the impulse response of a discrete-time system, the input sequence {1/T,0,0,0,...} and not the unit impulse is considered.

See also: initial, lsim, step

Source Code: impulse 

 clf;
 subplot (2,1,1)
 G = tf (1,[2 1 4]);
 impulse (G,16);
 title ("Impulse response PT_2");
 subplot (2,1,2)
 G = tf (1,[2 1 4 0 ]);
 T = 2/3;
 Gdzoh = c2d(G, T);
 Gdimp = c2d(G, T, 'impulse');
 impulse(G, Gdzoh, ';G_{d,zoh};', Gdimp, ';G_{d,imp};', 16);
 title ("Impulse response IT_2 zoh- and imp-discretization");
plotted figure 

 clf;
 warning ("off", "Control:convert-to-state-space");
 G1 = tf({[1],[1 0]},{[1 1],[1 1 1]});
 G2 = tf  ({[1 0],[0.25];[-2 1],[1]},{[1 1 0.25],[1 1];[1.4 1],[1 1 1]});
 impulse (G1,G2,1.5*G2,12);
warning: System "G2" has direct feedthrough!
The impulse -1.428571*delta(t) is omitted in the impulse response from input "u1" to output "y2"
warning: System "Sys3" has direct feedthrough!
The impulse -2.142857*delta(t) is omitted in the impulse response from input "u1" to output "y2"
 warning ("on", "Control:convert-to-state-space");
plotted figure