![]() Therefore, make = 20 in your m-file and run it again. Page in the section on characteristics of P, I, and D controllers, we see that by increasing we can lower the overshoot and decrease the settling time slightly. Now the system is stable but the overshoot is much too high and the settling time needs to go down a bit. Your plot should be similar to the following: System's response to this control method. Copy the following lines of code to an m-file and run it to view the Now, we will add a derivative term to the controller. Try changing the value of and note that the system remains unstable. Add the following line of code to your m-file and run it.Īs you can see, the system remains marginally stable with the addition of a proportional gain. Now, we can model the system's response to a step input of 0.25 m. The closed-loop transfer function for proportional control with a proportional gain ( ) equal to 100, can be modeled by copying the following lines of MATLAB code into a new m-file. Recall, that the transfer function for a PID controller is: ![]() Integral control will be added if necessary. ![]() The block diagram for this example with a controller and unity feedback of the ball's position is shown below:įirst, we will study the response of the system shown above when a proportional controller is used. To see the derivation of the equations for this problem refer to the Ball & Beam: System Modeling page. ![]()
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