Systeem en Regeltechniek FMT / Mechatronica. Toepassing: : PID regelaarontwerp

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1 Systeem en Regeltechniek FMT / Mechatronica Deel 5: Oefening: Toepassing: : PID regelaarontwerp Toepassing: Tunen PID regelaar mechatronisch systeem (update dd ) Gert van Schothorst Philips Centre for Technical Training (CTT) Philips Centre for Industrial Technology (CFT) Hogeschool van Utrecht - PTGroep Cursus Systeem en Regeltechniek Overzicht Deel 1 Wo Deel 2 Wo Deel 3 Wo Deel 4 Wo Deel 5 Wo Deel 6 Wo Blok 1. Inleiding Blok 2. Basisprincipes modelvorming massa-veersystemen Blok 3. De regelaar als veer-demper combinatie Blok 4. Frequentie-domein beschrijving Blok 5. Basisconcepten in de regeltheorie Blok 6. Verdere inleiding in de regeltheorie Blok 7. De PD regelaar als veer-demper combinatie Blok 8. Stabiliteit van regelsystemen Blok 9. De PID regelaar in het frequentie domein Blok 10. Bandbreedte en verstoringsonderdrukking Blok 11. Toepassing: Tunen PID regelaar mechatronisch systeem Extra regeltechniek Blok 12. Diverse onderwerpen Blok 13. Terugblik 2 1

2 Tuning the PID controller: what does that mean in practice?? 3 Mechatronic system Moving target: 3 Hz, 3mm Allowed tracking error: 40µm 4 2

3 Data Mechanics Motor inertia: [Kgm 2 ] Motor gear wheel inertia: [Kgm 2 ] Gear+pinion wheel inertia: [Kgm 2 ] Mass slide: 5.0 Kg Mass camera: 3.0 Kg Transmission gearbox: 0.2 [-] Diameter pinion wheel: 30 [mm] 5 Objective Exercise Dimension a stable control loop in which the error is reduced to 40 µm The phase margin at the crossover is about 50 degrees Moving target: 3 Hz, 3mm Allowed tracking error: 40µm 6 3

4 Exercise - Part 1 Solve the sketched control problem for a system without flexibilities Assignment 1: Sketch a simple model without flexibilities All elements included Reduced model with single mass Assignment 2: Implement the model in 20-sim Assignment 3: 7 Assignment 1: Model without flexibilities motor gear M camera T motor M slide x camera φ motor gear+pinion 8 4

5 Assignment 1: Model without flexibilities T motor motor φ motor i 1 = 0.2 [-] x camera gear M slide M camera Reduced model (to camera): gr+pin i 2 = [m/rad] x M red = M camera + M slide + gr+pin /i ( gear + motor )/(i 12 i 22 ) F M red 9 Constant1 Assignment 2: Implementation in 20-sim T TorqueActuator1 Inertia1 Linearise model via: Inertia2 Ctrl-R (Start Simulator) i 1 Gear1 Inertia3 RackPinionGear1 m Mass1 m Mass2 P PositionSensor1 Tools Model Linearisation; choose option Numeric Does the Mass of the obtained model correspond to the reduced mass? No! Why not? And why is the minus sign?! Use obtained linear system (transfer function properties) as Plant in new submodel Controlled Linear System 10 5

6 Build controlled linear system as follows: Assignment 2: Implementation in 20-sim 3 Hz, 3 mm WaveGenerator1 Constant1 r d F C P z M ControlledLinearSystem1 SignalMonitor1 Now the controller design can be performed 11 Assignment 3: Follow these steps: 1. Determine the needed reduction at 3 Hz 2. Determine the needed bandwidth f b (0 db crossing of open loop), assuming Kp controller 3. Tune a Lead Filter (also called lead-lag): 1. Adjust the width of the lead-lag filter (f 1 ; f 2 ) for the required phase margin; position the lead-lag around the required bandwidth by choosing: f 1 = f b /n; f 2 = f b *n 2. Adjust the gain to place the 0 db crossing of the open loop at the required bandwidth 4. Check stability in Nyquist; check the reduction at 3 Hz in sensitivity plot 5. Repeat tuning Lead Filter if necessary 6. Check the reduction via a time plot with 3 Hz sine 12 6

7 Assignment 3: Step 1: Determine the needed reduction at 3 Hz S (3Hz) = e (3Hz) / d (3Hz) = 40 µm / 3 mm = So a reduction of the error with a factor 75 is 3 Hz This corresponds to a sensitivity 3 Hz of -37,5 db With S = 1 / (1 + L), with L the open loop response C(s)H(s), this means roughly that L should be larger than 37,5 3 Hz 13 Assignment 3: Step 2: Determine the needed bandwidth f b So we have: C(s)H(s) > 37,5 3 Hz Assuming a Kp controller, the open loop looks like: K/s 2 37,5 db 0 db K/s Hz f b K/(2 3) 2 = 75; K/(2 f b ) 2 = 1 (f b /3) 2 = 75 f b = 26 Hz K p = K / = Note the minus sign! 14 7

8 Assignment 3: Step 3: Tune a Lead Filter K p, f 1, f 2 1 3: Select Lead Filter 4: Tune Parameters Assignment 3: Step 4a: Check Stability 16 8

9 Assignment 3: Step 4b: Check Sensitivity? 17 Assignment 3: Step 5: Retune Lead Filter if necessary 1 3: Select Lead Filter 4: Tune Parameters

10 Assignment 3: Step 6: Check time response on 3 Hz sine of 3 mm < 40 µm! WaveGenerator1 Constant1 r d F C P z M ControlledLinearSystem1 SignalMonitor1 19 Exercise - Part 2 Analyse the dynamics of a flexible system Assignment 1: Sketch and implement 2 models with flexibilities: Motor shaft k t = 20 [Nm/rad]; d t = [Nms/rad] Camera suspension k = [N/m]; d = 120 [Ns/m] Assignment 2: Compare the dynamic behavior of both systems using: a rotational measurement on the motor (φ motor ) a linear measurement on the slide (x slide ) 20 10

11 Assignment 1: Model(s) with flexibilities motor gear M camera T motor M slide x camera φ motor gear+pinion 21 Assignment 1: Model(s) with flexibilities φ motor x slide x camera T motor motor gear M slide M camera gr+pin φ motor x slide x camera T motor motor gear M slide M camera gr+pin 22 11

12 Assignment 2: Check Bode plots: Minus 2 slope with resonance Minus 2 slope with anti-resonance/resonance Compare and investigate differences: Physical interpretation of anti-resonance Effect on stability of control loop 23 Exercise - Part 3 Solve the control problem again now for the flexible system Step 1: Choose the system to be controlled: Choose type of flexibility: Motor shaft k t = 20 [Nm/rad]; d t = [Nms/rad] Camera suspension k = [N/m]; d = 120 [Ns/m] Choose location of feedback sensor: an encoder measurement on the motor (φ motor ) a linear measurement on the slide (x slide ) Step 2: Design a PID controller Follow same procedure as before Add filters if necessary 24 12

13 Example of implementation Motor feedback / motor flexibility T TorqueActuator1 Inertia1SpringDamper1 Inertia2 P PositionSensor2 1 K Attenuate1 i 1 m Gear1 Inertia3 RackPinionGear1 Mass1 WaveGenerator1 m Mass2 P PositionSensor1 100 s s e+005 s s LinearSystem1 SignalMonitor1 25 Constant1 Exercise - Part 4 Add flexibility s like shown here and solve the control problem again! T TorqueActuator1 Inertia1 i 1 SpringDamper2 Inertia2 m Gear1 SpringDamper3 Inertia3 RackPinionGear1 Mass1 m SpringDamper1 Mass2 P PositionSensor

14 Summary Modelling a mechatronic system in 20-sim Sketch (simplified) model Implement in 20-sim Loop shaping / design for performance: S small where disturbances occur High bandwidth - small S for low frequency Effect of mechatronic system design: Location of flexibilities Location of feedback sensors 27 14