Root Locus Analysis & Design. See attached file for full problem description.

1) Draw the root locus of L (attached). of for positive and negative gain on graph paper.

Find (graphically) the gain, k, to get l = 0.5 for the dominant poles and specify the corresponding corner frequency.

2) Draw the root locus of L (attached) of for positive and negative gain on graph paper. Calculate breakpoints, jw axis crossings and departure angles.

3) Draw the root locus of L (attached) of for positive and negative gain on graph paper.

Find (graphically) the gain k, to get l = 0.5 for the dominant poles and specify the corresponding frequency.

4) Draw the root locus of L (attached) of for positive and negative gain on graph paper. Calculate breakpoints, jw axis crossings and departure angles.

5) Draw the root locus of L (attached) of for positive and negative gain on graph paper.

Find (graphically) the gain k, to get l = 0.5 for the dominant poles and specify the corresponding frequency.

Design a proportional and integral controller, G= k_p ((a+1/T_1)/s) for the plant,
P = 1/((X+1)(S+3)) to have dominant poled with (see attachment)
i) Use rough sketches of the rootlocus to determine the location of the controller zero (i.e. find T_1)
ii) Calculate the required controller gain Kp, (An accurate root lo

Problem 1:
Using the riocus function, obtain the rootlocus for the following transfer function shown in Figure 1 when 0 < k < ∞ and G(s) is defined as the following:
G(s) = (s5+4s4+ 6s3+8s2+6s+4)/( s6+2 s5+2s4+s3+s2+10 -1)
1. Comment on the stability of the system as k varies.
Figure 2
Problem 2:
Consider

Sketch the rootlocus for the following closed loop system {see attachment} as {SYMBOL1} varies from -{SYMBOL2} to +{SYMBOL2}. You should calculate all steps and show the positive and negative gain loci. It is recommended that you first find the positive locus and then sketch the negative {SYMBOL2} locus.
(Real axis solutions o

A genetic locus that is analyzed in many forensic and paternity testing laboratories is the human leukocyte antigen locus known as HLA-DQ alpha. There are four major alleles at this locus known as 1, 2, 3, and 4. How many different genotypes are possible for these four alleles?
A. 8
B. 10
C. 12
D. 16
E. 24
Than

Consider the forward-loop transfer function in the sampled-data system as:
(a) Determine the corresponding z -transform G(z) and the characteristic equation for this system.
(b) Using the bilinear transformation and Routh's Stability Criterion, determine the range of K for stability when the sampling time T = 0.25 s.
(c) C

(Complete problem with equations found in attachment).
Problem 1
A very common industrial controller is the proportional and integral (PI) controller. It has
a transfer function,
, kp is the proportional gain, Ti is the "reset time"
For an integrating process, P(s) = 2/s, investigate the positive rootlocus for

How self-efficacy is related to the concept of locus of control? Design an assignment for an introductory psychology class that might increase student self-efficacy. Explain how the design of your assignment might change based on the two types of locus of control.

Can you show me how to solve the following equations?
Square roots confuse me.
Sq Root of X-1=3?
Sq Root of X^3=8?
and ^3sq root of x^2=4?
Is the sq root of x^2=x an identity?