Modeling and Control of Dynamical Systems
MANE - 4500
Midterm Exam #2 - points recovery
1 Consider the block diagram shown below:
Figure 1: System diagram
A) [0.5 pts] Find the overall closed loop transfer function from R(s) to Y (s).
B) [2.0 pts] Find the characteristic equation for this system, and then re-write it as 1 + KGOL(s) = 0. Hint: The “OL” in GOL stands for open loop and cannot have K within.
C) [5.0 pts] Plot the root locus of this system.
2 For a proportional feedback control system with plant trans-fer function P(s) and feedback transfer function F(s) as shown below. Answer the following about its root-locus diagram:
A) [0.5 pts] How many asymptotes are there? Where are they centered? What is/are the incidence angle(s)?
B) [0.5 pts] What sections of the real axis belong to the root locus?
C) [1.0 pts] Are there break-in/away points? If so, where are their locations?
D) [1.5 pts] What are the angles of departure/arrival at the complex poles/zeros?
E) [2.0 pts] Draw the root locus diagram, make sure to include all quantities calculated above.
F) [2.0 pts] For what range of gain Kp would this system be stable? For what range of gain Kp could this system be approximated as an underdamped 2nd order system?