Control Systems

Control Systems for GATE Electrical and Electronics Engineering, one topic per lesson: the theory in plain words, the formulas, a solved example, and GATE-style questions (MCQ, MSQ and NAT) whose numerical answers are recomputed by a program when the site is built.

Start the first lesson

1Modelling

Transfer Functions and Block DiagramsOpen and closed-loop systems, transfer functions, block diagram reduction rules, signal flow graphs and Mason's gain formula, effect of feedback, and modelling of mechanical and electrical systems.

2Time Domain

Time Response and Steady-State ErrorFirst and second-order step responses, damping ratio and natural frequency, rise time, peak time, overshoot and settling time, system type, error constants and steady-state error.

3Stability

Stability: Routh-Hurwitz and Root LocusBIBO stability, Routh-Hurwitz criterion and special cases, range of K for stability, root locus rules (asymptotes, centroid, breakaway points, jω crossing) and effect of adding poles and zeros.

4Frequency Domain

Bode, Nyquist, Compensators and State SpaceBode plots, gain and phase margins, Nyquist criterion, polar plots, lead and lag compensators, PID controllers, and state-space models with controllability and observability.