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Basics of control

Basics of control. Lin Zhong ELEC424, Fall 2010. How can we set the room temperature at 78°?. Room: the system Temperature: the state of the system or the process variable. Sensor to measure the system state. Actuator to change the system state. Feedback system. Controller.

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Basics of control

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  1. Basics of control Lin Zhong ELEC424, Fall 2010

  2. How can we set the room temperature at 78°? Room: the system Temperature: the state of the system or the process variable

  3. Sensor to measure the system state Actuator to change the system state

  4. Feedback system Controller Actuator Sensor

  5. Feedback system Control: u Controller Setpoint: r Output: y Actuator Sensor

  6. Feedback system (Contd.) Control: u Process Controller Setpoint: r Output: y

  7. Feedback system (Contd.) Error: e=r-y Control: u Process Controller Setpoint: r Output: y -

  8. On-off control • If e>0, u=1 (On); if (e<=0), u=0 (Off) Error: e=r-y Control: u Process Controller Setpoint: r Output: y -

  9. On-off control (Contd.) u On Off e

  10. On-off control with hysteresis u On Off e Reduction in switching frequency

  11. How is a controller evaluated? Targeted state Starting state

  12. Rise time Targeted state 10% Starting state Time for the state to rise to within 10% of the desired level for the first time

  13. Overshoot Difference between peak and the targeted state Targeted state Starting state

  14. Settling time Targeted state Starting state • time it takes the system to converge to the steady state

  15. Steady-state error Targeted state Starting state

  16. In practice Targeted state Starting state • Settling time

  17. Proportional control • u=K×e Control: u Process Error: e=r-y Controller Setpoint: r Output: y -

  18. Proportional control Heat dissipated at (100 Joules/s) • u=K×e Heat generated at 10*e (Joules/s) Control: u Process Error: e=r-y Controller Setpoint: r Output: y - Steady-state error: 10°

  19. Proportional control • Larger K  Smaller steady-state error •  Longer settling time •  Danger of oscillation http://www.cds.caltech.edu/~murray/courses/cds101/fa02/caltech/astrom.html

  20. Proportion/Integral (PI) control - Control: u Process Error: e=r-y Controller Setpoint: r Output: y

  21. PI control • Smaller Ti Danger of oscillation

  22. Proportion/Integral/Derivative (PID) control - Control: u Process Error: e=r-y Controller Setpoint: r Output: y

  23. Derivative • Larger Td  Reduced danger of oscillation • Too large Td Danger of oscillation increases again

  24. PID control • Developed early 20th century • Nicolas Minorsky (1922): automatic steering system for US Navy • Extremely widely used • 97% of regulatory controllers in refining, chemical, and pulp & paper industries • Very often PI control is used

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