倒立摆matlab仿真程序
时间: 2023-09-07 16:15:04 浏览: 39
以下是一个简单的倒立摆MATLAB仿真程序,使用了ODE45求解微分方程。您可以根据需要进行修改和调整。
```matlab
% Parameters
g = 9.81; % acceleration due to gravity (m/s^2)
L = 1; % length of pendulum (m)
m = 1; % mass of pendulum (kg)
M = 5; % mass of cart (kg)
b = 0.1; % damping coefficient
I = m*L^2; % moment of inertia
tspan = [0 10]; % simulation time interval
theta0 = 0.1; % initial angle of pendulum (rad)
x0 = 0; % initial position of cart (m)
v0 = 0; % initial velocity of cart (m/s)
w0 = 0; % initial angular velocity of pendulum (rad/s)
% Solve ODE
y0 = [x0; v0; theta0; w0];
[t, y] = ode45(@(t,y) pendcart(t,y,m,M,g,L,b,I), tspan, y0);
% Plot results
figure;
subplot(2,1,1);
plot(t, y(:,1));
xlabel('Time (s)');
ylabel('Position (m)');
title('Cart Position');
subplot(2,1,2);
plot(t, y(:,3));
xlabel('Time (s)');
ylabel('Angle (rad)');
title('Pendulum Angle');
function dydt = pendcart(t, y, m, M, g, L, b, I)
% Extract variables
x = y(1);
v = y(2);
theta = y(3);
w = y(4);
% Calculate derivatives
dxdt = v;
dwdt = (m*L^2*v^2*sin(theta) - (m+M)*g*L*sin(theta) - b*w)/(I + m*L^2);
dvdt = (m*L^2*w^2*sin(theta) + (m+M)*g*sin(theta)*cos(theta) - b*v)/(m+M);
dthetadt = w;
% Return derivatives
dydt = [dxdt; dvdt; dthetadt; dwdt];
end
```
这个程序模拟了一个带有阻尼的倒立摆,可以通过修改参数来进行不同的模拟实验。