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1. GROUP- 17 Abhishek Chaudhary(210036) Akshat Tiwari(210095) Vaibhav Kadiyan(211135) Vicky(201108) PRESENTATION CHE 492A: UNIT OPERATIONS AND PROCESS CONTROL LABORATORY Characteristics of a PID controller EXPERIMENT-10

2. AIM & OBJECTIVE Objective : To study the characteristics of a PID Controller Aim: To obtain the response curves experimentally after setting the values of Kc, Ti, and Td Obtain the Rise time, overshoot, decay ratio, and Time period using PI/PID controller

3. APPARATUS

4. Theory The different types of combinations of controller actions used in industrial processes are : Proportional Controller (P) Proportional – Integral Controller (PI) Proportional – Integral- Derivative Controller (PID)

5. The proportional controller (P) :   The output signal (P) is directly proportional to the error (ε) and is defined by the equation               P = K c ε + P s Where P = Output Signal from the controller , Kc = proportional controller gain, ε = error, Ps = a constant

6. Proportional-Integral Controller (PI) :  PI control combines integral action with proportional control, aiming to eliminate offset. It is characterized by the integral time ( τ i ), which helps maintain the controlled variable at its set point:              Where    = Integral Time               P =  Kc ε + Kc/ τi ∫ t ε dt + P s       0      τ i

7. Proportional-Integral-Derivative Controller (PID) :  The PID controller combines all three control effects, providing the benefits of proportional control stability, offset elimination from integral control, and immediate disturbance correction from derivative control. It ensures rapid variable stabilization with minimal oscillations.              Where   = Derivative Time               P =  Kc ε + Kc/ τi ∫ t ε dt + Kc   + P s       0      τ D      τ D      dε / dt  

8. Data

9. Data

10. Data

11. Sample Calculations

12. S.No. Parameter Notation Value 1 Rise Time t r 510 s 2 Time of 1st Overshoot t p 690 s 3 Overshoot a/b 0.19 4 Percentage Overshoot a/b *100 19 5 Decay Ratio c/a 0.789 6 Time Period of Oscillation P 1020 7 Angular Frequency of Oscillation 2π/P 0.006 S.No. Parameter Notation Value 1 Rise Time t r 510 s 2 Time of 1st Overshoot t p 690 s 3 Overshoot a/b 0.1264 4 Percentage Overshoot a/b *100 12.64 5 Decay Ratio c/a 0.54 6 Time Period of Oscillation P 630 s 7 Angular Frequency of Oscillation 2π/P 0.009 s -1 PI PID

13. RESULTS AND CONCLUSION ● The graph demonstrates that although the actual temperature increases initially, it does not achieve the target of 40°C . Instead, it stabilizes below the setpoint, indicating a steady-state error. This outcome suggests that the proportional controller, with a Kc value of 125 , is unable to eliminate the offset. The linear trend reveals that while the temperature does rise, it ultimately levels off below the desired setpoint, confirming the presence of a steady-state error. ●  Incorporating integral action into the PI controller eliminated the steady-state offset but introduced oscillations and overshoot. With an integral time constant (Ti) of 48 seconds and a proportional constant (Kc) of 125 , the process variable showed significant fluctuations around the setpoint. Despite this, the smaller magnitude of the second overshoot suggested that the system was gradually stabilizing as it approached the target temperature.   ● Incorporating derivative action (Td = 55 seconds) into the PID controller, alongside Kc = 125 and Ti = 48 seconds, greatly reduced overshoot and accelerated convergence. The comparison graph clearly illustrates these enhancements, demonstrating a more stable and responsive control system that stabilizes faster than the previous PI configuration.

14. Thank You