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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 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 Actuator Sensor
Feedback system Control: u Controller Setpoint: r Output: y Actuator Sensor
Feedback system (Contd.) Control: u Process Controller Setpoint: r Output: y
Feedback system (Contd.) Error: e=r-y Control: u Process Controller Setpoint: r Output: y -
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 -
On-off control (Contd.) u On Off e
On-off control with hysteresis u On Off e Reduction in switching frequency
How is a controller evaluated? Targeted state Starting state
Rise time Targeted state 10% Starting state Time for the state to rise to within 10% of the desired level for the first time
Overshoot Difference between peak and the targeted state Targeted state Starting state
Settling time Targeted state Starting state • time it takes the system to converge to the steady state
Steady-state error Targeted state Starting state
In practice Targeted state Starting state • Settling time
Proportional control • u=K×e Control: u Process Error: e=r-y Controller Setpoint: r Output: y -
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°
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
Proportion/Integral (PI) control - Control: u Process Error: e=r-y Controller Setpoint: r Output: y
PI control • Smaller Ti Danger of oscillation
Proportion/Integral/Derivative (PID) control - Control: u Process Error: e=r-y Controller Setpoint: r Output: y
Derivative • Larger Td Reduced danger of oscillation • Too large Td Danger of oscillation increases again
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