Consider the plant with transfer function G(s) connected in standard feedback configuration with the controller De(s) = K. 1) 2) = s+2 (s+1)²+1 Sketch the root locus for G(s). Explain what rules you used to plot it. (Be sure to describe the following: the number of branches, where they start and where they are going; the real-axis portion of the root locus; jw-axis crossings (if any); points of multiple roots (if any).) What conditions need to be imposed if we want our closed-loop system to have no oscillations under a step input? Explain the conditions from the root locus. + Ro Σ Dc(s) G(s) Figure 1: Control system in Problem 1.

Hi, I could use some help with the following problems for controls. I am trying to get this to work, but I keep getting stuck. I'm trying to review some problems for an upcoming test by using some online resources.

Solve the following problem by hand and without the use of AI. Thank You!

The differential equation of a cruise control system is provided by the following equation:    Find the closed loop transfer function with respect to the reference velocity (vr) . a. Find the poles of the closed loop transfer function for different values of K. How does the poles move as you change K? b. Find the step response for different values of K and plot in MATLAB. What can you observe? c. For the given transfer function, find tp, ts, tr, Mp . Plot the resulting step response. G(s) = 40/(s^2 + 4s + 40)

1) Consider the system below: Vehicle Controller Steering dynamics Desired Actual bearing angle bearing angle 50 1 K s2 + 10s + 50 s(s + 5) Figure 1: Simplified Block Diagram of a Self-Guiding Vehicle's Bearing Angle Control. • Find a K value that the system has minimum rise time and minimum overshoot. Let us call this proportional gain as Kopt Show each step while finding Kopt- Show the necessary graphical solutions. Simulate the system response with 3 different K values. (Kopt and two other K values close to Kopt) Show the system response (actual bearing angle) in a single graph for different K values. • Comment on the results.

Please solve the following by hand and without the use of AI. Thank you!

Solve the following without the use of AI. Show all steps. Thank You!

For the system with open loop transfer function given by R(s) K s(s + 1) (s² + 4s +13) where K is the feedback gain. Sketch the root locus a) How many asymptotes are there for this system's root locus? what are asymptote angles? What is the center of asymptotes? C(s) b) Does the root locus cross the imaginary axis? where and what is the value of K at that point? c) Is there any break away, break in points? What is the approximate values of these points?

draw the root locus clearly, no handwritten and copied solution plz. Upvote for well explained answer. Downvote for wrong and short answer.

DO NOT COPY SOLUTION The differential equation of a cruise control system is provided by the following equation:    Find the closed loop transfer function with respect to the reference velocity (vr) . a. Find the poles of the closed loop transfer function for different values of K. How does the poles move as you change K? b. Find the step response for different values of K and plot in MATLAB. What can you observe? c. For the given transfer function, find tp, ts, tr, Mp . Plot the resulting step response. G(s) = 40/(s^2 + 4s + 40)