create a pole placement in matlab

Pole placement is a technique used in control systems engineering to achieve desired system behavior by placing the poles of a system at specific locations in the complex plane. MATLAB has a built-in command for pole placement called place, which can be used to design a state feedback controller.

Here's an example code snippet that demonstrates how to use the place command to place the poles of a state feedback controller:

main.m
% Define the system matrices
A = [1 1; 0 1];
B = [0; 1];

% Define the desired pole locations
des_poles = [-1 -2];

% Use the 'place' command to calculate the appropriate gain matrix
K = place(A, B, des_poles);

% Define the initial condition
x0 = [1; 0];

% Define the simulation time span
tspan = 0:0.1:10;

% Simulate the system using 'ode45'
[t, x] = ode45(@(t, x) (A - B*K)*x, tspan, x0);

% Plot the state variables
plot(t, x(:,1), t, x(:,2))
legend('x_1', 'x_2')
xlabel('Time')
ylabel('State Variable')
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In this example, we first define the system matrices A and B for a 2nd-order system. We then use the place command to calculate the gain matrix K that places the poles of the closed-loop system at the desired locations des_poles. We then simulate the system using the state feedback control law u = -K*x and the ode45 solver. Finally, we plot the state variables x_1 and x_2 over time.