mathematical representation of the inverted pendulum system in matlab

To represent the inverted pendulum system mathematically in Matlab, you can use the state-space representation. The state variables of the system will be the angle of the pendulum and the angular velocity, and the control input will be the force applied to the cart.

First, you need to define the system parameters such as pendulum length, mass, cart mass, and gravitational acceleration. Let's assume the following parameter values:

• Pendulum length (l): 1 meter
• Pendulum mass (m): 0.5 kg
• Cart mass (M): 1 kg
• Gravitational acceleration (g): 9.81 m/s^2

Next, you can define the state-space equations that describe the dynamics of the system. The state vector x will have two elements: x(1) for the angle and x(2) for the angular velocity. The input vector u will represent the force applied to the cart.

The equations are as follows:

main.m
% System parameters
l = 1;     % pendulum length
m = 0.5;   % pendulum mass
M = 1;     % cart mass
g = 9.81;  % gravitational acceleration

% State-space representation
A = [0 1; (g/l) 0];
B = [0; 1/(M*l^2)];
C = eye(2);
D = zeros(2, 1);
sys = ss(A, B, C, D);
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In the above code, the state-space matrices A, B, C, and D are defined. The ss function is then used to create a state-space system representation sys.

You can use this sys object to further analyze and control the inverted pendulum system in Matlab.