Автоматизация анализа линейных систем, страница 2

h1=findobj(gcf,'tag','edit5'); S=get(h1,'string');

Lp=laplace(S, t, p)

R=2000

C=2*10^(-7)

L=0.2

Fout=Lp*L*C*p/(L*C*p^2+R*C*p+1)

S = ilaplace(Fout, p, t)

F  = fourier (S, t, w)

%Находим функции для вычисления действительной, мнимой,

% частей, а также амплитуды и фазы спектральной плотности %сигнала

Fr = vpa (real (F), 4)

Fi = vpa ( imag (F), 4)

Fa = vpa (sqrt (Fr^2 + Fi^2), 4)

Fph = vpa (-atan(Fi/Fr) , 4 )

h6=findobj(gcf,'tag','edit6');

set(h6,'string', char(S));

Fr = subs (Fr)

Fi = subs (Fi)

Fa = subs (Fa)

h7=findobj(gcf,'tag','edit7');

set(h7,'string', char(Fa));

Fph = subs (Fph)

h8=findobj(gcf,'tag','edit8');

set(h8,'string', char(Fph));

Результаты расчётов:

Выходная функция системы:

S =

472236648286964500*pi^(1/2)*ilaplace(p^(1/2)/(1888946593147858125*p^2+18889465931478580854784*p+47223664828696452136960000)*exp(1/4*p^2),p,t)-472236648286964500*pi^(1/2)*ilaplace(p^(1/2)/(1888946593147858125*p^2+18889465931478580854784*p+47223664828696452136960000)*exp(1/4*p^2)*erf(1/2*i*p),p,t)+236118324143482250*pi^(1/2)*ilaplace(p/(p-2*i)^(1/2)/(1888946593147858125*p^2+18889465931478580854784*p+47223664828696452136960000)*exp(1/4*(p-2*i)^2),p,t)-236118324143482250*pi^(1/2)*ilaplace(p/(p-2*i)^(1/2)/(1888946593147858125*p^2+18889465931478580854784*p+47223664828696452136960000)*exp(1/4*(p-2*i)^2)*erf(1/2*i*(p-2*i)),p,t)+236118324143482250*pi^(1/2)*ilaplace(p/(p+2*i)^(1/2)/(1888946593147858125*p^2+18889465931478580854784*p+47223664828696452136960000)*exp(1/4*(p+2*i)^2),p,t)-236118324143482250*pi^(1/2)*ilaplace(p/(p+2*i)^(1/2)/(1888946593147858125*p^2+18889465931478580854784*p+47223664828696452136960000)*exp(1/4*(p+2*i)^2)*erf(1/2*i*(p+2*i)),p,t)

Амплитуда спектральной плотности:

Fa =

((1635156250000000*fourier(ilaplace(p^(1/2)/(7378697629483821*p^2+73786976294838206464*p+184467440737095516160000)*exp(1/4*p^2),p,t),t,w)-1635156250000000*fourier(ilaplace(p^(1/2)/(7378697629483821*p^2+73786976294838206464*p+184467440737095516160000)*exp(1/4*p^2)*erf(1/2*i*p),p,t),t,w)+817968750000000*fourier(ilaplace(p/(p-2*i)^(1/2)/(7378697629483821*p^2+73786976294838206464*p+184467440737095516160000)*exp(1/4*(p-2*i)^2),p,t),t,w)-817968750000000*fourier(ilaplace(p/(p-2*i)^(1/2)/(7378697629483821*p^2+73786976294838206464*p+184467440737095516160000)*exp(1/4*(p-2*i)^2)*erf(1/2*i*(p-2*i)),p,t),t,w)+817968750000000*fourier(ilaplace(p/(p+2*i)^(1/2)/(7378697629483821*p^2+73786976294838206464*p+184467440737095516160000)*exp(1/4*(p+2*i)^2),p,t),t,w)-817968750000000*fourier(ilaplace(p/(p+2*i)^(1/2)/(7378697629483821*p^2+73786976294838206464*p+184467440737095516160000)*exp(1/4*(p+2*i)^2)*erf(1/2*i*(p+2*i)),p,t),t,w)+1/2*conj(3270312500000000*fourier(ilaplace(p^(1/2)/(7378697629483821*p^2+73786976294838206464*p+184467440737095516160000)*exp(1/4*p^2),p,t),t,w)-3270312500000000*fourier(ilaplace(p^(1/2)/(7378697629483821*p^2+73786976294838206464*p+184467440737095516160000)*exp(1/4*p^2)*erf(1/2*i*p),p,t),t,w)+1635156250000000*fourier(ilaplace(p/(p-2*i)^(1/2)/(7378697629483821*p^2+73786976294838206464*p+184467440737095516160000)*exp(1/4*(p-2*i)^2),p,t),t,w)-1635156250000000*fourier(ilaplace(p/(p-2*i)^(1/2)/(7378697629483821*p^2+73786976294838206464*p+184467440737095516160000)*exp(1/4*(p-2*i)^2)*erf(1/2*i*(p-2*i)),p,t),t,w)+1635156250000000*fourier(ilaplace(p/(p+2*i)^(1/2)/(7378697629483821*p^2+73786976294838206464*p+184467440737095516160000)*exp(1/4*(p+2*i)^2),p,t),t,w)-1635156250000000*fourier(ilaplace(p/(p+2*i)^(1/2)/(7378697629483821*p^2+73786976294838206464*p+184467440737095516160000)*exp(1/4*(p+2*i)^2)*erf(1/2*i*(p+2*i)),p,t),t,w)))^2-1/4*(3270312500000000*fourier(ilaplace(p^(1/2)/(7378697629483821*p^2+73786976294838206464*p+184467440737095516160000)*exp(1/4*p^2),p,t),t,w)-3270312500000000*fourier(ilaplace(p^(1/2)/(7378697629483821*p^2+73786976294838206464*p+184467440737095516160000)*exp(1/4*p^2)*erf(1/2*i*p),p,t),t,w)+1635156250000000*fourier(ilaplace(p/(p-2*i)^(1/2)/(7378697629483821*p^2+73786976294838206464*p+184467440737095516160000)*exp(1/4*(p-2*i)^2),p,t),t,w)-1635156250000000*fourier(ilaplace(p/(p-2*i)^(1/2)/(7378697629483821*p^2+73786976294838206464*p+184467440737095516160000)*exp(1/4*(p-2*i)^2)*erf(1/2*i*(p-2*i)),p,t),t,w)+1635156250000000*fourier(ilaplace(p/(p+2*i)^(1/2)/(7378697629483821*p^2+73786976294838206464*p+184467440737095516160000)*exp(1/4*(p+2*i)^2),p,t),t,w)-1635156250000000*fourier(ilaplace(p/(p+2*i)^(1/2)/(7378697629483821*p^2+73786976294838206464*p+184467440737095516160000)*exp(1/4*(p+2*i)^2)*erf(1/2*i*(p+2*i)),p,t),t,w)-conj(3270312500000000*fourier(ilaplace(p^(1/2)/(7378697629483821*p^2+73786976294838206464*p+184467440737095516160000)*exp(1/4*p^2),p,t),t,w)-3270312500000000*fourier(ilaplace(p^(1/2)/(7378697629483821*p^2+73786976294838206464*p+184467440737095516160000)*exp(1/4*p^2)*erf(1/2*i*p),p,t),t,w)+1635156250000000*fourier(ilaplace(p/(p-2*i)^(1/2)/(7378697629483821*p^2+73786976294838206464*p+184467440737095516160000)*exp(1/4*(p-2*i)^2),p,t),t,w)-1635156250000000*fourier(ilaplace(p/(p-2*i)^(1/2)/(7378697629483821*p^2+73786976294838206464*p+184467440737095516160000)*exp(1/4*(p-2*i)^2)*erf(1/2*i*(p-2*i)),p,t),t,w)+1635156250000000*fourier(ilaplace(p/(p+2*i)^(1/2)/(7378697629483821*p^2+73786976294838206464*p+184467440737095516160000)*exp(1/4*(p+2*i)^2),p,t),t,w)-1635156250000000*fourier(ilaplace(p/(p+2*i)^(1/2)/(7378697629483821*p^2+73786976294838206464*p+184467440737095516160000)*exp(1/4*(p+2*i)^2)*erf(1/2*i*(p+2*i)),p,t),t,w)))^2)^(1/2)