pid controller tuning 1.introduction 2.model-based pid tuning methods 3.two degree of freedom...
TRANSCRIPT
PID Controller Tuning
1. Introduction
2. Model-based PID tuning methods
3. Two degree of freedom controllers
4. On-line PID controller tuning
5. PID tuning guidelines and troubleshooting
6. Simulink example
Introduction
PID control law
Transfer function
Controller tuning» Need to select PID parameters (Kc, I, D) that yield
“good” closed-loop response to disturbances and setpoint changes
» Only know: KKc > 0, I > 0, D >0» Trial-and-error tuning difficult and time consuming» Need methods to determine good initial parameter
values » Refine parameter values by trial-and error fine tuning
t
DI
c dt
tdedtteteKptp
0
** )()(
1)()(
ss
KsGsE
sPD
Icc
1
1)()(
)('
Impact of Controller Tuning
120)()(
4
s
esGsG
s
dp
Closed-Loop Performance Criteria
1. Stability of closed-loop system
2. Minimization of disturbance effects
3. Rapid, smooth tracking of setpoint changes
4. Elimination of steady-state offset
5. Avoidance of excessive control action
6. Robustness to changes in process conditions
7. Robustness to errors in process model
Model-Based PID Controller Tuning
Often based on first-order-plus-time-delay model
Integral error criteria
1)(
)(
)(
s
KesG
sU
sY s
0
0
2
0
|)(|error absolute weighted timeof Integral
)(error squared of Integral
|)(|error absolute of Integral
dttetITAE
dtteISE
dtteIAE
ITAE Tuning Rules
General Trends
The controller gain (Kc) is inversely proportional to the process gain (K).
Kc decreases as the ratio of the time delay and the dominant process time () constant increases.
Both the integral time (I) and the derivative time (D) increase as / increases.
A reasonable initial guess for the derivative mode is D = 0.25I.
Kc decreases as integral control is added to a proportional controller. Kc increases as derivative control is added to a PI controller.
ITAE Controller Tuning Example
Process model
ITAE tuning for disturbance (more aggressive)
ITAE tuning for setpoint (less aggressive)
193.5
54.1)(
)(
)( 07.1
s
esG
sU
sY s
75.2)93.507.1(674.0
93.5
)(
97.293.5
07.1859.0
54.1
11
680.0
977.0
BI
B
c
A
AK
K
93.5)(
83.11
BA
AK
K
I
B
c
Two Degree of Freedom Controllers
Seek to tune the setpoint tracking response independent of the disturbance rejection response
Setpoint filtering
» Controller operates on Y*sp instead of Ysp
» Tuning parameter f determines speed of response
Setpoint weighting
» Tuning parameter determines speed of response
tm
DI
cmspc dt
tdydtteKtytyKptp
0
** )()(
1)]()([)(
1
1)(*
sY
sY
fsp
sp
On-Line PID Controller Tuning
Often a process model is not available for controller tuning
Need to determine tuning parameters directly from plant data
Continuous cycling method» Utilizing a proportional controller, find the Kc
value that produces sustained oscillations. This is the ultimate gain Kcu.
» Determine the period of the sustained oscillations. This is the ultimate period Pu.
» Kc and Pu can also be found from an available transfer function model by direct substitution.
Tuning Rules Based on Ultimate Gain
Shortcomings of Continuous Cycling Method
Time consuming for processes with large time constants
Process pushed to stability limit
Ultimate gain does not exist for first- and second-order systems without time delays
Generally not applicable to integrating and open-loop unstable systems because stability is achieved only for intermediate Kc values
First two shortcomings can be overcome using relay autotuning method to determine Kc and Pu (see text)
Step Test Method
Model structure
u
yKsU
s
KesY
s
)(1
)(
Step Test Method cont.
Model structure
Calculation of and » Determine times when output has reached 35.3%
(t35) and 85.3% (t85)
» Calculate and
Then use tuning method for FOTPD models
u
yKsU
s
KesY
s
)(1
)(
)(67.029.03.1 35858535 tttt
Shortcomings of Step Test Method
Experimental test performed under open-loop conditions
Method is not applicable to open-loop unstable processes
Step response can be sensitive to the direction and magnitude of the step change if the process is nonlinear
Guidelines for Common Control Loops
Flow rate control – aggressively tuned PI controller due to fast dynamics and few disturbances
Liquid level control – conservatively tuned P or PI controller depending on whether offset-free performance is required
Gas pressure control – moderately tuned PI controller with little integral action due to small time constants and stability concerns
Temperature control – PID controllers with application dependent tuning
Composition control – PID or more advanced controller due to sampling delay and measurement noise
Troubleshooting Control Loops
Surveys indicate that as many as 35% of industrial controllers are placed in manual at any given time
Determine if control problem is attributable to:» Transducer – degradation or complete failure
» Controller – poor tuning or inadequate design
» Final control element – control valve stiction
» Process – change in operating condition
Troubleshooting procedure» Collect data on control system performance
» Determine if operating conditions have changed
» Check individual control system components
» Retune or redesign the controller
Simulink Example: continuous_cycling.mdl
)15)(110(
2)(
ss
esG
s
TransportDelay
To Workspace1
input
To Workspace
output
System
2
50 s +15 s+12Setpoint
PID Controller
PID
Add
Determining the Ultimate Gain
0 10 20 30 40 50 60 70 80 90 100-0.5
0
0.5
1
1.5
2
2.5
Out
put
Time
Kc=7.50
Kc=7.88
Kc=8.00
PID Controller Tuning
Kc = 7.88, Pu = 11.66
Ziegler-Nichols tuning rules
45.18
83.52
73.46.0 uD
uIcuc
PPKK
0 5 10 15 20 25 30 35 40 45 500
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
Out
put
Time0 5 10 15 20 25 30 35 40 45 50
-2
-1
0
1
2
3
4
5
6
Inpu
t
Time