For each of the transfer functions shown below, find the locations of the poles and zeros, plot them on the s-plane, and then write an expression for the general form of the step response without solving for the inverse Laplace transform. State the nature of each response (overdamped, underdamped, and so on). [Sections: 4.3, 4.4]s

2) Proposing and implementing a PID controller for a simple system (e.g., electrical system) using MATLAB/Python. (5%) As a result, students will learn PID concepts through search, group discussion and coding. Also, they will be exposed to other skills needed for their future career, such as teamwork, giving a proposal, and implementing their knowledge in simulation work using MATLAB/Python.

Design a lead compensator to obtain the following requirements 1. Less than 5% SS error for unit step input. 2. Peak time < 0.6 s 3. Overshoot <= 15%

1. For the transfer function shown below, find the locations of the poles and zeros, plot them on the s-plane, and then write an expression for the general form of the step response without solving for the inverse Laplace transform. State the nature of each response (overdamped, underdamped, etc.).

2. For the second-order system that follows, find the damping ratio, natural frequency, 2% settling time, peak time, rise time, and percent overshoot.

For this discussion, you will work with your group to complete the following task: Give an example of a second-order system from daily life and discuss its important performance specifications.

Problem 4 : Obtain a state-space representation of the system shown below:

For this discussion, you will work with your group to complete the following task: Take a control system. Illustrate the design choices/parameters that impact its performance specifications.

Problem 1a (5 points): Find the inverse Laplace transform for: C(s)/R(s) = s+5/s3 + 3s2 + 2s

Problem 3 Reduce the block diagram shown in the figure to a single block representing the transfer function T(s) + C (s)/R(s):