Internationalof Computational
Intelligence
Systems
Journal ofJournal
Robotics,Networking andArtificial Life
Vol.
XX(Z);
Month(2018),(Year), pp.
pp. 180–183
xx–yy
Vol.
5(3);
December
DOI:
10.1080/XXXXXXXXXXXXXX;ISSN XXXX–XXXX
onlineDOI:
10.2991/jrnal.2018.5.3.8;
ISSN 2405-9021
print; 2352-6386
onlinehttps://www.atlantis-press.com/journals/ijndc
https://www.atlantis-press.com/journals/jrnal

Research Article

Control Performance Assessment Method as Assessmentof Programming Learning Achievement
Yoshihiro Ohnishi*
Faculty of Education, Ehime University, Ehime 790-8577, Japan

ARTICLE INFOABSTRACT

Article History

It is an important problem how to estimate the learning achievement of the programming learning. However, the quantitativeevaluation method according to learning achievement is difficult. On the other hand, “work” of a control program influences thecontrol performance of the plant by the petrochemical industry, and to have an influence on the operation cost. Improvement ofa program and am planning for productivity improvement are suggested by evaluating the control performance quantitatively.
This research considers the using control performance assessment method for the achievement value of the programminglearning.

Received 25 May 2018
Accepted 20 October 2018
Keywords
Programming learning
control performance assessment
minimum variancelearning achievement© 2018 The Author. Published by Atlantis Press SARL.
This is an open access article under the CC BY-NC license (http://creativecommons.org/licenses/by-nc/4.0/).

1. INTRODUCTION
It is an important problem how to estimate the learning achievement of the programming learning. However, the quantitative evaluation method according to learning achievement is difficult. On
the other hand, “work” of a control program influences the control performance of the plant by the petrochemical industry, andto have an influence on the operation cost, improvement of a program and am planning for productivity improvement are suggested
by evaluating the control performance quantitatively. The idea ofcontrol performance assessment is becoming important in the process control area [1–3]. This research considers the using control
performance assessment method for the achievement value otherthe programming learning.

2. CONTROL PERFORMANCE ASSESSMENT
The judgment of whether a controller is showing the desirable
performance has been formed out of the subjectivity of the expert
operator familiar with a plant concerned in the past. There is anindex of rising time, the overshoot amount and an attenuation
vibration characteristic as the quantitative control performanceindex of the controller. However, these indexes can be obtained in
the transient state which is at the time of a set value change. The
controlled value of the process control system represented by thepetrochemical plants can give the reference value as the constantvalue to the temperature, the pressure, and the flow rate. In thiscase, the steady state control performance which is the minimizingthe control error variance is more important than the target value* Email: ohnishi@ehime-u.ac.jp

tracking performance or the disturbance reply. For example, in thesystem of temperature control to keep the constant value of temperature as shown in Figure 1, it is required to keep the temperature
higher than some point. It is necessary to set the high reference
value to keep the minimum temperature before the adjustment
indicated on Figure 1 left side. It is possible to reduce the output
variance after the adjustment indicated on Figure 1 right side, andeven if the target value lower than the before adjustment, it is possible to keep the minimum temperature. The energy the adjustment
back requires more than this case and before an adjustment canbe done small. Thus it is sometimes tied with the efficiency of theenergy to disperse a control error small.
These ways have the method based on the benchmark of the minimum variance control [4], the method to consider a fluctuationof the manipulated value as well as output error [5], the method toexpress the control performance to compare with data in the past ina plant concerned, and the way to limit the structure of the controller for example the a model based predictive control or PID control
and express the control performance in the structure.
This research defines the good program makes the good control
which realizes the small output variance.

3. MV-INDEXThis section introduces the calculation of MV-index which is proposed by Desborough and Harris [6].
The generalized controlled object described as the following Eq. (1).	   y(t ) = z - dG p (z -1 )u(t ) + Gn (z -1 )x (t ) (1)

Y. Ohnishi / Journal of Robotics, Networking and Artificial Life 5(3) 180–183

181

And, Eq. (8) is expressed as the following Eq. (9) includinge(t ) = − {n0x (t ) +  + nd −1x (t − d − 1)b (t )	  

+ d0x (t − d ) + d1x (t − d − 1) + } (10)w (t − d )= − {b(t ) + w(t − d )}Here, b(t) is not associated with the control input and if w(t – d)is possible to be 0 by the control input, let b(t) minimum varianceoutput.
Figure 1 | The example of the temperature control systems
where y(t) and d system output and minimum estimate value ofdead time, respectively. u(t) is control input, and x(t) is probability noise including such as observation noise. In addition,
when information about dead time cannot obtain anything, d isset as 1. Feedback control law is given as the following Eq. (2)for Eq. (1).		 
u(t ) = Gc (z -1 )e(t ) (2)where e(t) means the control error signal which is defined as[Eq. (3)]:e(t ) : = r (t ) − y(t ) (3)		 From substituting (1), (2) into (3):-1r (t ) - Gn (z )x (t )e(t ) =		 (4)1 + z - dG p (z -1 )Gc (z -1 )2Here, s e2 shows the actual variance of control error and s MV
showsachievable the minimum variance of control error at this system.

Furthermore, minimum-variance control performance assessment
index h is shown by the following Eq. (11):			 h =

2s MV
(11)
s e2

2
The range is 0 £ h £ 1 because s e2 ³ s MV. The large value ofMV-index h means that good control performance.

MV-index h can be calculated by Eq. (11). However, the numeratorof Eq. (11) cannot be calculated directly. This term is obtained as
the following procedure.
The following equation can be derived by multiplying z–d for bothsides of Eq. (10).
-1-d-1	   e(t - d ) = -{Gn1 (z ) + z Gd (z )}x (t - d ) (12)x(t – d) can be expressed from Eq. (12).

Here, by considering the steady state, control error signal canobtain as the following Eq. (5).

e(t - d )		 x (t - d ) = - G (z -1 ) + z - dG (z -1 ) (13)-Gn (z -1 )x (t )		 (5)e(t ) =1 + z - dG p (z -1 )Gc (z -1 )The following Eq. (14) can be derived from Eqs. (8) and (14).

where the noise transfer function Gn(z–1) can be divided the term
about the dead time before and the term about the dead time after
by the following Diophantine Eq. (6):		 Gn (z -1 ) = Gn1 (z -1 ) + z - dGn2 (z -1 ) (6)where, Gn1(z–1) is polynomial given by the following Eq. (7).	    Gn1 (z −1 ) = n0 + n1z −1 +  + nd −1z − (d −1) (7)From Eqs. (5) and (6)-1-d-1	    e(t ) = -{Gn1 (z ) + z Gd (z )}x (t ) (8)where Gd(z–1) is defined as the following Eq. (9):Gd (z −1 ) : =	 Gn2 (z −1 ) − Gn1 (z −1 )G p (z −1 )G p (z −1 )1 + z − dG p (z −1 )Gc (z −1 )(9)n1	 e(t ) = -Gn1 (z -1 )x (t ) -dG d (z -1 )e(t - d ) (14)Gn1 (z -1 ) + z - dGd (z -1 )Here, the following Eq. (15) is also obtained because the first termof Eq. (14) is same as b(t) of Eq. (11).
e(t ) = -b(t ) -Gd (z -1 )e(t - d ) (15)Gn1 (z -1 ) + z - dGd (z -1 )Since the coefficient of the second term of Eq. (15) can be expressedas the finite transfer function, Eq. (16) can be expressed as the following AR model:p		 e(t ) = −b(t ) − ∑a ie(t − d − i) (16)i=0The order p must be enough larger than the order of the controlled
object. The relations of Eq. (16) are composed by the following
matrix Eq. (17) of the form:			e = Xk + b(17)Y. Ohnishi / Journal of Robotics, Networking and Artificial Life 5(3) 180–183

182

where, e and X are constructed by previous signals. And, k and b
are the autoregressive parameter vector and modeling error vector,respectively.
These are expressed as [Eqs. (18)–(21)]:T		e = e(n), e(n − 1),, e(d + p) (18)		 e(n − d )e(n − d − 1)
X=ep)(		k = [-a 1 , -a 2 ,, -a p ]T (20)		

b = b(n), b(n − 1),, b(d + p) (21) e(n − d − p + 1)
 e(n − d − p)  (19)



e(1)

T

where n is the sample length.

Figure 2 | The result of the ON–OFF control

The parameters of Eq. (20) can be obtained by:		  k = (X T X )-1 X T e (22)Therefore, the minimum variance can be obtained by Eq. (22).
 )T (e − X K ) (23)		 s 2 MV = (e − X K

4. SIMULATION EXAMPLEThis section demonstrates the effectiveness of the proposed schemeby a simulation example. The following Eq. (24) are used as thecontrolled object:
0.5 - Ls
G( s ) =e (24)		  
20s + 1
These models are discredited by 1.0 (s) sampling interval.
The following Eq. (25) is obtained as follows:	 y(t ) = 0.951 y(t - 1) + 0.0243u(t - 3) + x (t ) (25)where the mean value of x is 0, x _ s = 0.052 . The manipulate valueu is limited as 0 < u < 100.
First, the ON–OFF control expressed as the following rule (26) wasused for the controlled object (25).

Figure 3 | The result of the PID control

Figure 3 shows the control result by this PID control method. AndMV-index is 0.2585 which is calculated on 200 ≤ t ≤ 1200.
From the result of Figure 2, the input value is very oscillatory. Thevariance of the output value becomes large by the oscillatory input.
From Figure 3, the variance of the output signal becomes small by
the PID control. The MV-index can be the good metric to evaluate
the programming performance.

If (y(t ) < 30) then u(t )=100 else u(t )=0 (26)	 5. CONCLUSION

This method is an example algorithm which is used by a beginner.
This algorithm is conditional branch type which is studied on technology class in Junior high school.

This paper considers the using control performance assessment
method for the achievement of the programming learning. In thispaper, a method based on the controller performance assessment
was proposed.

Figure 2 is the control result by using the ON–OFF control. And
MV-index is 0.0208 which calculated on 200 ≤ t ≤ 1200.
Next, the following PID control method (27) is used.		

u(t ) = k p {e(t ) +e(t )+ TD De(t )} (27)DTI

where kp is the proportional gain, TI is the reset time, TD is the derivative time. Each value was set as kp = 7.7, TI = 17, TD = 0.9, respectively.

The effectiveness of the proposed method was evaluated by thesimulation example.

ACKNOWLEDGMENT
This work was supported by JSPS KANKENHI (Grant Number18K02980).

Y. Ohnishi / Journal of Robotics, Networking and Artificial Life 5(3) 180–183

REFERENCES[1] B. Huang, S.L. Shah, Performance Assessment of Control Loops:
Theory and Applications, Springer, London, 1999.
[2] M. Jelali, An overview of control performance assessment technology and industrial applications, Control Eng. Pract. 14 (2006),
441–466.
[3] M. Jelali, Control Performance Management in Industrial
Automation, Springer, London, 2013.

Author Introduction
Dr. Yoshihiro Ohnishi
He received his B.E. and M.E. fromOkayama Prefectural University in1997 and 1999, respectively. And hereceived his Dr. Eng. from Osaka
Prefecture University in 2002. He isan associate professor at Faculty of
Education in Ehime University. He isa member of SICE, ISCIE, IEEJ andIEEE.

183[4] T.J. Harris, Assessment of closed loop performance, Can. J. Chem.
Eng. 67 (1989), 856–861.
[5] M.J. Grimble, Controller performance benchmarking and tuning
using generalized minimum variance control, Automatica 38(2002), 2111–2119.
[6] L. Desborough, T. Harris, Performance assessment measures forunivariate feedback control, Can. J. Chem. Eng. 70 (1992), 1186–1197.