Basics of control Lin Zhong ELEC424, Fall

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

Sensor to measure the system stateActuator to change the system state 3

Actuator Sensor Controller Feedback system 4

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

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

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

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

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

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

Targeted state Starting state How is a controller evaluated? 11

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

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

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

Targeted state Starting state Steady-state error 15

Targeted state Starting state In practice 16 Settling time

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

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

Proportional control Larger K  Smaller steady-state error  Longer settling time  Danger of oscillation 19

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

PI control Smaller T i  Danger of oscillation 21

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

Derivative 23 Larger T d  Reduced danger of oscillation Too large T d  Danger of oscillation increases again

PID control Developed early 20 th 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 24