单级倒立摆仿真
时间: 2023-07-02 19:16:54 浏览: 84
好的,您可以使用MATLAB进行单级倒立摆的仿真。下面是一个简单的示例代码:
```matlab
%% Parameters
m = 0.5; % mass of the ball
M = 2; % mass of the cart
L = 0.5; % length of the rod
g = 9.81; % acceleration due to gravity
%% State-Space Model
A = [0 1 0 0;
0 0 -m*g/M 0;
0 0 0 1;
0 0 (m+M)*g/(L*M) 0];
B = [0; 1/M; 0; -1/(L*M)];
C = eye(4);
D = 0;
sys = ss(A,B,C,D);
%% Control Design
Q = diag([10 1 100 1]); % state weights
R = 0.1; % input weight
[K,S,e] = lqr(A,B,Q,R);
%% Simulation
x0 = [0; 0; 0.2; 0]; % initial state
tspan = 0:0.01:5; % simulation time
[t,x] = ode45(@(t,x)cart_pend(x,m,M,L,g,-K*(x-[1;0;0;0])),tspan,x0);
%% Plotting
figure;
subplot(2,1,1);
plot(t,x(:,1),'-',t,x(:,3),'--');
legend('Cart Position','Pendulum Angle');
xlabel('Time (s)');
ylabel('Position (m) / Angle (rad)');
subplot(2,1,2);
plot(t,-K*(x-[1;0;0;0])');
legend('Force on the Cart');
xlabel('Time (s)');
ylabel('Force (N)');
```
这段代码会生成一个单级倒立摆的仿真结果,包括图形和数据。你可以根据自己的需要调整参数和控制设计。