An open loop transfer function of a certain unit feedback control system is described as below, where K is an adjustable gain (Proportional Controller) and G(s) is a process transfer function.

1. In the space provided (see attached), sketch a Root Locus plot of the closed loop system for positive Proportional Controller gains. Show all relevant coordinates (centroid, asymptotes, crossovers with Inn axis, if any, break-away/break-in coordinates, if any).

2. Find the value of the Proportional Gain such that the closed loop system exhibits a damping ratio of 0.707. For this value of the gain, briefly explain whether the closed loop dynamics can be adequately represented by a second order system model. If it can, find the appropriate parameters of the model.

3. For the same value of the gain, evaluate the following specifications of the closed loop step response: percent overshoot, settling time, and steady state error.

I have completed the block diagram for the attached question, however I am having problems deriving an expression for the transferfunction, in terms of parameters k1, k2, k0 and kt.

Consider a unity-feedbackcontrolsystem with the closed loop transferfunction:
C(s)/R(s) = Ks+b/s^2+as+b
Determine the open loop transferfunction G(s).
Show that the steady-state error in the unit-ramp response is given by:
e_ss = 1/K_v = a-K/b
See attached file for equations in equation editor. Please use Micros

Problem 1:
A unity negative feedbacksystem has the open-loop transferfunction.
G(s) = (s + 1)/(s3 + 4s2 + 6s + 10)
1. Using MATLAB, determine the closed-loop transferfunction.
2. Using MATLAB, find the roots of the characteristic equation.
3. Is the system stable, marginally stable, or unstable?
4. Use ltiview to d

The open loop transferfunction of a unity feedbackcontrolsystem is given:
G(s) = K/s(s+3)^2
Sketch the root locus of the system.
See attached file for the problem as well.

Determine:
a) the values of K and k of the closed-loop system shown in Fig. 1 (see attached file) so that the maximum overshoot in unit-step response is 25% and peak time is 2 sec., assume that J=1 kg-m^2 . Consider a unity-feedbackcontrolsystem with the closed loop transferfunction.
b) whether system is stable or not.

For a unity feedbacksystem with open-loop transferfunction, G(s) = K(s+alpha)/(s^2 + 4s + 1):
a) Find all values of alpha such that the system is stable for K = 2.
b) If the unity feedback closes around this G(s) and an input is a unit step r(t) = 1u(t), what is the stead-state error, e_ss, as a function of alpha and K?
c)

A system described in the attachment is under feedbackcontrol of the form u = Kx + r where r is the reference input.
(i) Show that (A,C) is observable.
(ii) Compute a K of the form {see attachment} so that (A - BK, C) is unobservable. (I.e., the closed loop system is unobservable)
(iii) Find the transferfunction of the open

Consider a controlsystem described by the attached state space model.
(1) For the system in question do the following:
- Find the systemtransferfunction, {see attachment}
- Find the system eigenvalues
- Check the systemcontrollability and observability
(2) Assume the state feedback of the form: {see attachment} and