1. MESB374 System Modeling and Analysis PID Controller Design
ME375 Handouts - Spring 2002
MESB374 System Modeling and Analysis PID Controller Design

2. PID Controller Structure of Controller
ME375 Handouts - Spring 2002
PID Controller
Structure of Controller
Effects of Proportional, Integral and Derivative Actions
Design of PID Controllers

3. (prediction of) future information
ME375 Handouts - Spring 2002
PID Controller
GC (s)
H(s) + -
Reference Input
R(s)
Error
E(s)
Output
Y(s)
Disturbance
D(s)
Plant
G(s)
Control Input
U(s)
Gf (s)
Proportional plus Integral plus Derivative (PID) Control
In time domain
current information
passed information
(prediction of) future information
In s-domain

4. Effect of P-I-D Actions
Derivative Action (KCD s):
Provides added damping to the closed-loop system; reduces overshoot and oscillation in step response; tends to slow down the closed-loop system response. Dominant during initial transient, due to the effect of differentiation.
Integral Action (KCI /s):
Eliminates steady-state error to step inputs; tends to destabilize the closed-loop system; has averaging effect. Dominant during steady-state by producing an accumulation of steady-state error to increase control effort.
Proportional Action (KCP):
Introduces immediate action due to error; improves system response time. Has similar control authority for both transient and steady-state.

5. Effect of PID Actions Ex: For a given process
Reference input
R(s) +
Output
Y(s)
Disturbance
D(s)
Ex: For a given process
Unit step reference response
Unit step disturbance response

6. (A.) Let’s try Proportional control: GC(s)=KCP
Effect of P Action
Objective:
Design a system that has zero steady state error for step inputs with %OS<10% and Ts (2%)<6 [sec]
GC (s) + -
Reference Input
R(s)
Error
E(s)
Output
Y(s)
Disturbance
D(s)
Plant
Control Input
U(s)
(A.) Let’s try Proportional control: GC(s)=KCP
CLTF:

7. (A.1) Design P Control using Root Locus:
Effect of P Action
Stability:
0<K CP <14.1
(A.1) Design P Control using Root Locus:
CLCE:
Real
Axis
-25
-20
-15
-10 -5 5 10 15
Img. Axis
-7.5
-0.667
-10
-15
Not valid

8. Effect of P Action (A.2) Check for Steady State Error:
Unit Step Reference Response
Do NOT forget
Stability:
0<K CP <14.1
Larger gain results in smaller steady-state error.
Unit Step Disturbance Response
Larger gain results in stronger attenuation of disturbance.
Think about the change of overshoot when gain increases

9. (B.) Add integral action (PI control):
Effect of PI Actions
GC (s) + -
Reference Input
R(s)
Error
E(s)
Output
Y(s)
Disturbance
D(s)
Plant
Control Input
U(s)
(B.) Add integral action (PI control):
CLTF:

10. (B.1) Design PI Control using Root Locus:
Effect of PI Actions
Stability:
0<K CP <11
(B.1) Design PI Control using Root Locus:
Real
Axis
-25
-20
-15 -2 -1 1 5
Img. Axis
-10 -5 10 15
CLCE:
Choose zPI = -0.5:
-7.3
Not valid

11. Effect of PI Actions (B.2) Check for Steady State Error:
Unit Step Reference Response
By using Integral action. steady state error is eliminated.
Unit Step Disturbance Response
By using Integral action, the effect of a constant disturbance can also be eliminated.
Has transient performance been improved?
Not much

12. (C.) Add derivative action (PID control):
Effect of PID Actions
GC (s) + -
Reference Input
R(s)
Error
E(s)
Output
Y(s)
Disturbance
D(s)
Plant
Control Input
U(s)
(C.) Add derivative action (PID control):
CLTF:

13. (C.1) Design PI Control using Root Locus:
Effect of PID Actions
Stability:
0<K CD
(C.1) Design PI Control using Root Locus:
Real
Axis
-20
-10
-15 -2 -1 1 5
Img. Axis -5 10 15
CLCE:
Choose z1 = -0.5, z 2=-2.1
-9.95
-2.1
-9.92
-2.6
-1.62

14. Effect of PID Actions (C.2) Check for Steady State Error:
Unit Step Reference Response
By using Integral action. steady state error is eliminated.
Unit Step Disturbance Response
By using Integral action, the effect of a constant disturbance can also be eliminated.
Has transient performance been improved?
Yes

15. PID Controller Design via Root Locus
Pole-Zero structure of PID Controller:
PID Controller adds one open-loop pole at origin and two open-loop zeros, z1 and z2. These two open-loop zeros could be either real or complex conjugate pair.
Design Procedure
Step1: Select the position of the two zeros such that the root locus will intersect
with the desired performance region.
Step 2: Pick the controller gain KC such that CL poles are in the performance region
Step 3: Find the corresponding PID gain using the above formula.

16. Design of PID Controller
Ex: ( Motion Control of Hydraulic Cylinders )
Recall the example of the flow control of a hydraulic cylinder that takes into account the capacitance effect of the pressure chamber. The plant transfer function is: A V C M B
Output
V(s)
GC (s) + -
Reference Velocity
R(s)
Error
E(s)
Plant
Control Input
QIN (s)
Disturbance D (s)
qIN

17. Design of PID Controller
Output
V(s)
GC (s) + -
Reference Velocity
R(s)
Error
E(s)
Plant
Control Input
QIN (s)
Disturbance D (s)
We would like to design a controller such that the closed loop system is better damped (smaller OS%)
CLTF:

18. Design of PID Controller
PID controller design
Closed-loop Characteristic Equation
Real
Axis
-30
-25
-20
-15
-10 -5 5 10 15
Img. Axis 20
Transient performance region
Can a PID controller be designed to satisfy the transient design specifications (smaller overshoot and faster settling time) ?