Electrical Control System

For the first part, transfer function...I am getting a weird answer that is not working in MatLab, need help to get transfer function Also, if you can help with parts b, c and d. ******THE LOAD RESISTANCE IS 1 OHM************

Writing time domain equations

Please see illustrated circuit diagram to write all the time domain equations. See attached file for full problem description.

Block Diagram

For a VTOL (Vertical Take Off and Landing) aircraft, there is the following Block Diagram (see attached VTOL_BlockDiagram file). a) Find the system response for step input and determine the steady state error b) Find the variation of Kc in the stability of VTOL c) Is the system always stable? a = 0.5; b = 10; c =3 Ka = 1; Kb = 17; Kc = 1 u(t) = step distance = 0.1 r(t) = step input = 1 Solve parts a, b and c by both methods: 1) Classical Method using Laplace Transform, Final Value Theorem and Routh's Stability Criterion. 2) Signal Flow Graph, State Variables, State Equation, Transition Matrix, Eigenvalues

Root Locus

I have the question and the answer, but I could use a more detailed explanation on how to find the closed-loop characteristic equation, how to plot the root locus, and explain how to find the characteristic equation with K2 including how to plot the root locus. See attachment for problem description and answers.

Graphing the root locus and finding range of stability

I understand how to use Matlab to graph the loci, but I need help to understand how to graph the loci by hand. Sketch the Loci and find range of K for stability for these two problems K(s+1) ------------------ (s-1)(s^2 + 4s + 16) and K ------------------- (s-1)(s^2 + 4s + 7)