连续时间系统零状态响应的数值计算

系统函数模型

sys = t( b,a )

输出响应函数

y = lsim( sys, f, t )%sys为系统函数，f为激励函数，t为抽样向量

例3-1零状态响应

ts = 0; te = 5; dt = 0.01;

sys = tf( [ 1 ], [ 1 2 100 ] );%前者为激励系数后者为响应系数

t = ts : dt : te;

f = 10 * sin( 2 * pi * t );

y = lsim( sys, f, t );

plot( t, y );

xlabel( ‘Time(sec)’ );

ylabel( ‘y(t)’ );

连续时间系统冲激响应和阶跃响应

对于连续系统LTI系统的冲激响应和阶跃响应可分别用impuls和step来求解

冲击响应

y = impuls( sys, t )

阶跃响应

y = step( sys, t )

例3-2冲击、阶跃响应

ts = 0; te = 5; td = 0.01;

sys = tf( [ 10 ], [ 1, 2, 100 ] );

t = ts : td : te;

h = impulse( sys, t );

figure;

plot( t, h );

grid on;

xlabel( ‘Time(sec)’ );

ylabel( ‘h(t)’ );

g = step( sys, t );

figure;

plot( t, g );

grid on;

xlabel( ‘Time(sec)’ );

ylabel( ‘g(t)’ );

连续时间信号的卷积

例3-3连续系统卷积

dt=0.01; t=-1:dt:2.5;

f1=Heaviside(t)-Heaviside(t-2);

f2=exp(-3*t).*Heaviside(t);

f=conv(f1,f2)*dt; n=length(f); tt=(0:n-1)*dt-2;

subplot(221), plot(t,f1), grid on;

axis([-1,2.5,-0.2,1.2]); title(‘f1(t)’); xlabel(‘t’)

subplot(222), plot(t,f2), grid on;

axis([-1,2.5,-0.2,1.2]); title(‘f2(t)’); xlabel(‘t’)

subplot(212), plot(tt,f), grid on;

title(‘f(t)=f1(t)*f2(t)’); xlabel(‘t’)

课后习题

2

ts = 0; te = 5; dt = 0.01;

sys = tf( [ 1 3 ], [ 1 4 4 ] );

t = ts : dt : te;

f = exp( -t );

y = lsim( sys, f, t );

plot( t, y );

xlabel( ‘Time(sec)’ );

ylabel( ‘y(t)’ );

3

ts = 0; te = 10; td = 0.01;

sys1 = tf( [ 1 ], [ 1 3 2 ] );

sys2 = tf( [ 1 0 ], [ 1 2 2 ] );

t = ts : td : te;

%**********************************************************

h1 = impulse( sys1, t );

subplot(2,2,1)

plot( t, h1 );

grid on;

xlabel( ‘Time(sec)’ );

ylabel( ‘h1(t)’ );

%**********************************************************

g1 = step( sys1, t );

subplot(2,2,2)

plot( t, g1 );

grid on;

xlabel( ‘Time(sec)’ );

ylabel( ‘g1(t)’ );

%**********************************************************

h2 = impulse( sys2, t );

subplot(2,2,3)

plot( t, h2 );

grid on;

xlabel( ‘Time(sec)’ );

ylabel( ‘h2(t)’ );

%**********************************************************

g2 = step( sys2, t );

subplot(2,2,4)

plot( t, g2 );

grid on;

xlabel( ‘Time(sec)’ );

ylabel( ‘g2(t)’ );

4

Heaviside.m

function f = Heaviside(t)

f = ( t >= 0 );

运行

dt=0.01; t=-1 : dt : 4;

f1=Heaviside(t)-Heaviside(t-2);

f=conv(f1,f1)

dt; n=length(f); tt=(0:n-1)

dt-2;

%


*******************************************************

subplot( 2, 2, 1 ), plot(t,f1), grid on;

axis([-1,2.5,-0.2,1.2]); title(‘f1(t)’); xlabel(‘t’)

%*********************************************************

subplot( 2, 1, 2 ), plot(tt,f), grid on;

title(‘f(t)=f1(t)*f2(t)’); xlabel(‘t’)