5ba6d0be22fdfa513bae0a5e30835060.ppt

- Количество слайдов: 47

Master of Science assignment Demonstrator of advanced controllers Hans Dirne May 25 th, 2005 Supervisors prof. dr. ir. J. van Amerongen dr. ir. J. F. Broenink dr. ir. T. J. A. de Vries ir. P. B. T. Weustink

Why this assignment? The Major ‘Mechatronics’ provides several courses in control theory, in which theory is often supported by simulations. A physical setup might, in addition to simulations, be an enrichment for demonstrating control theory. Such a demonstration setup will be able to make theory more insightful and will show real limitations in practical setups. May 25 th, 2005 Demonstrator of advanced controllers 2

Objectives 1. To design, build and test a mechatronic demonstration setup, with which several control algorithms can be shown in practice 2. To be able to demonstrate performance differences of control algorithms in practice May 25 th, 2005 Demonstrator of advanced controllers 3

Overview 1. 2. 3. 4. 5. 6. Demonstration setup options Control systems Design of the new demonstrator Experiments Demonstration Conclusions & recommendations May 25 th, 2005 Demonstrator of advanced controllers 4

Demonstration setup options May 25 th, 2005 Demonstrator of advanced controllers 5

Criteria 1. 2. 3. 4. 5. 6. Mechatronic system Portable and easy to set up Robust, safe and failsafe design High level of observability Representable by linear 4 th order model Clear link with well known device May 25 th, 2005 Demonstrator of advanced controllers 6

Three options 1. ‘Linix’ laboratory setup 2. 2. Setup of ‘Controllab Products B. V. ’ 3. 3. New build May 25 th, 2005 Demonstrator of advanced controllers 7

Option 1: ‘Linix’ Laboratory Setup May 25 th, 2005 Demonstrator of advanced controllers 8

‘Linix’ Laboratory Setup encoders motor inertia 2 transmission May 25 th, 2005 Demonstrator of advanced controllers inertia 1 9

‘Linix’ Laboratory Setup May 25 th, 2005 Demonstrator of advanced controllers 10

‘Linix’ Laboratory Setup Major disadvantage: slip between belt and inertias May 25 th, 2005 Demonstrator of advanced controllers 11

Option 2: CLP setup May 25 th, 2005 Demonstrator of advanced controllers 12

CLP setup May 25 th, 2005 Demonstrator of advanced controllers 13

CLP setup May 25 th, 2005 Demonstrator of advanced controllers 14

Sensor positions May 25 th, 2005 Demonstrator of advanced controllers 15

Option 3: New Build Advantage • Pure design freedom Disadvantage • Requires very much time and effort to design May 25 th, 2005 Demonstrator of advanced controllers 16

Overview demonstrators New build Linix CLP-setup Mechatronic system √ Linear 4 th order model √ Portable, easy to set up √ √ not in current form Robust, safe, failsafe √ √ feasible Observability √ yes, 2 position yes, 4 position Sensors sensors Link with practical device √ transmission Shows controller differences √ no, due to To be nonlinearities determined Remarks Time constraint √ √ limited linear to be determined printer

Control Systems May 25 th, 2005 Demonstrator of advanced controllers 18

Mathematical model – 6 th order Viscous PLUS coulomb friction May 25 th, 2005 Demonstrator of advanced controllers 19

Focus 1. Linear Quadratic Gaussian (LQG) 2. Proportional, Integral, Differential (PID) May 25 th, 2005 Demonstrator of advanced controllers 20

LQG explanation A LQG control algorithm is a combination of 1. Lin. Quad. Regulator (state feedback) 2. Lin. Quad. Estimator (state estimation) 4 th order linear model required! May 25 th, 2005 Demonstrator of advanced controllers 21

4 th order linear model Required steps: 1. Downsize system order 2. Linearize system: discard coulomb friction Result: linear 4 th order model (e. g. State Space) May 25 th, 2005 Demonstrator of advanced controllers 22

LQG controlled system May 25 th, 2005 Demonstrator of advanced controllers 23

PID May 25 th, 2005 Demonstrator of advanced controllers 24

Tuning (1) For proper comparison of the PID with the LQG controlled system, tuning with the same criteria is required. 1. Avoid actuator saturation 2. Minimization of criterion: position error May 25 th, 2005 controller output Demonstrator of advanced controllers 25

Tuning (2) Tuning procedure: 1. Set Q and R 2. Minimize criterion J by optimizing 3. controller gains (KLQG and KP, KI, KD) May 25 th, 2005 Demonstrator of advanced controllers 26

Tuning (3) Optimization results KP = 15. 7 KI = 42 KD = 1. 6 KLQG = [3. 7, 74, 8. 2, 70]T May 25 th, 2005 Demonstrator of advanced controllers 27

PID vs LQG (1) • • The PID controlled system consumes twice the power of the LQG system The maximum frame movement in the PID controlled system is twice compared to LQG May 25 th, 2005 Demonstrator of advanced controllers 28

PID vs LQG (2) The LQG control algorithm leads to an unacceptable position error with the nonlinear process May 25 th, 2005 Demonstrator of advanced controllers 29

LQG+ May 25 th, 2005 Demonstrator of advanced controllers 30

LQG+ vs LQG Effect of integrator: Static error is minimized! Interesting to see the performance of LQG+ in practice… May 25 th, 2005 Demonstrator of advanced controllers 31

Design of the new demonstrator May 25 th, 2005 Demonstrator of advanced controllers 32

Procedure Goal: to test a control algorithm on a physical setup How? May 25 th, 2005 Demonstrator of advanced controllers 33

System overview (1) Client: • Runs MS Windows • Generating models • Model control (start/stop/upload/delete) • Setting parameters of controlled system real-time • View parameters of controlled system real-time Server: • Runs Linux, with real-time kernel • Runs control system • Performs I/O May 25 th, 2005 Demonstrator of advanced controllers 34

System overview (2) May 25 th, 2005 Demonstrator of advanced controllers 35

Realization Mechatronics Embedded PC + I/O Power (CPU) Power (motor) Motor amplifier May 25 th, 2005 Demonstrator of advanced controllers 36

Experiments May 25 th, 2005 Demonstrator of advanced controllers 37

Experiments • Comparison of PID/LQG+ performance on the new demonstration setup • Same controller parameters used as in simulation (after tuning) • Performance comparison on: 1. Static error 2. Frame vibration 3. Power usage May 25 th, 2005 Demonstrator of advanced controllers 38

May 25 th, 2005 Demonstrator of advanced controllers 39

Results The LQG+ controlled system outperforms the PID controlled system: • • • Maximum frame movement differs factor 3 Total power consumption differs a factor 2 Both control algorithms minimize the static error, but the LQG controlled system is faster More performance increase is expected with a better model Differences in performance between 2 nd order PID and 4 th order LQG have now been demonstrated in practice May 25 th, 2005 Demonstrator of advanced controllers 40

Demonstration May 25 th, 2005 Demonstrator of advanced controllers 41

Demonstration What will be shown: 1. 2. ‘Homing’ of the demonstrator 1. Determining absolute position PID controller in practice with various controller gains Furthermore: 1. 2. 3. Online adjustment of parameters Real-time variable monitoring Real-time animation of demonstration setup May 25 th, 2005 Demonstrator of advanced controllers 42

Conclusions & Recommendations May 25 th, 2005 Demonstrator of advanced controllers 43

Conclusions 1. 2. 3. The new mechatronic demonstration setup is a compact, integrated machine that forms a versatile development environment for testing various control algorithms in practice 2. 3. The new demonstrator allows for easy comparison of different control algorithms 3. 1. 2. Non-linear friction elements in the process will lead to lower performance in position control of a 4 th order LQG-controlled system compared to a 2 nd order PID control algorithm 1. 2. 3. 4. Addition of an integrating term leads to an ‘LQG+’ control algorithm that can compensate for differences between process and reference model. May 25 th, 2005 Demonstrator of advanced controllers 44

Recommendations Hardware • Expand safety system • Reduce weight of the demonstrator (next version) • Add parallel processing (e. g. distributed control) Software / control • Experiment with more control systems (MRAS, (L)FF, ILC etc) • Perform system identification General 1. Set up lab work assignments for student May 25 th, 2005 Demonstrator of advanced controllers 45

Questions…? May 25 th, 2005 Demonstrator of advanced controllers 46

THANK YOU FOR YOUR ATTENTION you are all invited for DRINKS at ‘De Tombe’, floor 0 May 25 th, 2005 Demonstrator of advanced controllers 47