Now the PID for the system needed to be tuned using the previously designed model. Slight adjustments were made to the model, allowing for the implementation of the PID controller. Again, the main goal was to zero out the derivatives and analyze any graphs produced until a desired outcome is reached. Most of the codes were tested in regular MATLAB, producing graphs that ultimately showed the responses of the pendulum position to an impulse disturbance under PID control for different Kp, Ki, and Kd values (Figures 3, 4, and 5). From Figure 3, it can be observed that the response isn't stable. This would require modification of the response, so the proportional gain was increased (Kp = 100) to see what would happen. From Figure 4, it can be observed that an improved graph was produced due to the change of the proportional gain. The setting time turned out to be less than the required time. It can also be confirmed that the steady-state error approaches zero in a very efficient and fast manner. paraphrase