Control Systems and Instrumentation
Control Systems and Instrumentation tests dynamic system models, feedback, stability, PID control, sensors, signal conditioning, and measurement uncertainty. Expect transfer functions, block-diagram reduction, steady-state error, Bode plots, and calibration.
Core rules
- Closed-loop transfer T(s)=G(s)/(1+G(s)H(s)) for negative feedback.
- A system is stable if all closed-loop poles have negative real parts.
- Steady-state error depends on system type and input: step, ramp, or parabola.
- PID output u=Kp e + Ki∫e dt + Kd de/dt; integral removes offset, derivative adds damping but amplifies noise.
- Sensor loading and calibration affect accuracy; uncertainty combines in quadrature for independent random errors.
Worked example
G(s)=10/(s+2), H(s)=1. T(s)=10/(s+12), so the closed-loop pole is at −12 and the system is stable. For a unit step, DC gain is 10/12=0.833, so steady-state output is 0.833 and error is 0.167. Increasing proportional gain would raise DC gain but may reduce phase margin.
Traps
Do not call a system stable because its open-loop poles are stable; feedback can destabilize. Use radians/s consistently in Bode and PID calculations. Derivative kick and integral windup are implementation problems, not tuning preferences. In instrumentation, a high-impedance sensor can be loaded by a low-impedance input, causing a systematic error. Calibration slope and offset are separate from random noise.