create a pid controller graph in matlab

To create a PID controller graph in MATLAB, you can follow the steps below:

1. Define the transfer function of the plant that you want to control using the tf command. For example, if you want to control a first-order system with a time constant of 1 and gain of 2, you can use:

   main.m
   G = tf(2, [1 1]);
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2. Define the transfer function of the PID controller using the pid command. For example, if you want to use a PID controller with a proportional gain of 1, integral time constant of 0.5, and derivative time constant of 0.1, you can use:

   main.m
   C = pid(1, 1/0.5, 0.1);
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3. Connect the plant and the controller using the feedback command. For example, if you want to connect the plant G and the controller C, you can use:

   main.m
   sys = feedback(G*C, 1);
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4. Define the time vector for the simulation and the initial conditions for the system. For example, to simulate the system for 10 seconds with a time step of 0.01 seconds, you can use:

   main.m
   t = 0:0.01:10;
   x0 = 0;
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5. Simulate the system using the lsim command. For example, if you want to simulate the system sys with an input of 1 for the entire simulation time, you can use:

   main.m
   y = lsim(sys, ones(size(t)), t, x0);
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6. Plot the output of the system using the plot command. For example, to plot the output of the system over time, you can use:

   main.m
   plot(t, y);
   xlabel('Time (s)');
   ylabel('Output');
   title('PID Controller Response');
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This will create a graph of the response of the system to the PID controller. You can modify the parameters of the plant and the controller to see how they affect the response of the system.