Lecture 12-Auto-tuning and gain Introduction Scheduling · Tuning and adaptation 1. Introduction Prior knowledge 2. Tuning chniques Initialization of adaptive controllers 3. Relay tuning PID Control 4. Applications Operational aspects 5. Gain Scheduling Operator interface 6. How to find schedules e Views from the field 7. Applications 8. Conclusions Views from the field Auto-tuning Techniques Canadian mill audit. average paper mill The Ziegler-Nichols method has 2000 loops, 97% use Pi the remaining 3%are PID, adaptive etc. Bill Bialkowski Transient response methods CCA93 Frequency response methods · Default settings Poor control performance due to bad Poor control performance due to valves, actuators or positioner problems Process Performance is not as good as you think. D. Ender, Control Engineering 1993 . More than 30%of installed controllers operate in manual More than 30% of the loops actually increase short term variability About 25% of the loops use default About 30% of the loops have equip ment problems O K.J.Astrom and BWittenmark
Lecture 12—Auto-tuning and Gain Scheduling 1. Introduction 2. Tuning Techniques 3. Relay tuning 4. Applications 5. Gain Scheduling 6. How to find schedules 7. Applications 8. Conclusions Introduction • Tuning and adaptation • Prior knowledge • Initialization of adaptive controllers • PID Control • Operational aspects • Operator interface • Views from the field Views from the Field Canadian mill audit. Average paper mill has 2000 loops, 97% use PI the remaining 3% are PID, adaptive etc. Bill Bialkowski CCA’93. • Default settings • Poor control performance due to bad tuning • Poor control performance due to valves, actuators or positioner problems Process Performance is not as good as you think. D. Ender, Control Engineering 1993. • More than 30% of installed controllers operate in manual • More than 30% of the loops actually increase short term variability • About 25% of the loops use default settings • About 30% of the loops have equipment problems Auto-tuning Techniques • The Ziegler-Nichols method • Transient response methods • Frequency response methods c K. J. Åström and B. Wittenmark 1
Transient Response Methods Difficulties with Ziegler-Nichols The three parameter model Difficult to determine parameters G()=k · Too low damping 1+87e~ Two parameters not enough Step response methods Area methods 0.63k Parameters are given by The Ziegler-Nichols method ControlleraKcT/L Ta/L Tp/L k P 093 5.7 PID 1220.534 Ziegler-Nichols Frequency Relay Tuning Response Method The experiment ldea: Run a proportional controller, increase gain until the system starts to oscillate Observe "ultimate gain Ku, and " ultimate perod T Interpretation: Find features of frequency response The results Controller parameters Time Controller Kc/Ku T/T Ta/Tu Tp/Tu 0.5 Closed loop experiment 04 0.8 14 Stable limit cycle for large class of processes PID 0.60.5|0.12085 Much control energy close to @180 O K.J.Astrom and BWittenmark
Transient Response Methods The three parameter model G(s) k 1 + sT e−sL Step response methods k a L T Time 0.63k The Ziegler-Nichols method Controller aKc Ti/L Td/L Tp/L P 1 4 PI 0.9 3 5.7 PID 1.2 2 0.5 3.4 Difficulties with Ziegler-Nichols • Difficult to determine parameters • Too low damping • Two parameters not enough Area methods A0 L + T k A 1 Parameters are given by T + L A0 k T eA1 k Ziegler-Nichols Frequency Response Method Idea: Run a proportional controller, increase gain until the system starts to oscillate. Observe "ultimate gain Ku, and "ultimate period Tu. Interpretation: Find features of frequency response G(iω) − 1 N(a) Controller parameters Controller Kc/Ku Ti/Tu Td/Tu Tp/Tu P 0.5 1 PI 0.4 0.8 1.4 PID 0.6 0.5 0.12 0.85 Relay Tuning The experiment Σ Process PID Relay A T u y − 1 The results 0 5 10 −1 0 1 Time • Closed loop experiment • Stable limit cycle for large class of processes • Much control energy close to ω180 c K. J. Åström and B. Wittenmark 2
Practical issues Automatic Tuning of the double Prior information Tank How to start the experiments Consider the double tank used in our Feedback to limit the amplitiude of the laboratory experiments oscillation Here is the results obtained with one of our Modified Ziegler-Nichols rules earliest auto-tuners Change values in the tables Tuning PID control Use three parameters ku, Tu and K How to cope with disturbances A人 Load disturbances 200s Measurement noise Hysteresis Mnrf Flow Control Temperature Control O K.J.Astrom and BWittenmark
Practical Issues • Prior information? • How to start the experiments • Feedback to limit the amplitiude of the oscillation • Modified Ziegler-Nichols rules – Change values in the tables – Use three parameters ku, Tu and Kp • How to cope with disturbances – Load disturbances – Measurement noise – Hysteresis Automatic Tuning of the Double Tank Consider the double tank used in our laboratory experiments. Here is the results obtained with one of our earliest auto-tuners. y u 0 100 200 s 0 0 1 uc Tuning PID control 0 100 200 s 0.5 Flow Control Temperature Control c K. J. Åström and B. Wittenmark 3
Composition Control Adding Dynamics in the Feedback oop Other information can be obtained by introducing dynamics in the feedback loop n integrator giy a differentiator gives @270 1+m Closed Loop Experiments Summary of Relay Feedback Close to industrial operation Controler · One-button tuning Easy to expl Works well for standard loops An integrator can also be added Little prior information ery robust Generates automatically a perturbation signal with a lot of energy at 180 Many possibilities not exploited O K.J.Astrom and BWittenmark
Composition Control Adding Dynamics in the Feedback Loop Other information can be obtained by introducing dynamics in the feedback loop • An integrator gives ω90 • A differentiator gives ω270 Process –1 1 s Σ a) Process –1 1 s Σ b) Closed Loop Experiments Controller Process –1 –1 Σ Σ An integrator can also be added –1 Im L(iω) Re L(iω) L(iω) B A Summary of Relay Feedback • Close to industrial operation • Easy to use • One-button tuning • Easy to explain to users • Works well for standard loops • Little prior information • Very robust • Generates automatically a perturbation signal with a lot of energy at ω180 • Many possibilities not exploited c K. J. Åström and B. Wittenmark 4
On-ine Iteration Gain Scheduling Idea: Find features of the online response 1. What is it? due to set point or load disturbances 2. How to find schedules Modify controller settings based on the observed features 3. Applicatio Features: damping d and overshoot o Controller modified based on heuristic rules Easy for PI more difficult for PID Prior informatic Pre-tuning Gain Scheduling How to Find schedules Controller Select scheduling variables Make control design for different Operating operating conditions Command Control Use automatic tuning Process Transformations Example of scheduling variables Production rate · Machine speed Mach number and dynamic pressure e K.J. Astrom and BWittenmark
On-line Iteration Idea: Find features of the online response due to set point or load disturbances. Modify controller settings based on the observed features. e1 e2 e3 Tp Features: damping d and overshoot o d e3 − e2 e1 − e2 o −e2 e1 Controller modified based on heuristic rules. Easy for PI more difficult for PID. • Prior information • Pre-tuning Gain Scheduling 1. What is it? 2. How to find schedules? 3. Applications 4. Conclusions Gain Scheduling Process schedule Gain Output Control signal Controller parameters Operating condition Command signal Controller Example of scheduling variables • Production rate • Machine speed • Mach number and dynamic pressure How to Find Schedules? • Select scheduling variables • Make control design for different operating conditions • Use automatic tuning • Transformations c K. J. Åström and B. Wittenmark 5