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 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 Motivation

3 Outline 1.Existing approaches to PI tuning 2.SIMC PI tuning rules 3.Closed-loop setpoint experiment 4.Correlation between setpoint response and SIMC-settings 5.Final choice of the controller settings (detuning) 6.Analysis and Simulation 7.Conclusion

4 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 1. Common approach: PI-tuning based on open-loop model

5 Ziegler-Nichols (1942) closed-loop method Step 1. Closed-loop experiment Use P-controller with sustained oscillations. Record: 1.Ultimate controller gain (K u ) 2.Period of oscillations (P u ) Step 2. Simple PI rules: K c =0.45K u and τ I =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 > -180 o (does not work on second-order) Alternative approach: PI-tuning based on closed-loop data only

6 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! This work. Improved closed-loop PI-tuning method 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 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 K c0 2. Overshoot = (Δy p -Δy ∞ )/Δy ∞ 3. Time to reach peak (overshoot), t p 4. Steady state change, b = Δy ∞ /Δy s. Estimate of Δy ∞ without waiting to settle: Δy ∞ = 0.45(Δy p + Δy u ) Advantages compared to ZN: * Not at limit to instability * Works on a simple second-order process. 3. Closed-loop setpoint experiment Closed-loop step setpoint response with P-only control.

9 Various overshoots (10%-60%) Closed-loop setpoint experiment Overshoot of 0.3 (30%) with different τ’s 30% τ=0 τ=100 τ=2 Small τ: K c0 small and b small

10 Estimate of Δy ∞ using undershoot Δy u Data: 15 first-order with delay processes using 5 overshoots each (0.2, 0.3, 0.4, 0.5, 0.6). y s =1 Conclusion: Δy ∞ ≈ 0.45(Δy p +Δy u )

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 (K c,τ I ) –Generate setpoint responses with 6 different overshoots (0.10, 0.20, 0.30, 0.40, 0.50, 0.60) and record “key parameters”(K c0, overshoot, t p, b)

12 Fixed overshoot: Slope K c /K c0 = A approx. constant, independent of the value of τ/θ Correlation Setpoint response and SIMC PI-settings Controller gain (K c ) K c0 KcKc 10%: A= %: A= %: A=0.45 Agrees with ZN (approx. 100% overshoot): Original: K c /K cu = 0.45 Tyreus-Luyben: K c /K cu = cases: Plot K c as a function of K c0

13 Overshoots between 0.1 and 0.6 (should not be extended outside this range). Conclusion: K c = K c0 A A = slope overshoot

14 SIMC-rules Case 1 (large delay): τ I1 = τ Case 2 (small delay): τ I2 = 8 θ Case 1 (large delay): τ = 2·kK c ·θ (substitute τ = τ I into the SIMC rule for K c ) Correlation Setpoint response and SIMC PI-settings Integral time ( τ I ) (from steady-state offset) Conclusion so far: Still missing: Correlation for θ

15 Correlation between θ and t p θ/tpθ/tp overshoot Use: θ/t p = 0.43 for τ I1 (large delay) θ/t p = for τ I2 (small delay) Conclusion: tptp θ

16 Choice of detuning factor F: F=1. Good tradeoff between “fast and robust” (SIMC with τ c =θ) F>1: Smoother control with more robustness F<1 to speed up the closed-loop response. From P-control setpoint experiment record “key parameters”: 1. Controller gain K c0 2. Overshoot = (Δy p -Δy ∞ )/Δy ∞ 3. Time to reach peak (overshoot), t p 4. Steady state change, b = Δy ∞ /Δy s Proposed PI settings (including detuning factor F) 5. Summary setpoint overshoot method

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

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

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

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

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

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

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

24 FKcKc τIτI MsMs Effect of detuning factor F Second-order process Analysis: Simulation PI-control

25 6. Conclusion From P-control setpoint experiment obtain: 1. Controller gain K c0 2. Overshoot = (Δy p -Δy ∞ )/Δy ∞ 3. Time to reach peak (overshoot), t p 4. Steady state change, b = Δy ∞ /Δy s, Estimate: Δy ∞ = 0.45(Δy p + Δy u ) PI-tunings for “Setpoint Overshoot Method”: F=1: Good trade-off between performance and robustness F>1: Smoother F<1: Speed up ”Probably the fastest PI-tuning approach in the world”

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 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) 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, AIChE Journal 28 (3) Ziegler, J. G., Nichols, N. B. (1942). Optimum settings for automatic controllers. Trans. ASME, 64,

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

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.