Oct 16, 2014 - First Order Plus Dead Time (FOPDT) model represents one of the ... Integral Plus Dead Time (IPDT) plant models may be considered as a.
Comparing FOPDT and IPDT Model Based PI Controllers with Disturbance Observer ˇ ak1 Peter Tap´
Mikul´aˇs Huba1
1 Slovak
University of Technology in Bratislava Ilkoviˇ cova 3, 812 19 Bratislava, Slovakia
2014 International Conference and Exposition on Electrical and Power Engineering (EPE) ˇ ak, Mikul´ Peter Tap´ aˇs Huba (STU FEI)
FOPDT vs IPDT based DO-PI
October 16, 2014
1 / 14
Introduction Why it is interesting to discuss relations between FOPDT and IPDT plant models? —————————————————————– First Order Plus Dead Time (FOPDT) model represents one of the most frequently chosen starting models Integral Plus Dead Time (IPDT) plant models may be considered as a special case of FOPDT models, but they have also a special meaning of more general models Ziegler and Nichols - low ratio of the dead time and the plant time constant - Integral Plus Dead Time (IPDT) approximation IPDT approximation for the FOPDT process - plant feedback may lead to asymmetrical behavior - oscillations asymmetry laboratory plant model will be extended by an additional dead time to illustrate the pros and cons of the both models ˇ ak, Mikul´ Peter Tap´ aˇs Huba (STU FEI)
FOPDT vs IPDT based DO-PI
October 16, 2014
1 / 14
Two possible models for the simplest plant dynamics Introduction
FOPDT approximation G (s) =
IPDT approximation (a = 0)
Ks −Td s e s +a
G (s) =
Ks −Td s e s
May also be interpreted as a model not considering a T = 1/ |a| - process time Plant feedback approximation by the constant zeroth Taylor term aTd - dead time to process time No reference point for the dead time constant ratio value Td - dead time
ˇ ak, Mikul´ Peter Tap´ aˇs Huba (STU FEI)
FOPDT vs IPDT based DO-PI
October 16, 2014
2 / 14
Dead Time to Process Time Constant Ratio Influence Identification - Simulation Results
FOPDT model parameters:Ks = 0.5, a = 0.5 IPDT parameters were obtained by relay feedback experiment Dead time varies on the interval Td ∈ [0.01, 10]
IPDT Model Parameters
IPDT Model Parameters Dependancy on FOPDT Plant Dead Time to Process Time Constant Ratio 0.6
6
0.4
4
0.2
2
IPDT Process Gain Real Process Gain Real Dead Time IPDT Dead time 0
0
ˇ ak, Mikul´ Peter Tap´ aˇs Huba (STU FEI)
1
2 3 4 Deadtime to Process Time constant Ratio
FOPDT vs IPDT based DO-PI
5
0
October 16, 2014
3 / 14
Dead Time to Process Time Constant Ratio Influence PI1 - Controller - Simulation Results 1
Control scheme used for demonstrating dead time influence on the plant modeling - Predictive Disturbance Observer based (PDO) PI controller —————————————————————–
ˇ ak, Mikul´ Peter Tap´ aˇs Huba (STU FEI)
FOPDT vs IPDT based DO-PI
October 16, 2014
4 / 14
Dead Time to Process Time Constant Ratio Influence Control Performance - Simualtion - Low aTd
30 29 28
System output
27 26 25 24 Setpoint IPDT based control FOPDT based control
23 22 21 20 1
1.05
1.1
1.15 1.2 Time [s]
1.25
1.3
1.35
—————————————————————– No difference between FOPDT and IPDT plant models ˇ ak, Mikul´ Peter Tap´ aˇs Huba (STU FEI)
FOPDT vs IPDT based DO-PI
October 16, 2014
5 / 14
Dead Time to Process Time Constant Ratio Influence Control Performance - Simualtion - Higher aTd
30 29 28
System output
27 Setpoint IPDT based control FOPDT based control
26 25 24 23 22 21 20 100
105
110
115
120 125 Time [s]
130
135
140
145
Figure: Control Performance - aTd = 0.5 - IPDT yields conservative results ˇ ak, Mikul´ Peter Tap´ aˇs Huba (STU FEI)
FOPDT vs IPDT based DO-PI
October 16, 2014
6 / 14
Real Experiment - Light intensity Thermo-Optical Plant
Basic features Based on Arduino platform USB connection Sample time starting from 20ms Matlab/Simulink compatible without additional toolboxes no Simulink model compilation required Actuators: bulb, LED, fan Outputs: temperature, light intensity, fan rpm
ˇ ak, Mikul´ Peter Tap´ aˇs Huba (STU FEI)
FOPDT vs IPDT based DO-PI
October 16, 2014
7 / 14
Real Experiment - Light intensity Light Channel Overview
Bulb - actuator - 0-100%
Input−output characteristic y=f(u) 80
Light intensity sensor → first order low pass filter - time constant 2s
60 50 −−−> y
Non-linear
70
Measured points of IO characteristics Linear interpolation of IO characteristics
40 30 20 10 0
0
20
40
60
80
100
−−−> u
Figure: Input-to-output characteristic of the light channel
ˇ ak, Mikul´ Peter Tap´ aˇs Huba (STU FEI)
FOPDT vs IPDT based DO-PI
October 16, 2014
8 / 14
Real Experiment - Identificaton Identification Results - No Additional Delay
In general, the plant identification yields not just differences in a, but also in Ks and Td —————————————————————– The IPDT model parameters were G1 (s) =
Ks1 −Td1 s 0.3718 −0.3035s e = e s s
The FOPDT model parameters were G2 (s) =
Ks2 −Td2 s 1.6771 −0.0812s e = e s +a s + 0.4993
ˇ ak, Mikul´ Peter Tap´ aˇs Huba (STU FEI)
FOPDT vs IPDT based DO-PI
October 16, 2014
9 / 14
Real Experiment - Identification Identification Results - 200ms Additional Delay
In general, the plant identification yields not just differences in a, but also in Ks and Td The IPDT model parameters were G1 (s) =
Ks1 −Td1 s 0.2752 −0.4994s e = e s s
The FOPDT model parameters were G2 (s) =
Ks2 −Td2 s 1.6771 −0.2861s e = e s +a s + 0.4993
ˇ ak, Mikul´ Peter Tap´ aˇs Huba (STU FEI)
FOPDT vs IPDT based DO-PI
October 16, 2014
10 / 14
Real Experiment - Identificaton Model vs Real Data
46 45 44 43 42 Setpoint Measured values Model output − IPDT Model output − FOPDT
41 40 39 38 37 10
ˇ ak, Mikul´ Peter Tap´ aˇs Huba (STU FEI)
11
12
13
FOPDT vs IPDT based DO-PI
14
15
October 16, 2014
11 / 14
Real Experiment - Control Linearized System Performance - Setpoint Step
The intrinsic plant delay is already long enough to approve use of more complex FOPDT models —————————————————————– System Output
System Output 70 Light Intensity
Light Intensity
70
65 Setpoint FOPDT IPDT
60
55
0
1
2
3
4 5 Time [s] Control Signal
6
7
8
0
5
10
15 Time [s] Control Signal
20
25
30
80 Bulb Power
Bulb Power
Setpoint FOPDT IPDT
60
55
9
80
70
60
50
65
FOPDT IPDT 0
1
2
3
4 5 Time [s]
6
7
8
Figure: no additional delay ˇ ak, Mikul´ Peter Tap´ aˇs Huba (STU FEI)
9
70
60
50
FOPDT IPDT 0
5
10
15 Time [s]
20
25
30
Figure: 200 ms additional delay
FOPDT vs IPDT based DO-PI
October 16, 2014
12 / 14
Real Experiment - Control Non-Linear System Performance - Setpoint Step
Simpler IPDT models may be advantageous in a simplified approach not using nonlinearity compensation by its inverse —————————————————————– System Output
System Output 70 Light Intensity
Light Intensity
75 70 65 Setpoint FOPDT IPDT
60 55
0
1
2
3
4 5 Time [s] Control Signal
6
7
8
0
5
10
15 Time [s] Control Signal
20
25
30
20
25
30
40 FOPDT IPDT
60
Bulb Power
Bulb Power
Setpoint FOPDT IPDT
60
55
9
80
40 20 0
65
0
1
2
3
4 5 Time [s]
6
7
8
Figure: no additional delay ˇ ak, Mikul´ Peter Tap´ aˇs Huba (STU FEI)
9
FOPDT IPDT
30
20
10
0
5
10
15 Time [s]
Figure: 200 ms additional delay
FOPDT vs IPDT based DO-PI
October 16, 2014
13 / 14
Conclusions Experiments and simulation showed expected results: —————————————————————– The FOPDT model based controller performed better with ideal FOPDT plant non-linear real plant - the IPDT model worked better (they are less sensitive to different modeling uncertainties) For the IPDT model based controller the transients were slower - thus more robust Thus, one has to think about, which model might be useful for the considered loop Relay experiment can be used in very convenient way to obtain model parameters
ˇ ak, Mikul´ Peter Tap´ aˇs Huba (STU FEI)
FOPDT vs IPDT based DO-PI
October 16, 2014
14 / 14
