Control Systems

A transfer function G(s) = C(s)/R(s) is the Laplace-domain ratio of output to input with zero initial conditions; its poles and zeros determine the system’s dynamic behaviour.

The time response of a standard second-order system is set by the damping ratio ζ and natural frequency ω_n; ζ controls overshoot and settling while ω_n controls the speed of response.

The root locus plots how the closed-loop poles migrate in the s-plane as the loop gain K varies from zero to infinity, revealing at a glance the range of K for stability and the achievable damping.

Frequency response evaluates G(jω) as ω varies; the gain and phase margins read from Bode or Nyquist plots quantify how much extra gain or phase lag the system can tolerate before instability.

PID = Proportional + Integral + Derivative — adjusts output from error signal to hold temperature, speed, or pressure at setpoint. Used in every process plant and automation interview.