Page 64 – PWM Control & Small-Signal Modeling (Introduction)
Subject: Power Electronics + Control Systems
Level: GATE / PSU Conceptual
🔹 1️⃣ Why Control is Needed?
DC-DC converters are nonlinear systems. To maintain constant output voltage despite load or input variation, we use feedback control.
- Regulate output voltage
- Improve stability
- Reduce steady-state error
- Improve transient response
🔹 2️⃣ Pulse Width Modulation (PWM)
PWM controls output voltage by varying duty cycle (D).
Principle:
- Compare control voltage with triangular carrier
- When Vcontrol > Vtri → Switch ON
- Duty cycle ∝ Control voltage
Output Voltage ∝ Duty Cycle
🔹 3️⃣ Feedback Control Block Diagram
- Reference voltage (Vref)
- Error amplifier
- PWM generator
- Power stage
- Output feedback
Closed Loop = Stable + Regulated Output
🔹 4️⃣ Why Small-Signal Modeling?
Converters are nonlinear (switching systems). We linearize around operating point to analyze stability.
Idea:
Total variable = DC steady-state + small perturbation Example: D = D + d~ Vo = Vo + v~
🔹 5️⃣ Linearized Control-to-Output Transfer Function
For Buck Converter (CCM):Gvd(s) = Vo(s) / d(s) = Vin / (1 + s(RC) + s²(LC))
Key Observations:- Second order system
- Has double pole
- ESR introduces zero
🔹 6️⃣ Important Frequency Concepts
Natural Frequency:
ω₀ = 1 / √(LC)
Quality Factor:
Q = R √(C/L)
Zero due to ESR:
ωz = 1 / (RESR × C)
🔹 7️⃣ Stability Design (Very Important)
- Use Type I, Type II, Type III compensator
- Ensure phase margin > 45°
- Ensure gain margin adequate
GATE often asks:
✔ Location of poles
✔ Effect of ESR zero
✔ Stability conditions
🔥 Exam Memory Capsule
✔ PWM controls duty cycle ✔ Small-signal model = linearized model ✔ Buck converter → 2nd order system ✔ ESR introduces zero ✔ Control ensures voltage regulation
Power Electronics Control Series – Shaktimatha Learning
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