Control Systems
Control systems theory provides the mathematical framework for making dynamic systems behave as desired through feedback. It is fundamental to power system operation, motor drives, inverter control, and any automated engineering system.
Core Topics
System Modeling
Transfer functions, block diagrams, signal flow graphs. Linearization of nonlinear systems. State-space representation.
Time Domain Analysis
Step response, impulse response, transient specifications: rise time, settling time, overshoot, steady-state error.
Frequency Domain Analysis
Bode plots, Nyquist criterion, gain and phase margins. Frequency response methods.
Stability Analysis
Routh-Hurwitz criterion, root locus, Lyapunov stability. BIBO stability.
PID Control
Proportional, integral, and derivative action. Tuning methods: Ziegler-Nichols, Cohen-Coon. Anti-windup.
State-Space Control
Pole placement, observer design (Luenberger), LQR optimal control, Kalman filter.
Digital Control
Sampling, z-transform, discretization methods, implementation in microcontrollers and DSPs.
Modern & Robust Control
control, model predictive control (MPC), adaptive control. Applications in power electronics and grid systems.
Key Questions These Notes Answer
- How do I design a feedback controller to meet transient and steady-state specs?
- How do I determine if a closed-loop system is stable?
- How does a PID controller work, and how do I tune it?
- How do I design a state observer when I can’t measure all states?
- How does model predictive control differ from classical PID?
Prerequisites
- Mathematical Foundations — differential equations, Laplace transforms, linear algebra
Connects To
- Power Electronics — converter and inverter control loops
- Power Systems — AGC, AVR, PSS
- Renewable Energy & DER — microgrid control, grid-forming inverters
- FE Exam — control systems section
- PE Exam — Power