FE Electrical & Computer Practice Question Solution included after investigation
CASE E-034 · FE

The Higher-Gain Loop That Crossed Into Instability

Increasing gain improved response—until the characteristic equation crossed the stability limit.

▶ INTERACTIVE CASE FILE • 5–10 MIN • CLICK TO INVESTIGATE

Inspect, commit, prove, fix, and sign off.

Case E-034 engineering failure visual
HOW THIS WORKS

Think like
a real engineer.

Follow the investigation process used in the field — in five guided steps.

1

Inspect

Review the problem, diagram, and evidence.

2

Commit

Choose your hypothesis.

3

Prove

Run calculations and test your idea.

4

Fix

Select and validate a safe correction.

5

Sign Off

See the full debrief and key takeaways.

Case Brief

SAME PRINCIPLES. HIGHER STANDARDS.
PROBLEM STATEMENT

A unity negative-feedback plant has G(s)=K/[s(s+1)(s+3)]. A tuning note raises K to 20 to reduce tracking error. The closed loop then oscillates and diverges. Derive the characteristic equation, use the Routh criterion to find the stable gain range, and choose a gain that remains stable.

Control Systems Electrical & Computer Design Verification Root Cause Analysis Safe Correction
E-034
INVESTIGATION WORKSPACE WORK THROUGH THE CASE — YOUR CHOICES MATTER.
🔒
DEBRIEF (LOCKED)

Complete the investigation
to unlock the full debrief.

Find the root cause, confirm the fix, and see how this connects to the exam.

🔒Root causeComplete the case
to reveal
🔒Correct fixComplete the case
to reveal
🔒Exam takeawayComplete the case
to reveal
CASE CLOSED · ENGINEERING VERDICT

What actually failed — and what should change.

What failed

K=20 exceeded the closed-loop stability range.

What was assumed

More negative-feedback gain was assumed to be automatically safer.

Corrected model

Form the characteristic equation and verify stability before accepting gain changes.

QUICK ANSWER

For unity feedback with G(s)=K/[s(s+1)(s+3)], the characteristic polynomial is s^3+4s^2+3s+K. Routh-Hurwitz requires K>0 and (12-K)/4>0, so the strictly stable range is 0<K<12.

ENGINEERING TAKEAWAY

Controller gain must satisfy both performance and stability constraints. Form the closed-loop characteristic polynomial and test stability before increasing gain.

CASE QUESTIONS

Questions this case should settle.

What is the stable gain range for s^3+4s^2+3s+K?

Using the Routh criterion, 0<K<12.

Does negative feedback guarantee stability for any positive gain?

No. Stability must still be checked from the closed-loop characteristic equation.

NEXT FE PRACTICE QUESTION

The Bode Plot That Lost 20 dB in One Decade

Control Systems · 5–10 min

Continue Practice →
WHAT YOU’LL LEARN

Real failures. Lasting skills.

Each case is designed to build the judgment, analysis, and confidence you need for engineering exams — and beyond.

  • Apply core engineering concepts to real-world problems
  • Practice structured troubleshooting and analysis
  • Strengthen exam-ready thinking through realistic scenarios
COMMON QUESTIONS
Do I need prior knowledge to use these cases?

Basic subject familiarity helps, but every case is designed to teach through the investigation itself.

How long does a case take?

Most cases are designed for a focused 5–10 minute investigation.

Are the cases aligned with engineering exams?

Each case is mapped to a verified exam, subject, topic, and misconception before publication.

What happens after I complete a case?

The sealed debrief unlocks with the root cause, corrected reasoning, fix, and takeaway.