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# Control Systems Comparison

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Problem 1:
Using the riocus function, obtain the root locus 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 the feedback system shown in Figure 2 above. There are three potential controllers for your system:

• Gc (s) = K (proportional controller)

• Gc (s) = K/s (integral controller)

• Gc (s) = K(1+1/s) (proportional, integral (PI) controller)

The design specifications are T(s) ≤ 10 seconds P.O. ≤ 10% for a unit step input.

1. For the proportional controller, sketch the root locus using MATLAB with 0 < K < ∞. Determine the range of K which results in stability. Determine the value of K, K/s, and K(1+1/s) so that the design specifications are satisfied

2. Co-plot the unit step responses for the closed-loop systems with each controller designed.

3. Compare and contrast the three controllers, concentrating on the steady-state errors and transient performance.

4. Recommend a controller and justify your choice.

https://brainmass.com/engineering/electrical-engineering/control-systems-221557

#### Solution Preview

The solution is provided in the attached files. The MATLAB script is also included in the zip file.

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#### Solution Summary

The solution examines control system comparisons. Three different controllers are compared and contracted concentration on the steady-state errors and transient performance.

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## General and Application Controls

10-16. Identify one or more control procedures (either general or application controls, or both) that would guard against each of the following errors or problems.

a. Leslie Thomas, a secretary at the university, indicated that she had worked 40 hours on her regular time card. The university paid her for 400 hours worked that week.

b. The aging analysis indicated that the Grab and Run Electronics Company account was so far in arrears that the credit manager decided to cut off any further credit sales to the company until it cleared up its account. Yet, the following week, the manager noted that three new sales had been made to that company-all on credit.

c. The Small Company employed Mr. Fineus Eyeshade to perform all its accounts receivable data processing. Mr. Eyeshade's 25 years with the company and his unassuming appearance helped him conceal the fact that he was embezzling cash collections from accounts receivable to cover his gambling losses at the racetrack.data security

d. The Blue Mountain Utility Company was having difficulty with its customer payments. The payment amounts were entered directly onto a terminal, and the transaction file thus created was used to update the customer master file. Among the problems encountered with this system were the application of customer payments to the wrong accounts and the creation of multiple customer master file records for the same account.

e. The Landsford brothers had lived in Center County all their lives. Ben worked for the local mill in the accounts payable department, and Tom owned the local hardware store. Ben had the mill pay for this merchandise in its usual fashion, and he wrote off the missing goods as "damaged inventory." The sheriff couldn't believe that the brothers had created several dummy companies that sold fictitious merchandise to the mill.

a. A bank deposit transaction was accidentally coded with a withdrawal code.

b. The key-entry operator keyed in the purchase order number as a nine-digit number instead of an eight-digit number.

c. The date of a customer payment was keyed 2001 instead of 2010.

d. A company employee was issued a check in the amount of \$-135.65 because he had not worked a certain week, but most of his payroll deductions were automatic each week.

e. A patient filled out her medical insurance number as 123465 instead of 123456.

f. An applicant for the company stock option plan filled out her employee number as 84-7634-21. The first two digits are a department code. There is no department 84.

g. A high school student was able to log onto the telephone company's computer as soon as he learned what telephone number to call.

h. The accounts receivable department sent 87 checks to the computer center for processing. No one realized that one check was dropped along the way and that the computer therefore processed only 86 checks.

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