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Unformatted text preview: TUTORIAL on LOGICBASED CONTROL Part I: SWITCHED CONTROL SYSTEMS Daniel Liberzon Coordinated Science Laboratory and Dept. of Electrical & Computer Eng., Univ. of Illinois at UrbanaChampaign MED 02, Lisbon OUTLINE Switched Control Systems Stability of Switched Systems Questions, Break OUTLINE Switched Control Systems Stability of Switched Systems Questions, Break SWITCHED and HYBRID SYSTEMS Switching can be: Statedependent or Timedependent Hybrid systems: interaction of continuous and discrete dynamics Switched systems: continuous systems with discrete switchings emphasis on properties of continuous state ) ( x f x = and is a switching signal P ) , [ : where is a family of systems P p x f x p = ), ( Autonomous or Controlled SWITCHING CONTROL Classical continuous feedback paradigm: u y P C u y P Plant: But logical decisions are often necessary: The closedloop system is hybrid u y C 1 C 2 l o g i c P REASONS for SWITCHING Nature of the control problem Sensor or actuator limitations Large modeling uncertainty Combinations of the above REASONS for SWITCHING Nature of the control problem Sensor or actuator limitations Large modeling uncertainty Combinations of the above PARKING PROBLEM 2 x 1 x cos 1 1 w x = sin 1 2 w x = 2 w = Nonholonomic constraint: wheels do not slip OBSTRUCTION to STABILIZATION Solution: move away first ? REASONS for SWITCHING Nature of the control problem Sensor or actuator limitations Large modeling uncertainty Combinations of the above OUTPUT FEEDBACK switched system Example : harmonic oscillator y u = y u 2 1 = u y y = + QUANTIZED FEEDBACK PLANT QUANTIZER CONTROLLER u x q(x) x q(x) sensitivity M values OBSTRUCTION to STABILIZATION Assume: fixed , M Asymptotic stabilization is impossible MOTIVATING EXAMPLES 1. Temperature sensor normal too low too high 2. Camera with zoom Tracking a golf ball 3. Coding and decoding VARYING the SENSITIVITY zoom out zoom in Why switch ?...
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This note was uploaded on 01/12/2011 for the course MAT 116 A MAT 116 A taught by Professor Hawkins during the Spring '10 term at University of Phoenix.
 Spring '10
 HAWKINS

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