Control Systems Analysis and Design
Core concepts
A feedback loop consists of sensor, controller, final element, and process. The PID controller has proportional, integral (reset), and derivative (rate) terms. Process dynamics are described by gain, time constant, and dead time; dead time is the main limit on achievable loop speed. Stability is assessed with gain and phase margins or ultimate gain. Tuning methods include open-loop reaction-curve and closed-loop ultimate-gain approaches. Advanced structures include cascade, feedforward, ratio, split-range, and selector/override control. Practical requirements include anti-windup, bumpless transfer, derivative on measurement rather than error, and a sample time fast relative to the process.
Traps
Proportional band and controller gain are inversely related: Kc = 100/PB% when PB is in percent. Reset may be expressed in repeats per minute or minutes per repeat, which are reciprocals. Integral windup occurs when the controller keeps integrating while the valve is saturated. Derivative on error causes setpoint-change kick. A cascade slave must be faster than its master. Feedforward corrects a measured disturbance but does not by itself stabilize the feedback loop. If dead time exceeds the dominant time constant, PID tuning alone is unlikely to solve the problem.
Worked example
A controller has a 200% proportional band. Kc = 100/200 = 0.5. A 10% error produces a proportional output change of 0.5 × 10% = 5%. If reset is 0.5 repeats per minute, integral time is 1/0.5 = 2 minutes per repeat.