1. Salman Bin Abdulaziz University
EE3511: Automatic Control Systems
PID Controller
Dr. Ahmed Nassef
EE3511_L12
Salman Bin Abdulaziz University

2. The need for PID control
Desired output
r(t)
Actual output
y(t)
Error
e(t)
Controller u
Plant
PID controllers
More than 50% of industrial controllers
Easy to implement
Applicable to most control systems
Adjustable on site
Satisfactory performance.
EE3511_L12
Salman Bin Abdulaziz University

3. Salman Bin Abdulaziz University
PID controller
Desired output
r(t)
Actual output
y(t)
Error
e(t)
Controller u
Plant
EE3511_L12
Salman Bin Abdulaziz University

4. Salman Bin Abdulaziz University
PID controller
Desired output
r(t)
Controller
Plant
Actual output
y(t)
Error
e(t) u
How do we select the PID parameters?
EE3511_L12
Salman Bin Abdulaziz University

5. General Guidelines for PID controller
Desired output
r(t)
Controller
Plant
Actual output
y(t)
Error
e(t) u
Steady state error
Settling time
overshoot
Rise time
Closed loop response
decrease
Small change
increase Kp
eliminate KI KD
conflicting objectives
EE3511_L12
Salman Bin Abdulaziz University

6. Salman Bin Abdulaziz University
PID controller
Desired output
r(t)
Controller
Plant
Actual output
y(t)
Error
e(t) u
We need to select the PID parameters so that we have
Fast rise time
Small overshoot
No steady state error
EE3511_L12
Salman Bin Abdulaziz University

7. P controller (proportional)
Desired output
r(t)
Controller
Plant
Actual output
y(t)
Error
e(t) u -
With P controller we can
Reduce rise time
Reduce steady state error
But
Overshoot may increase
EE3511_L12
Salman Bin Abdulaziz University

8. Salman Bin Abdulaziz University
PI controller
Desired output
r(t)
Controller
Plant
Actual output
y(t)
Error
e(t) u -
Integral action of the PI controller
Eliminate steady state error
Decrease rise time
Increase overshoot
Increase settling time
EE3511_L12
Salman Bin Abdulaziz University

9. Salman Bin Abdulaziz University
PID controller
Desired output
r(t)
Controller
Plant
Actual output
y(t)
Error
e(t) u -
Derivative action of the PID controller
Decrease overshoot
Decrease settling time
EE3511_L12
Salman Bin Abdulaziz University

10. General guidelines for Designing PID controller
Obtain an open loop response and determine what is needed
Add proportional gain to reduce rise time
Add derivative control to reduce overshoot
Add integral control to eliminate steady state error
Adjust gains to get desired response
EE3511_L12
Salman Bin Abdulaziz University

11. Salman Bin Abdulaziz University
Adjusting PID gains
It may not be simple to get the best gains by trial and error.
Some rules can be used to get good response
Ziegler Nichols Rules is one example
EE3511_L12
Salman Bin Abdulaziz University

12. Salman Bin Abdulaziz University
Ziegler Nichols Rules
Two Ziegler Nichols Methods
Obtaining 25% maximum overshoot in step response
Open Loop Method
Based on open loop model
Closed Loop Method
may not be applied for some practical systems
EE3511_L12
Salman Bin Abdulaziz University

13. Open Loop Ziegler Nichols Rules
Plot an open loop step response
Determine T, L, K K T L
Input Output
EE3511_L12
Salman Bin Abdulaziz University

14. Open Loop Ziegler Nichols RulesK
L : dead time
T : time constant
K : process gain T L
Step response
EE3511_L12
Salman Bin Abdulaziz University

15. Open Loop Ziegler Nichols Rules
Step response K
P controller
KP =T/L
PI controller
KP =0.9 T/L,
KI=0.3KP/L
PID controller
KP =1.2 T/L,
KI=KP/(2L);
KD=0.5KPL T L
EE3511_L12
Salman Bin Abdulaziz University

16. Closed loop Ziegler Nichols Rules
Use Proportional control only
Generate step response for different KP
Increase KP until stable oscillations is achieved. This gain is known as ultimate gain Ku
Read the oscillation period Pu Pu
EE3511_L12
Salman Bin Abdulaziz University

17. Closded Loop Ziegler Nichols Rules
P controller
KP =0. 5*Ku
PI controller
KP =0.45*Ku,
KI=1.2*KP/Pu
PID controller
KP =0.6 Ku ,
KI=Kp/(0.5*Pu) ;
KD=0.12*Pu*KP Pu
Step response
EE3511_L12
Salman Bin Abdulaziz University

18. Salman Bin Abdulaziz University
Example
Desired output
r(t)
Controller
Plant
Actual output
y(t)
Error
e(t) u - 60 X X X
EE3511_L12
Salman Bin Abdulaziz University

19. Salman Bin Abdulaziz University
Example X
jwn X -a -2 -1 X
-jwn
EE3511_L12
Salman Bin Abdulaziz University

20. Salman Bin Abdulaziz University
Example
Ku=K =6
Pu = 2π/ωn = 2π/ , note: Pu =T=1/f
P controller
KP =0. 5 Ku = 0.5*6 = 3
PI controller
KP =0.45 Ku=2.7; KI=1.2*KP/Pu=0.73
PID controller
KP =0.6 Ku=3.6 ; KI=Kp/(0.5*Pu)=1.27 ; KD=0.12*Pu* KP =1.92
EE3511_L12
Salman Bin Abdulaziz University