Automatic Control Engineering
From transcript: 20ME821 Automatic Control Engineering (D)
Cheat sheet
Formulas
TF G(s)=Y(s)/U(s) (zero ICs)
1st order: τ ẏ + y = K u ; step → K(1−e^{−t/τ})
2nd order: ÿ + 2ζωn ẏ + ωn² y = K ωn² u ; ωn, ζ overshoot/settling
Settling ~4/(ζωn) ; overshoot e^{−ζπ/√(1−ζ²)} (underdamped)
Closed loop T = G/(1+GH) ; characteristic 1+GH=0
Routh–Hurwitz stability from coeff array
Root locus: branches start open-loop poles end zeros/∞
Bode: gain/phase margins from |G| and ∠G plots
PID: u = Kp e + Ki ∫e + Kd ė ; P↑ speed, I kills SS error, D damps
Nyquist: encirclements of −1 for closed-loop stability
G(s) = Y(s)/U(s) (linear time-invariant)
Closed loop: T = G/(1+GH) (unity feedback H=1 → G/(1+G))
1st order: τẏ + y = K u ; settling ~4τ (2%)
2nd order: ωn, ζ ; %OS ≈ exp(−ζπ/√(1−ζ²))
Routh–Hurwitz: necessary stability on characteristic polynomial
PID: u = Kp e + Ki ∫e + Kd ė
Definitions
- Plant / process
- System being controlled
- Open vs closed loop
- No feedback vs feedback correction
- Disturbance rejection
- Hold output despite external loads
- Steady-state error
- Final error to reference — depends on system type & input
- Stability
- Bounded output for bounded input — poles left-half s
- Gain/phase margin
- Distance to instability on Bode
- Observability / controllability
- State-space structural properties
- Actuator saturation
- Nonlinear limit — windup on I term
Topic-wise short notes
System modeling & TF
- Mechanical: m–c–k ; electrical RLC analogs.
- Block diagram algebra: series, parallel, feedback reduction.
- Signal flow / Mason if needed.
- State-space ẋ=Ax+Bu ; y=Cx+Du — modern control entry.
PID & stability
- Ziegler–Nichols tuning as starting point — refine on plant.
- Lead/lag compensators shape Bode.
- Digital control: sampling, ZOH, z-plane poles.
- Safety: always limit commands; watch integrator windup.
Time response specs
- Rise time, peak time, overshoot Mp, settling time, SS error — sketch 2nd-order step.
- ζ≈0.7 often good compromise damping vs speed.
- Type 0/1/2 systems: ramp error depends on system type & Kv.
Frequency domain
- Bandwidth ↔ speed of response; resonant peak ↔ damping.
- Gain margin & phase margin targets (rules of thumb ~6 dB, 30–60°).
- Lead adds phase near crossover; lag improves SS error.
Implementation
- Sensor noise: filter before D term or use filtered derivative.
- Saturation & rate limits → nonlinear; anti-windup essential.
- Sample time Ts << plant dominant τ (rule of thumb 1/10…1/30).
Exam traps & quick notes
- Draw block diagram before math.
- Mechatronics: sensors → controller → actuator is the same story.
- Farm/IoT: on-off vs PID for moisture/pressure loops.
- Linearize about operating point for TF models.
- Too much P → oscillation; too much D → noise amplification.
- Anti-windup when using integral with saturation.
- Sensor lag & delay kill margins — model them.
- Verify time response AND frequency margins.
Comprehensive notes
System modeling & TF
Mechanical/electrical analogs; linearization; block diagram algebra.
External: CTMS Control Tutorials ↗ NPTEL Control Engineering ↗
PID & stability
Ziegler–Nichols intuition; root locus / Bode basics; gain/phase margins.
External: MATLAB PID tuning guide ↗
Models & transfer functions
Linearization; G(s)=Y/U; block diagrams; 1st/2nd order specs (τ, ζ, ωn, overshoot).
External: NPTEL ↗ Engineering Toolbox ↗
PID & stability
P/I/D roles; Routh–Hurwitz idea; Bode margins intuition; windup. Sensors→controller→actuators in mechatronics/IoT.
External: NPTEL ↗ Engineering Toolbox ↗
Interview Q&A for this subject
Q: Effect of pure P control on step?
A: Speeds response, leaves steady-state error on many plants; too high gain can oscillate.
External: ASQ / quality ↗ MIT OCW ↗