The setpoint overshoot method: A simple and fast closed-loop approach for PI tuning

1. The setpoint overshoot method:A simple and fast closed-loop approach for PI tuning Mohammad Shamsuzzoha Sigurd Skogestad Department of Chemical Engineering Norwegian University of Science and Technology (NTNU) Trondheim Dycops symposium, Leuven, July 2010

2. Motivation • Desborough and Miller (2001): More than 97% of controllers are PID • Vast majority of the PID controllers do not use D-action. • PI controller: Only two adjustable parameters … • but still not easy to tune • Many industrial controllers poorly tuned • Ziegler-Nichols closed-loop method (1942) is popular, but • Requires sustained oscillations • Tunings relatively poor • Big need for a fast and improved closed-loop tuning procedure

3. Outline • Existing approaches to PI tuning • SIMC PI tuning rules • Closed-loop setpoint experiment • Correlation between setpoint response and SIMC-settings • Final choice of the controller settings (detuning) • Analysis and Simulation • Conclusion

4. 1. Common approach:PI-tuning based on open-loop model • Step 1: Open-loop experiment: • Most tuning approaches are based on open-loop plant model • gain (k), • time constant (τ) • time delay (θ) • Problem: “Loose control” during identification experiment • Step 2: Tuning Many approaches • IMC-PID (Rivera et al., 1986): good for setpoint change • SIMC-PI (Skogestad, 2003): Improved for integrating disturbances

5. Alternative approach:PI-tuning based on closed-loop data only Ziegler-Nichols (1942) closed-loop method Step 1. Closed-loop experiment Use P-controller with sustained oscillations. Record: • Ultimate controller gain (Ku) • Period of oscillations (Pu) Step 2. Simple PI rules: Kc=0.45Ku and τI=0.83Pu. Advantages ZN: • Closed-loop experiment • Very little information required • Simple tuning rules Disadvantages: • System brought to limit of instability • Relay test (Åström) can avoid this problem but requires the feature of switching to on/off-control • Settings not very good: Aggressive for lag-dominant processes (Tyreus and Luyben) and quite slow for delay-dominant process (Skogestad). • Only for processes with phase lag > -180o (does not work on second-order)

6. This work. Improved closed-loop PI-tuning method Want to develop improved and simpler alternative to ZN: • Closed-loop setpoint response with P-controller • Use P-gain about 50% of ZN • Identify “key parameters” from setpoint response: • Simplest to observe is first peak! • Idea: Derive correlation between “key parameters” and SIMC PI-settings for corresponding process

7. 2. SIMC PI tuning rules First-order process with time delay: PI controller: SIMC PI controller based on direct synthesis: “Fast and robust” setting:

8. 3. Closed-loop setpoint experiment • Procedure: • Switch to P-only mode and make setpoint change • Adjust controller gain to get overshoot about 0.30 (30%) • Record “key parameters”: • 1. Controller gain Kc0 • 2. Overshoot = (Δyp-Δy∞)/Δy∞ • 3. Time to reach peak (overshoot), tp • 4. Steady state change, b = Δy∞/Δys. • Estimate of Δy∞ without waiting to settle: Δy∞ = 0.45(Δyp + Δyu) • Advantages compared to ZN: • * Not at limit to instability • * Works on a simple second-order process. Closed-loop step setpoint response with P-only control.

9. Closed-loop setpoint experiment Various overshoots (10%-60%) Overshoot of 0.3 (30%) with different τ’s 30% τ=100 τ=2 τ=0 Small τ: Kc0 small and b small

10. Estimate ofΔy∞ using undershoot Δyu Conclusion: Δy∞≈ 0.45(Δyp+Δyu) Data: 15 first-order with delay processes using 5 overshoots each (0.2, 0.3, 0.4, 0.5, 0.6). ys=1

11. 4. Correlation between Setpoint response and SIMC-settings • Goal: Find correlation between SIMC PI-settings and “key parameters” from 90 setpoint experiments. • Consider 15 first-order plus delay processes: τ/θ = 0.1, 0.2, 0.4, 0.8, 1, 1.5, 2, 2.5, 3, 5, 7.5, 10, 20, 50, 100 • For each of the 15 processes: • Obtain SIMC PI-settings (Kc,τI) • Generate setpoint responses with 6 different overshoots (0.10, 0.20, 0.30, 0.40, 0.50, 0.60)and record “key parameters”(Kc0, overshoot, tp, b)

12. Correlation Setpoint response and SIMC PI-settingsController gain (Kc) 90 cases: Plot Kcas a function of Kc0 10%: A=0.87 30%: A=0.63 60%: A=0.45 Kc Kc0 Fixed overshoot: Slope Kc/Kc0 = A approx. constant, independent of the value of τ/θ Agrees with ZN (approx. 100% overshoot): Original: Kc/Kcu = 0.45 Tyreus-Luyben: Kc/Kcu = 0.33

13. Conclusion: Kc = Kc0 A A = slope overshoot Overshoots between 0.1 and 0.6(should not be extended outside this range).

14. Correlation Setpoint response and SIMC PI-settingsIntegral time (τI) SIMC-rules • Case 1 (large delay): τI1 = τ • Case 2 (small delay): τI2 = 8θ Case 1 (large delay): τ= 2·kKc·θ(substitute τ = τI into the SIMC rule for Kc) (from steady-state offset) Conclusion so far: Still missing: Correlation forθ

15. Correlation between θ and tp θ/tp θ tp Use: θ/tp= 0.43 for τI1 (large delay) θ/tp = 0.305 for τI2 (small delay) overshoot Conclusion:

16. 5. Summary setpoint overshoot method From P-control setpoint experiment record “key parameters”: 1. Controller gain Kc0 2. Overshoot = (Δyp-Δy∞)/Δy∞ 3. Time to reach peak (overshoot), tp 4. Steady state change, b = Δy∞/Δys Choice of detuning factor F: • F=1. Good tradeoff between “fast and robust” (SIMC with τc=θ) • F>1: Smoother control with more robustness • F<1 to speed up the closed-loop response. Proposed PI settings (including detuning factor F)

17. 6. Analysis: Simulation PI-control First-order + delay process • ”in training set” • similar response as SIMC t=0: Setpoint change t=40: Load disturbance

18. Analysis: Simulation PI-control Pure time delay process • ”in training set”

19. Analysis: Simulation PI-control Integrating process • ”in training set”

20. Analysis: Simulation PI-control Second-order process • Not in ”training set” Responses for PI-control of second-order process g=1/(s+1)(0.2s+1).

21. Analysis: Simulation PI-control High-order process • Not in ”training set” Responses for PI-control of high-order process g=1/(s+1)(0.2s+1)(0.04s+1)(0.008s+1).

22. Analysis: Simulation PI-control Third-order integrating process • Not in ”training set”

23. Analysis: Simulation PI-control First-order unstable process • Not in ”training set” • No SIMC settings available

24. Analysis: Simulation PI-control Effect of detuning factor F Second-order process

25. 6. Conclusion ”Probably the fastest PI-tuning approach in the world”  • From P-control setpoint experiment obtain: 1. Controller gain Kc0 2. Overshoot = (Δyp-Δy∞)/Δy∞ 3. Time to reach peak (overshoot), tp 4. Steady state change, b = Δy∞/Δys, Estimate: Δy∞ = 0.45(Δyp + Δyu) • PI-tunings for “Setpoint Overshoot Method”: F=1:Good trade-off between performance and robustness F>1:Smoother F<1:Speed up

26. REFERENCES • Åström, K. J., Hägglund, T. (1984). Automatic tuning of simple regulators with specifications on phase and amplitude margins, Automatica, (20), 645–651. • Desborough, L. D., Miller, R. M. (2002). Increasing customer value of industrial control performance monitoring—Honeywell’s experience. Chemical Process Control–VI (Tuscon, Arizona, Jan. 2001), AIChE Symposium Series No. 326. Volume 98, USA. • Kano, M., Ogawa, M. (2009). The state of art in advanced process control in Japan, IFAC symposium ADCHEM 2009, Istanbul, Turkey. • Rivera, D. E., Morari, M., Skogestad, S. (1986). Internal model control. 4. PID controller design, Ind. Eng. Chem. Res., 25 (1) 252–265. • Seborg, D. E., Edgar, T. F., Mellichamp, D. A., (2004). Process Dynamics and Control, 2nd ed., John Wiley & Sons, New York, U.S.A. • Shamsuzzoha, M.,Skogestad. S. (2010). Report on the setpoint overshoot method(extended version) http://www.nt.ntnu.no/users/skoge/. • Skogestad, S., (2003). Simple analytic rules for model reduction and PID controller tuning, Journal of Process Control, 13, 291–309. • Tyreus, B.D., Luyben, W.L. (1992). Tuning PI controllers for integrator/dead time processes, Ind. Eng. Chem. Res. 2628–2631. • Yuwana, M., Seborg, D. E., (1982). A new method for on-line controller tuning, AIChEJournal 28 (3) 434-440. • Ziegler, J. G., Nichols, N. B. (1942). Optimum settings for automatic controllers. Trans. ASME, 64, 759-768.

27. SIMC PI tuning rules On dimensionless form, the SIMC (τc = θ) Scaled proportional and integral gain for SIMC tuning rule. is known as the integral gain. Note: Integral term (KI΄) is most important for delay dominant processes (τ/θ<1). Proportional term Kc΄ is most significant for processes with a smaller time delay.

28. Abstract • The PI controller is widely used in the process industries due to simplicity and robustness, It has wide ranges of applicability in the regulatory control layer. • The proposed method is similar to the Ziegler-Nichols (1942) tuning method. • It is faster to use and does not require the system to approach instability with sustained oscillations. • The proposed tuning method, originally derived for first-order with delay processes and tested on a wide range of other processes and the results are comparable with the SIMC tunings using the open-loop model. • Based on simulations for a range of first-order with delay processes, simple correlations have been derived to give PI controller settings similar to those of the SIMC tuning rules. • The detuning factor F that allows the user to adjust the final closed-loop response time and robustness. • The proposed method is the simplest and easiest approach for PI controller tuning available and should be well suited for use in process industries.