1. Application of adaptive lambda-tracking for control of a fan heater Monika Bakošová, Magdaléna Ondrovičová, Mária Karšaiová Department of Information Engineering and Process Control, Faculty of Chemical and Food Technology, Slovak University of Technology, Radlinského 9, 812 37 Bratislava, Slovakia tel. + +421 2 59 325 353; fax: ++ 421 2 52 496 469; e-mail: monika.bakosova@stuba.sk

2. CONTENTS 1.Introduction 2.Theoretical fundamentals of -tracking 3.Controlled process 4.Experimental results 5.Conclusions

3. The concept of  tracking is a simple modification of the ”high-gain control concept”. INTRODUCTION Control law:

4. THEORETICAL FUNDAMENTALS OF -TRACKING I Multivariable nonlinear system: Assumptions: 1.

5. THEORETICAL FUNDAMENTALS OF -TRACKING II 2. for MIMO system: for SISO system:

6. THEORETICAL FUNDAMENTALS OF -TRACKING III 3. solution of satisfies for all t and z 0 condition

7. CONCEPT OF - TRACKING I  stabilization (  tracking): the output is no longer controlled to a setpoint, but rather to a -neighbourhood of the setpoint or the reference trajectory to be tracked. For where holds (y(t) + n(t))

8. CONCEPT OF - TRACKING II Tuning parameters: ,,  Control law of a -tracker:

9. CONTROLLED SYSTEM – LABORATORY FAN HEATER Fig. 1 Laboratory Airstream and Temperature Control Plant LTR 700

10. EXPERIMENTAL RESULTS The structure of an adaptive -tracker for control of the fan heater: with where

11. AIR STREAM CONTROL BY MANIPULATING THE SPEED OF THE FAN I Fig. 2 Controlled output for air stream control by fan speed (prietok=air stream, cas = time): ____ setpoint, ____ -tracker, ---- - neighbourhood

12. AIR STREAM CONTROL BY MANIPULATING THE SPEED OF THE FAN II Fig. 3 Control input for air stream control by fan speed (otacky = fan speed, cas = time): ___ - tracker

13. AIR STREAM CONTROL BY MANIPULATING THE SPEED OF THE FAN III Fig. 4 Controlled output for air stream control by fan speed (prietok =air stream, cas = time): ____ setpoint, ____ P-controller, ---- - neighbourhood

14. AIR STREAM CONTROL BY MANIPULATING THE SPEED OF THE FAN IV Fig. 5 Control input for air stream control by fan speed (otacky = fan speed, cas = time): ___ P-controller

15. AIR TEMPERATURE CONTROL BY MANIPULATING THE FAN SPEED I Fig. 6 Controlled output for air temperature control by fan speed (teplota = temperature, cas = time): ____ setpoint, ____ - tracker, ____ P- controller, _ _ _ - neighbourhood

16. AIR TEMPERATURE CONTROL BY MANIPULATING THE FAN SPEED II Fig. 7 Control input for air temperature control by fan speed (otacky = fan speed, cas = time): ____ - tracker, ____ P-controller

17. AIR TEMPERATURE CONTROL BY MANIPULATING THE FAN SPEED III Fig. 8 Closed loop behaviour with -tracker (cas = time): ____ reference value, ____ air temperature, ____ disturbance, ____ fan speed, ____ k(t)

18. AIR TEMPERATURE CONTROL BY MANIPULATING THE FAN SPEED IV Fig. 9 Closed loop behaviour with P controller (cas = time): ____ reference value, ____ air temperature, ____ disturbance, ____ fan speed

19. CONCLUSIONS I Advantages of a  tracker  simple structure  very easy to implement on almost any process control equipment  no tuning is necessary  no process model is needed  controlled process can be nonlinear  stable closed-loop  robust for a large class of uncertainties (parameter uncertainties, uncertainty of system order, etc.)  the main goal is to control the output to a pre-defined neighbourhood of the setpoint or the reference trajectory to be tracked

20. CONCLUSIONS II Disadvantages of a  tracker  not proper for solving of all control problems, only for “simple control problems”  not proper for control of the output to the setpoint or the reference trajectory to be tracked  controlled system has to be a minimum-phase system  sensitivity of a high-gain control scheme to a measurement noise

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