First, fill in the transfer function of the continuous system, then convert it into a state-space model system. Next, determine the time interval and simulation time, followed by defining the input sine wave signal. Then, use the 4th-order Runge-Kutta method to solve the system of differential equations in state-space, and finally observe the system’s output … Read more
1.Description The concept of numerical methods, in brief, is that when analytical solutions cannot be obtained or cannot be computed within a limited time, numerical methods are used to iteratively compute a series of data that satisfy the equation. Such results are called numerical solutions, and the methods used to obtain them are referred to … Read more
Solving differential equations using MATLAB Write the system of differential equations in a column format, and then solve the system using the Runge-Kutta method. % Runge-Kutta method to solve differential equations step1=0.01; t0=0:step1:10; y0=[0.5;0.6;0.7]; Len=length(t0); y_out=zeros(Len,3); y_out(1,1:3)=y0′; for m1=2:1:Len tt0=t0(m1-1); yy0=(y_out(m1-1,1:3))’; KK1=step1*function1(tt0,yy0); KK2=step1*function1(tt0+step1/2,yy0+0.5*KK1); KK3=step1*function1(tt0+step1/2,yy0+0.5*KK2); KK4=step1*function1(tt0+step1,yy0+0.5*KK3); yy0=yy0+(KK1+KK2*2+KK3*2+KK4)/6; y_out(m1,1:3)=yy0′; end figure(1),plot(t0,y_out(:,1)); figure(2),plot(t0,y_out(:,2)); figure(3),plot(t0,y_out(:,3)); function y_out=function1(tt1,yy1) y_out=zeros(3,1); y_out(1)=yy1(2)+tt1*0.1; … Read more