--- title: "Use of PID controllers" subject: "Control Systems" chapter: 7 key: "semester_3/control_systems:pid-use" source: https://www.bctengineer.com/q/semester_3/control_systems/pid-use site: BCT Engineering --- # Use of PID controllers Control Systems · Chapter 7: Performance Specifications and Compensation Design - Asked in: 2070 Chaitra (old course), 6 marks; 2066 Jestha (old course), 6 marks (asked 2 times) - Video: [PID Controller Explained](https://www.youtube.com/watch?v=fv6dLTEvl74) — RealPars - Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14 - Page: https://www.bctengineer.com/q/semester_3/control_systems/pid-use - Whole chapter: https://www.bctengineer.com/md/semester_3/control_systems/chapter-7 ## Question Discuss in brief the use of PID controllers in control system. ## Short answer PID controllers combine proportional, integral, and derivative actions. They achieve zero steady-state error (via integral action), improved transient response and stability (via derivative), and are widely used in industrial process control with simple tuning rules. ## Answer A **PID controller** combines proportional, integral and derivative actions on the error. It is the most widely used controller in industry (process control of temperature, pressure, flow, level; motor speed and position control) because it can fix both transient and steady-state behaviour with three tunable gains. $$ u(t)=K_pe(t)+K_i\int_0^te\,dt+K_d\frac{de}{dt},\qquad G_c(s)=K_p+\frac{K_i}{s}+K_ds=\frac{K_ds^2+K_ps+K_i}{s} $$ ```text +-->[ Kp ]---+ e ---->+-->[ Ki/s ]--(+)--> u ---> Plant ---> c +-->[ Kd s ]---+ ``` PID adds one pole at the origin and two zeros to the open loop. #### Role of each term | Term | Acts on | Main effect | |---|---|---| | P | present error | faster response, reduces (not removes) error; too high → oscillation | | I | past (accumulated) error | removes steady-state error (type +1); may raise overshoot | | D | future trend (rate) | adds damping, reduces overshoot and settling time, improves stability | #### Uses / advantages 1. **Zero steady-state error** to step inputs (and ramp for a type-1 plant) due to the integral term. 2. **Good transient response:** derivative action limits overshoot introduced by P and I. 3. **Better relative stability** (PD part acts like a lead compensator, PI part like a lag; PID behaves like a lag-lead compensator). 4. **Simple tuning** without an exact model, e.g. Ziegler–Nichols rules: $K_p=0.6K_{cr}$, $T_i=0.5P_{cr}$, $T_d=0.125P_{cr}$. 5. Available as standard industrial hardware and in PLC/DCS software. #### Limitations - D action amplifies noise, so a filtered derivative is used. - Integral wind-up when the actuator saturates (anti-wind-up needed). **Example:** in a boiler temperature loop, P gives quick heating, I removes the final offset from the set point, and D stops the temperature overshooting when the setpoint is changed. ## Check yourself The answer's key points as multiple-choice questions, with the correct option and why. 1. What does the PID controller Gc(s) = Kp + Ki/s + Kd s add to the open loop? A. Two poles at the origin and one zero B. One pole at the origin and two zeros C. One pole and one zero only D. Three zeros Answer: B. Gc = (Kd s^2 + Kp s + Ki)/s: one pole at the origin and two zeros. (Key point: PID structure) 2. Which assignment of effects to terms is correct? A. P removes steady-state error, I adds damping, D speeds the response B. I removes steady-state error, D adds damping and reduces overshoot, P speeds response C. D removes steady-state error, I adds damping D. P adds damping, D removes error Answer: B. Integral action removes steady-state error, derivative adds damping, proportional gives faster response. (Key point: Role of terms) 3. In frequency-domain terms, PID behaves like which compensator? A. Lead only B. Lag only C. Lag-lead (PI like lag, PD like lead) D. Notch filter Answer: C. The PD part acts like a lead and the PI part like a lag, so PID behaves like a lag-lead compensator. (Key point: Equivalent compensator) 4. Which are limitations of PID? A. It cannot remove steady-state error B. D amplifies noise and integral windup occurs when the actuator saturates C. It always reduces system type D. It needs an exact plant model Answer: B. Derivative action amplifies noise (use filtered D) and integral wind-up needs anti-windup. (Key point: Limitations) ## Related in Control Systems - [True/false: derivative controllers always used with others](https://www.bctengineer.com/question.md?key=semester_3%2Fcontrol_systems%3Aderivative-always-with-others) — Control Systems, chapter 7, asked 3× - [P, I, D controllers and role of PI, PD](https://www.bctengineer.com/question.md?key=semester_3%2Fcontrol_systems%3Apid-pi-pd-role) — Control Systems, chapter 7 - [PID controller block diagram, transfer function, characteristics](https://www.bctengineer.com/question.md?key=semester_3%2Fcontrol_systems%3Apid-bd-tf-characteristics) — Control Systems, chapter 7 - [Define control system and closed loop block roles](https://www.bctengineer.com/question.md?key=semester_3%2Fcontrol_systems%3Adefine-cs-bd-role) — Control Systems, chapter 1, asked 5× - [Closed loop control system block diagram explained](https://www.bctengineer.com/question.md?key=semester_3%2Fcontrol_systems%3Awhat-is-cs-bd-closed-loop) — Control Systems, chapter 1, asked 4× - [Control system and its significance in engineering](https://www.bctengineer.com/question.md?key=semester_3%2Fcontrol_systems%3Awhat-is-cs-significance) — Control Systems, chapter 1 ## Related in other subjects - [When to prefer lag/lead or PID controllers](https://www.bctengineer.com/question.md?key=semester_6%2Fdigital_control_system%3Alag-lead-vs-pid) — Digital Control System, chapter 4 - [PID control operation with block diagram](https://www.bctengineer.com/question.md?key=semester_6%2Fembedded_system%3Apid-operation-block-diagram) — Embedded System, chapter 7, asked 4× - [PID tuning and computer control issues](https://www.bctengineer.com/question.md?key=semester_6%2Fembedded_system%3Apid-tuning-practical-issues) — Embedded System, chapter 7 - [Purpose of PID tuning; computer control benefits](https://www.bctengineer.com/question.md?key=semester_6%2Fembedded_system%3Apid-tuning-purpose-benefits) — Embedded System, chapter 7