Control Systems and Automation
What this domain tests
Expect transfer functions, transient and steady-state response, stability criteria, PID control, and automation topics such as PLC scan cycles and SCADA architecture.
Core rules
- A linear time-invariant system is described by its transfer function G(s) = output/input with zero initial conditions.
- Second-order standard form: s^2 + 2 zeta omega_n s + omega_n^2. Damping ratio zeta sets overshoot; omega_n sets speed.
- Routh-Hurwitz gives the number of right-half-plane poles without solving the characteristic equation. A sign change in the first column indicates instability.
- Steady-state error depends on system type: a type-0 system has finite position error, type-1 has zero position error but finite velocity error, type-2 has zero velocity error.
- Gain margin and phase margin are read from the Bode plot; positive margins indicate stability for the closed loop.
- PLC operation is cyclic: read inputs, execute logic, update outputs, then housekeeping. Scan time affects response to fast events.
Worked example
A unity-feedback system has G(s) = K/[s(s+2)]. Find K for zeta = 0.5. Closed-loop characteristic: s^2 + 2s + K = 0. Compare with s^2 + 2 zeta omega_n s + omega_n^2: omega_n = sqrt(K), and 2 zeta omega_n = 2. With zeta = 0.5, omega_n = 2, so K = 4.
Traps
- Confusing open-loop and closed-loop transfer functions.
- Mixing gain margin with phase margin.
- Ignoring integral windup and derivative noise in PID loops.
- Assuming PLC outputs update instantly rather than at the end of the scan.