write an introduction part in about 250 words for a lab according to the information in brackets In this lab matlab and simulink are used to investigate the following content A second order pendulum s

In this lab, the second order pendulum system is studied using Matlab and Simulink. The lab covers various aspects of the system including the Proportional gain - Open loop transfer function, Closed-loop transfer function, Disturbance, Closed-loop transfer function with proportional gain, Closed-loop transfer function with disturbance, PI controller in a closed-loop system, PD controller in a closed-loop system, and PID controller.

The lab aims to investigate different parameters in different systems such as MP output overshoot, ts output settling time, tp time where the maximum output peak occurs, tr rise time, 𝜔𝑛 the natural undamped frequency, and 𝜔𝑑 the damped frequency. These parameters define the system's behavior and performance, and hence, it is crucial to understand and compare them in different systems.

Additionally, zero-pole diagrams for different systems are plotted to investigate system characteristics. The zero-pole diagram consists of the system's poles and zeros, which are essential in determining the system's stability and response. By analyzing the zero-pole diagram, we can determine the system's frequency response and stability.

Overall, this lab provides a comprehensive understanding of the second order pendulum system and its behavior in different controllers. It also equips the students with the necessary skills to analyze and compare system parameters and characteristics using Matlab and Simulink