How to solve nonlinear equation?
조회 수: 2 (최근 30일)
이전 댓글 표시
댓글 수: 0
채택된 답변
Sam Chak
2022년 12월 21일
Hi @GUANGHE HUO
The nonlinear matrix ODE with time-varying stiffness matrix K can be transformed into a nonlinear state-space model. See example below.
tspan = [0 40];
x0 = [1 0.5 0 0];
[t, x] = ode45(@odefcn, tspan, x0);
plot(t, x), grid on, xlabel('t')
function xdot = odefcn(t, x)
xdot = zeros(4, 1);
M = diag([3 5]);
C = 2*eye(2);
K = [1+0.5*sin(2*pi/40*t) 0; 0 1+0.5*sin(2*pi/40*t)]; % time-varying K
A = [zeros(2) eye(2); -M\K -M\C];
B = [zeros(2); eye(2)];
F = [0; 0]; % Requires your input
u = M\F;
xdot = A*x + B*u;
end
댓글 수: 4
Sam Chak
2022년 12월 23일
Hi @GUANGHE HUO
I use ordinary numeric array in my simulations. Perhaps you can try using the cell2mat() command to convert the selected cell array into the desired numeric array.
If your Force vector and the Stiffness matrix are time series data (cannot be expressed in any fundamental mathematical form), then you need to use the interp1() function to interpolate and to obtain the value of the time-dependent terms at the specified time.
Here is an example of using a data-driven Force to stabilize the Double Integrator system:
% Force data set recorded over some intervals of time
ft = linspace(0, 20, 2001);
f = 2*exp(-ft).*ft - exp(-ft).*(1 + ft); % made-up to generate the data
tspan = [0 20];
y0 = [1 0];
opts = odeset('RelTol', 1e-4, 'AbsTol', 1e-8);
[t, y] = ode45(@(t, y) doubleInt(t, y, ft, f), tspan, y0, opts);
plot(t, y), grid on, xlabel('t'), ylabel('Y(t)')
legend('y_{1}(t)', 'y_{2}(t)')
% Double Integrator system
function dydt = doubleInt(t, y, ft, f)
dydt = zeros(2, 1);
f = interp1(ft, f, t); % Interpolate the data set (ft, f) at time t
dydt(1) = y(2);
dydt(2) = f;
end
추가 답변 (1개)
참고 항목
카테고리
Help Center 및 File Exchange에서 Ordinary Differential Equations에 대해 자세히 알아보기
Community Treasure Hunt
Find the treasures in MATLAB Central and discover how the community can help you!
Start Hunting!