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FAQ Coverage Gaps

This report identifies concepts from the learning graph that are not directly addressed in FAQ questions, organized by priority for future additions.

Summary

Priority Level Count Action
Critical Gaps 8 Add questions in next revision
Medium Priority 23 Consider adding when FAQ is updated
Low Priority 23 Address in future versions
Total Uncovered 54 Out of 300 concepts

Current Coverage: 246/300 (82%)

Critical Gaps (High Priority)

These are high-centrality concepts with many dependencies that should be covered in the FAQ.

1. Mason's Gain Formula

  • Centrality: High (used for all signal flow graph analysis)
  • Category: Block Diagrams
  • Why Important: Essential technique for complex systems
  • Suggested Question: "What is Mason's Gain Formula and when do I use it?"

2. Pole-Zero Cancellation

  • Centrality: High (affects controllability/observability)
  • Category: Laplace/Transfer
  • Why Important: Can hide unstable modes if not understood
  • Suggested Question: "What is pole-zero cancellation and why can it be dangerous?"

3. Convolution Integral

  • Centrality: High (foundational for system analysis)
  • Category: Time-Domain
  • Why Important: Links impulse response to general input response
  • Suggested Question: "What is convolution and how does it relate to system response?"

4. Partial Fraction Expansion

  • Centrality: High (essential for inverse Laplace)
  • Category: Laplace/Transfer
  • Why Important: Core technique for finding time responses
  • Suggested Question: "How do I use partial fraction expansion to find inverse Laplace transforms?"

5. Signal Flow Graph

  • Centrality: High (alternative to block diagrams)
  • Category: Block Diagrams
  • Why Important: Sometimes easier than block diagram reduction
  • Suggested Question: "What is a signal flow graph and how does it differ from a block diagram?"

6. Asymptotic Approximation

  • Centrality: Medium-High (core Bode plot technique)
  • Category: Frequency
  • Why Important: Essential for hand-sketching Bode plots
  • Suggested Question: "How do I use asymptotic approximation to sketch Bode plots?"

7. Dominant Poles

  • Centrality: High (key design concept)
  • Category: Laplace/Transfer
  • Why Important: Simplifies higher-order system analysis
  • Suggested Question: "What are dominant poles and why do they matter for design?"

8. Final Value Theorem

  • Centrality: High (steady-state analysis)
  • Category: Laplace/Transfer
  • Why Important: Quick way to find steady-state values
  • Suggested Question: "How do I use the Final Value Theorem to find steady-state response?"

Medium Priority Gaps

These concepts are covered implicitly or partially but could benefit from dedicated questions.

Physical System Modeling (8 concepts)

  • RLC Circuit
  • RC Circuit
  • Mass-Spring-Damper
  • DC Motor
  • Motor Transfer Function
  • Gear Train
  • Thermal Systems
  • Fluid Systems

Suggested Addition: "How do I model common physical systems as transfer functions?"

Block Diagram Details (5 concepts)

  • Pickoff Point
  • Summing Junction
  • Cascade Connection
  • Parallel Connection
  • Block Diagram Algebra

Suggested Addition: "What are the rules for block diagram manipulation?"

Frequency Response Details (6 concepts)

  • First-Order Bode Plot
  • Second-Order Bode Plot
  • Integrator Bode Plot
  • Differentiator Bode Plot
  • Half-Power Point
  • Quality Factor

Suggested Addition: "How do I construct Bode plots for basic transfer function factors?"

Root Locus Details (4 concepts)

  • Breakaway Point
  • Break-In Point
  • Departure Angle
  • Arrival Angle

Suggested Addition: "How do I find breakaway points and angles on the root locus?"

Low Priority Gaps

These are specialized or advanced concepts that are less frequently needed.

Analogies and Special Topics (8 concepts)

  • Impedance Analogy
  • Mobility Analogy
  • Force-Voltage Analogy
  • Force-Current Analogy
  • Analogous Systems
  • Lever System
  • Pendulum System
  • Op-Amp Circuits

Specialized Frequency Concepts (7 concepts)

  • Octave
  • Time Delay in Bode
  • All-Pass System
  • Minimum Phase System
  • Conditionally Stable (partially covered)
  • Encirclement
  • Nyquist Contour

Specialized Controller Concepts (8 concepts)

  • Derivative Kick (partially covered)
  • Integral Time
  • Derivative Time
  • Ultimate Period
  • Reaction Curve Method
  • Maximum Phase Lead
  • Compensation Zero
  • Compensation Pole

Recommendations for FAQ Improvement

Immediate Actions (Next Revision)

  1. Add 8 Critical Gap Questions
  2. Mason's Gain Formula
  3. Pole-Zero Cancellation
  4. Convolution Integral
  5. Partial Fraction Expansion
  6. Signal Flow Graph
  7. Asymptotic Approximation
  8. Dominant Poles

  9. Final Value Theorem

  10. Expand Physical Systems Coverage

  11. Add one comprehensive question on modeling electrical/mechanical systems
  12. Reference specific chapter content

Future Improvements

  1. Add Technical Details Section
  2. Bode plot construction procedures
  3. Root locus calculation details

  4. Block diagram manipulation rules

  5. Add Worked Examples Section

  6. Step-by-step solutions for common problem types

  7. Links to MicroSims for interactive practice

  8. Add Troubleshooting Expansion

  9. More specific debugging scenarios
  10. Common Python errors

Coverage by Chapter

Chapter Concepts Covered in FAQ Gap Count
1. Introduction 12 12 0
2. Dynamic Properties 8 8 0
3. Time-Domain Response 22 19 3
4. Transient Specs 12 11 1
5. Laplace Methods 18 12 6
6. Poles and Zeros 16 13 3
7. Physical Modeling 28 12 16
8. Linearization 10 8 2
9. Block Diagrams 20 14 6
10. Stability/Routh 20 18 2
11. Root Locus 22 17 5
12. Bode Plots 35 30 5
13. Nyquist 14 12 2
14. Steady-State Error 14 13 1
15. PID Control 21 19 2
16. Compensators 20 18 2

Highest Gap Chapters: 1. Chapter 7: Physical Modeling (16 gaps) 2. Chapter 9: Block Diagrams (6 gaps) 3. Chapter 5: Laplace Methods (6 gaps)

These chapters may need additional FAQ questions or improved cross-referencing.

Conclusion

With 82% concept coverage, the FAQ provides solid support for students. Priority should be given to adding the 8 critical gap questions, which would raise coverage to 85%. Full coverage of all 300 concepts is not necessary—some detailed procedural concepts are better addressed in chapter content rather than FAQ format.