Control Systems and Instrumentation
Control Systems and Instrumentation tests transfer functions, feedback, stability, transient response, PID tuning, sensors, and signal conditioning.
Core rules
- Closed-loop transfer function for unity negative feedback is G/(1+G).
- A first-order step response reaches 63.2% in one time constant; settling to 2% takes about 4τ.
- Stability requires all closed-loop poles in the left half-plane; Bode phase margin indicates damping.
- Integral action removes step error but can reduce phase margin; derivative action adds damping and amplifies noise.
- Sensor loading and bridge offset can dominate measurement error.
Worked example
G(s)=10/(s+2) in unity feedback. Closed loop T(s)=G/(1+G)=10/(s+2+10)=10/(s+12). The pole is at -12 rad/s, so τ=1/12 s≈83 ms. For a unit step, dc gain is 10/12=0.833, so the steady output is 0.833, not 1. The position error constant is Kp=lim G(s)=5, so ess=1/(1+Kp)=1/6≈0.167, matching 1-0.833.
Traps
Confusing open-loop and closed-loop poles; using degrees in phase calculations where radians are required; ignoring actuator saturation; adding integral gain without checking windup; and treating a sensor's nominal output as its actual loaded output.