Control Systems Engineering
Transfer functions, mathematical modeling of physical systems, block diagram reduction, signal flow graphs, time response, Routh-Hurwitz, Root Locus, and Bode/Nyquist stability.
Syllabus Units (4)
- Unit 1
Mathematical Modeling, Block Diagrams & Signal Flow Graphs
Differential equations of physical systems, mechanical translational and rotational systems, Force-Voltage (F-V) and Force-Current (F-I) analogies, transfer function derivations, block diagram algebra and reduction rules, and Mason’s Gain Formula for Signal Flow Graphs (SFG).
Read note - Unit 2
Time Response Analysis & Transient Specifications
Standard test signals, first-order step and impulse responses, prototype second-order system dynamics across undamped, underdamped, critically damped, and overdamped regimes, transient response specifications (delay, rise, peak time, %Mp, and settling time), steady-state error analysis, static error constants (Kp, Kv, Ka), and system types.
Read note - Unit 3
Stability Analysis & Root Locus Techniques
Concept of BIBO and asymptotic stability, characteristic equation and s-plane pole locations, Routh-Hurwitz stability criterion with special cases (first column zero and all-zero row / auxiliary polynomial), marginal stability, Evans Root Locus fundamentals, angle and magnitude criteria, construction rules (real-axis segments, asymptotes, centroid, breakaway points, departure angles, jω crossings), and s-plane transient design bounds.
Read note - Unit 4
Frequency Response & State Variable Analysis
Frequency domain specifications (resonant peak Mr, resonant frequency ωr, bandwidth ωBW), Bode magnitude and phase plots, gain and phase margins, polar plots, Nyquist stability criterion (encirclement formula N = P - Z), state variable concepts, canonical state-space forms (controllable, observable), Resolvent matrix (sI - A)⁻¹, State Transition Matrix (STM) Φ(t) = e^(At), and Kalman controllability and observability rank tests.
Read note