2013 3rd International Conference on Instrumentation Control and Automation (ICA) Bali, Indonesia, August 28-30, 2013
PID-Hybrid Tuning to Improve Control Performance in Speed Control f DC Motor Base on PLC Hari Maghfiroh Electrical Eng. And Information Tech.Dept., UGM IEEE SB UGM Yogyakarta, Indonesia
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Oyas Wahyunggoro Electrical Eng. And Information Tech.Dept. Universitas Gadjah Mada(UGM) Yogyakarta, Indonesia
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A.I. Cahyadi Electrical Eng. And Information Tech.Dept. Universitas Gadjah Mada(UGM) Yogyakarta, Indonesia
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Abstract—This paper presents an experimental studies of PID tuning. PID tuning can be done in two ways, namely offline and online tuning. Offline tuning method used in this study is the Ziegler - Nichols Quarter Decay, while the online tuning method used is Fuzzy Logic Controller (FLC). In this research, combination between offline and online tuning is performed to form, what so called, hybrid tuning. The hybrid tuning provides significant improvement compared to offline tuning alone. The settling time has been improved to 42, 86%, while percent overshoot (%OS) and Integral of Absolute Error (IAE) can be decreased to 63, 63% and 8, 49% respectively. While in set-point variations, hybrid tuning has better performance than offline tuning.
implemented in simple controller such as PLC. In this research, algorithm of PID hybrid tuning is made simple in order to implement on PLC. This paper is organized as follows: Section I, introduces the research, Section II describes PID tuning, Section III describes the design of PID hybrid tuning, Section IV discuss the experimental result and analysis, and Section V presents conclusions. II.
INTRODUCTION
PID control plays an important role in a control system, as shown in survey paper [8]. PID control is widely used because of its simplicity and reasonably good performance[1]. However, PID has two major shortcomings, namely the determination of the parameters of PID and its performance decreases as system conditions change. Determination of the PID parameters, or tuning, is usually done by finding mathematical models of the system. However, this way become difficult if the system controlled is too complex. For this reason, experimental method is developed. PID tuning usually can be done in two ways, namely offline and online tuning. Offline tuning is done when the system is not working, while online tuning is done when the system in working states. Therefore, online tuning can handle changes in the condition of the system when the system is running, but generally these methods needs to long computation. The offline tuning method used in this study is the Ziegler - Nichols Quarter Decay type, while the online tuning method use is Fuzzy Logic Controller (FLC). In this research, combination between offline and online tuning is called hybrid tuning. The hybrid is done by replaces some of the components in the online tuning with offline tuning components in order to improve control performance. The control algorithm then implemented on PLC to control DC motor speed. There has been many researches about PID hybrid tuning as shown in [2], but the configuration between PID and FLC(as online tuning) requires long computation that can’t be
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PID TUNING
A. PID Offline Tuning Offline tuning is performed when the system is not working. There are many methods in the offline tuning such as Ziegler-Nichols and Cohen-Coon [3]. Ziegler - Nichols method itself is divided in to two ways: Curves Reaction that done in open-loop and Ultimate Cycle that done in close-loop. The former way, parameters are rather difficult to estimate in noisy environment, the last one can be quite detrimental to the system because not all of system can tolerate sustain oscillation condition [4]. So in this research, Ziegler – Nichols Quarter Decay [9] is used, this method provides an approximation of the desired quarter – amplitude response as shown in Figure 1.
Keywords- PID, Tuning, Ziegler-Nichols, Quarter Decay, Fuzzy
I.
Supriyanto Praptodiyono Electrical Engineering Department Universitas Sultan Ageng Tirtayasa
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Figure 1. Quarter Decay Response Ziegler-Nichol Quarter Decay is done by tuning KP and disabling Integral (I) and Derivative (D) control function until a quarter – amplitude response(Figure 1) got. KP that makes system has this response is namely KU1/4 so KU = 2 * KU1/4 [5], while ultimate period(TU) is obtained from the curve, Figure 1..Then value of KP, KI and KD for PID controller sought by formula in Table 1.
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B. PID Online Tuning On - line tuning of PID parameter is performed when the system is working. Some methods in this tuning are Fuzzy Logic Controller (FLC), Genetic Algorithm (GA), Neural Network (NN), etc. FLC for PID online tuning is done in [5]. However, this method requires long computational time because the tuning is aimed to the three gain parameters KP, KI, and KD. The system is shown in Figure 2.
prefer to select KP to be tuned online and the others tuned offline.
Table 1 Ziegler – Nichols Quarter Decay PID’s formula[9]
(a)
Controller Type
Kp
Ti
P
0,5 Ku
PI
0, 45 Ku
0,5 Pu
PID
0,6 Ku
0,5 Pu
Td
0, 125 Pu
(b) Figure 4. PID Stucture (a) serial, (b) parallel B. PID offline tuning Offline tuning method used in this study is Ziegler Nichols Quarter Decay because the closed loop system is used. Block diagram of the system is shown in Figure 5. The constant K in the integral and derivative term is used to disable the function of the two controllers by setting K to 0.
Figure 2. Fuzzy – PID Controller[1]
Figure 5. PID Offline Tuning
Figure 3. Experimental setup III.
CONTROL SYSTEM DESIGN
As a test bed DC motors are used as a plant while PLC is used as a digital controller. Illustration of this system is shown in Figure 3. A. PID Structure There are two common structure of PID controller. First is serial or cascade structure shown in Figure 4.a, with formula in Equation (1.a) [4] [6], second is parallel structure shown in Figure 4.b, with Equation (1.b) [2] [3]. y(t) = KP e(t) + (KI e(t)dt) + KD
de(t) dt
y(t) = (KP e(t)) + (KI e(t)dt) + KD
de(t) dt
Figure 6. PID Hybrid Tuning
(1.a)
C. Hybrid Tuning Hybrid tuning is the combination of offline and online tuning. Offline tuning used in this work is the Ziegler Nichols Quarter Decay while online tuning used FLC. In this system, FLC used only to tune KP while KI and KD values determined by offline tuning. This method is expected to produce a control system that can cope with variations in system conditions adaptively as fast as possible computation
(1.b)
From Figure 4 seen that in the first structure, KP has the dominant effect for controller, while in second structure, KP, KI, and KD has the same contribution to the output. Therefore, as the reason, we are going to provide first structure to use in this researh. Because the dominan gain controller was KP, we
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time. The composition of the control system block diagram is shown in Figure 6.
e)
Point F and J, E is small and CE is zero, KP is set to medium to stop undershoot.
Base on the analysis above, the matrix of rules compiled in Table 2. This rule can be changed according to the results of tests on the system.
D. FLC Design FLC in this system, Figure 6, have two inputs, namely error (E) and change of error (CE) and one output that is value of KP (multi-input single output). 1) Fuzzification Membership functions that used is triangular functions with five membership limit, Negative Big (NB), Negative Small (NS), Zero (ZE), Positive Small (PS), and Positive Big (PB). The maximum value (PB) of E is 500 to cope with the maximum speed used in the test, i.e., 500 rpm. To avoid trial and error, the limit values for CE and KP are determined from the results of offline tuning as seen in Figure 7.
Figure 8. Transient Respont Table 2 Matrix of Rules (a)
NB
NS
ZE
PS
PB
PB
NB
NS
ZE
PS
PB
PS
NS
ZE
ZE
ZE
PS
ZE
NB
ZE
ZE
ZE
PB
NS
NS
ZE
ZE
ZE
PS
NB
NB
NS
ZE
PS
PB
CE
(b)
E
3) Defuzzification Defuzzification is conversion of the magnitude of fuzzy output into real scale. The method used in this study is Weighted Average (WA)[7], as
(c) Figure 7. Membership functions (a) E, (b) CE, (c) KP
Z =
2) Rule Base The arrangement of rule base is base on transient response graphs as seen in Figure 8, E is positive when the curve is below the set-point and negative when the curve is above it. As for CE, it will be positive if the curve moves towards the valley of waves and vice versa. The value of KP changes according to the point on the graphic, shown in Figure 8 as follow:
.
(2) Where
Z0 = output FLC µz = output degree of membership z = output membership limits IV.
RESULT AND ANALYSIS
A. Open – loop system Open-loop testing used to investigate characteristics of the plant. Testing is done with a set-point of 500 rpm, the results shown in Figure 9, while the response parameter data is in Table 3. Based on Table 3, known that open - loop system has a long response time and large error despite having no overshoot. In addition, the open - loop system also has a steady state error.
a)
Point A, the value of E and CE are big we so need a big value of KP to quickly reach the set-point. b) Point B, the value of E and CE are shrinking so KP’s value is reduced to prevent overshoot. c) Point C, E, G, I, and K, E is zero and CE is small, so KP’s value is at the middle of membership limits (ZE). d) Point D and H, E is small and CE is zero, KP is set minimum to reduce the overshoot.
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before as faster response speed and IAE reduced and tolerable amount of overshoot. Another advantage is steady state response error is reduced.
Figure 9. Open – loop response Table 3 Parameter respon open - loop Parameter
Value
Ts
13, 5 second
% OS
0%
IAE
5195
Figure 11. System respons with PID gain as in Table 4
B. Offline Tuning Offline tuning with Ziegler-Nichols Quarter Decay method give quarter-amplitude respond, Figure 10, when KU1 / 4 = 1, so that KU = 2. Based on Table 1, the value of KP, KI and KD determined and listed in Table 4. The testing results of the system with PID parameters from Table 4 are shown in Figure 11. However, this response still has high overshoot so fine tuning is done.
Figure 12. System respons after fine tuning C. Hybrid Tuning As mentioned earlier, in this tuning, KP value is obtained from the FLC whereas KI and KD are obtained from ZieglerNichols Quarter Decay. 1) Validate Algorithm Validate algorithm is to ensure the proposed algorithm can work as expected, the value of KP change according to the value of the system error. Graph changes in the value of KP is shown in Figure 13, initial value of KP = 0.5 when E = CE = 0. Then when the system starts running then the value of KP up to the limit of the maximum value of KP = 0.7 and back to 0.5 when error gone to small value. So the proposed algorithm has been concluded as expected.
Figure 10. Quarter Amplitude Response Table 4 PID gain from Ziegler – Nichols Quarter Decay Tuning Parameter
Value
Kp
1. 2
Ki
0. 3
Kd
0. 9
Fine tuning is re-election of KP value to obtain the expected results, the tests performed on KP
