Control and automatic systems: open/closed loop, sensors, actuators and logic control
What the exam tests
Block diagrams, feedback, steady-state error, stability, sensor/actuator selection, and combinational logic for automated systems.
Open vs closed loop
Open loop: the controller acts without measuring the output; cheap but sensitive to disturbance. Closed loop: a sensor measures the output, a comparator forms error e = r − y, and the controller acts on e. Negative feedback reduces sensitivity and steady-state error but can cause oscillation.
Block algebra and response
- Series blocks multiply; parallel blocks add; feedback transfer function G/(1+GH) for negative feedback.
- First-order step response: y(t) = K(1 − e^(−t/τ)); τ is the time constant. Second-order: overshoot depends on damping ratio ζ; ζ < 1 oscillates.
- PID: u = K_p e + K_i∫e dt + K_d de/dt. P reduces rise time, I removes offset, D damps.
- Stability: poles in the left half-plane; Routh–Hurwitz checks polynomials.
Sensors and actuators
Sensors: potentiometer (position), LVDT, encoder (incremental/absolute), thermistor/thermocouple/RTD, strain gauge, photodiode, ultrasonic, inductive proximity. Choose by range, linearity, resolution, response time and environment. Actuators: DC motor, stepper (open-loop positioning), servo, solenoid, pneumatic cylinder. Motor speed control by PWM; direction by H-bridge.
Logic control
Boolean algebra, truth tables, Karnaugh maps. PLC ladder logic: contacts in series = AND, parallel = OR, normally closed = NOT. Safety circuits are hard-wired and fail-safe.
Worked example
A conveyor must start only if the guard is closed (G=1), a start button is pressed (S=1), and no emergency stop is active (E=0). Let the emergency-stop signal be 1 when pressed. Output M = G·S·E′. If G=1, S=1, E=0, then M=1 and the motor runs. If the guard opens, M=0 immediately. A truth table confirms M=1 only in that row.
Traps
- Forgetting that feedback sign matters in G/(1+GH).
- Using a sensor outside its linear range.
- Confusing PLC normally-open contacts with the physical device state.
- Tuning integral action too high, causing windup.
- Treating a stepper as a closed-loop servo.