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, Bratislava, Slovakia tel ; fax: ;

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

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

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

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

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

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))

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

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

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

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

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

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

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

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

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

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)

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

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

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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