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1 SYS635 ADAPTIVE CONTROL – INTRODUCTION A person who can drive any of these vehicles in all kinds of road conditions can be considered to a very adaptive system.

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2 LINEAR MODEL DESCRIPTION OF A CONTROL SYSTEM Recall that a closed-loop control system can be represented by An example of a conventional pole assignment control design for a simple Proportional + Integral Controller: - 2 1 s + 12 2 2( ) (1 2 ) 2 ks k s + ++ + PI-controller to be designed Plant dynamics is known s + - () c Gs p Command Reference r Error e Control input u Controlled output y () () 1( ) ( ) cp GsG s + r y Closed-loop transfer function controller plant 2 1 2 1 1 ss + + + + + 2 26 36 s s s + + + If k 1 = 1 and k 2 = 3, then the dynamics of the resultant closed-loop system is as shown above. Output speed & direction Throttle & steer inputs Desired speed & direction
3 ADAPTATION TO INTERNAL CHANGE IN PLANT DYNAMICS Same example. If the dynamics of the original system changes, then the resultant closed-loop system will behave differently. Adaptation may be required when parameters of the plant change. Resulting closed-loop system - 0.3 0.2 s + Plant dynamics changes ks k s 12 + 2 0.3( ) (0.2 0.3 ) 0.3 s ks k + ++ + If k 1 = 1 and k 2 = 3 (no change in control (driving) scheme), then the closed-loop systems behaves differently (more sluggishly). 2 0.3 0.9 0.5 0.9 s s s + + + Output speed & direction Throttle & steer inputs Desired speed & direction If k 1 = 9 and k 2 = 20 (change in control (driving) scheme), then the closed-loop systems behaves as stable as 2 26 36 s s s + ; the system may respond slightly differently because of the different zero. Note: Just as you’d control your action to move faster when you feel that you are slowing down. 2 2.7 6 2.9 6 s s s + + +

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4 ADAPTATION TO EXTERNAL CONDITION Adaptation (control strategy) may be required depending on external stimuli or operation conditions.
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