Fuzzy_Logic_Lecture_With_Figures - and applications

Fuzzy logic controller with its applications in control systems - case study

1. Fuzzy Logic: From First Principles to Control Applications Comprehensive Lecturer Notes with Figures & Examples Prepared for Control Systems Lectures

2. Motivation for Fuzzy Logic • Classical (crisp) logic = binary (0/1). • Fuzzy logic handles uncertainty and linguistic knowledge. • Example: Air conditioning – 'If temperature is hot, then fan speed is high'. • Advantage: Smooth transition between states.

3. Fuzzy Sets & Membership Functions • Fuzzy set: defined by membership function μ(x) ∈ [0,1]. • Common shapes: triangular, trapezoidal, Gaussian. • Terms: Support, Core, α-cut. • Example: 'Cold' temperature fuzzy set. [Figure: Triangular & Gaussian MFs]

4. Fuzzy Operations • Complement: μ¬A(x) = 1 - μA(x). • Intersection (AND): min(μA(x), μB(x)). • Union (OR): max(μA(x), μB(x)). • Example: 'Tall AND Heavy' fuzzy classification.

5. Fuzzy Inference Systems • Mamdani: rules with fuzzy consequents. • TSK: rules with functional consequents. • Inference pipeline: 1. Fuzzification 2. Rule evaluation 3. Aggregation 4. Defuzzification [Figure: Inference pipeline block diagram]

6. Defuzzification Methods • Centroid (Center of Gravity) – most common. • Bisector of Area. • Mean of Maxima (MOM). • TSK weighted average (efficient). • Example: Fan controller crisp output = 65% speed. [Figure: Centroid illustration]

7. Fuzzy Logic Controller (FLC) • Inputs: error (e), error rate (de). • Output: control action (u). • Components: knowledge base, inference engine, defuzzifier. • Example: Cruise control fuzzy rule base. [Figure: Block diagram of FLC]

8. Worked Example: Room Temperature Control • Plant: heater + room thermal dynamics. • Inputs: error (°C), rate of error. • Output: heater power %. • Rules: – IF e is Positive & de is Zero → Heater = High. – IF e is Zero & de is Zero → Heater = Medium. [Figure: Error membership functions]

9. Applications of Fuzzy Control • DC Motor speed regulation. • Washing machines (water level, spin control). • Camera autofocus (lens movement speed). • Robotics path following. • pH control in chemical processes.

10. Pitfalls & Remedies • Too many rules → Rule explosion. – Remedy: reduce MFs or use clustering. • Dead zones near setpoint. – Remedy: overlap MFs properly. • Contradictory rules. – Remedy: visualize and adjust control surface. [Figure: Control surface plot]

11. Lab Assignment Example • Build fuzzy controller for room temperature in MATLAB/Python. • Define membership functions. • Construct 5×5 rule base. • Simulate step response & compare vs PID. • Deliverables: plots, rule tables, report.