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Intellicon: An Industrial Multiloop Adaptive Regulator
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INTELLICON: AN INDUSTRIAL MULTILOOP ADAPTIVE REGULATOR L. Keviczky*, I. Vajk** and
J.
Hetthessy**
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Abstract. The paper des c ribes the design conception of an industrial multi loop adaptive regulat or and th e prac ti c al approach of the implementation of a hi ghly r e liable adaptive control strate gy . Keywords . Ada pt i ve contro l; multiloop regulator; PID regulator. INTRODUCTION In the iast few years some adaptive controllers appeared on the market. Two years ago a project was started to develop a multiloop intelligent re gulator with adaptive fa c ilities in Hungary, too. The project has successfully been finished and now this equipment, called INTELLICON, is already a factory produc t. The key features of INTELLICON are the very high level man/machine communication (the very flexible configuration and "softwiring" possibilities) and the adaptively tunable PID loops. A general description of IN TELL ICON has already released by Rbzsa and co-workers (1984) and this paper will concentrate only f or the adaptation. Therefore a very short in f ormation will be only given on the sp ec ifi c da ta of the equipment here -inb e low . INTELLICON is a microcomputer-based pre-programmed digital controller, whose capabilities meet the most up-to-date requirements. (The front-panel can be seen on Fig. 1.) . INTELLICON continuously accepts, measures and processes - in a way selected by the user to solve the control problem at hand - all information coming from the proc ess and computes and outputs those signa ls which are required to keep it under its control, to the actuators . Moreover it makes all information required by the process operator available and displays them using character displays and LED-s. There are over 50 pre-programmed FUNCTIONS (program blocks desi gned to implement a welldefined function) permanently stored in EPROM memory. They provide alarm generation, integration, counting, limiting, PID ratio, cascade and feedforward control, mathematical operations, set-point generation, timing and logical functions, and more. In order to solve a control problem, the user s elects and references ("wires") the required functions from the function library in the same way as he should do it if they were not implemented by a computer program, but by an analogue electrical equipment. This opera tion is the CONFIGURATION of INTELLICON, which can be made by using the displ ays and push-buttons mounted on the controller's front panel. Neither computer-programming expertise nor knowledge of a programmin g language are required for the on the-spot configuration of the controller. Once configured, the c ontro l problem is stored in battery-backed up CMOS RAM memory and can be activated without delay.
ation, required by the proc ess operator, easil y available. The chosen operating mode (MANUAL, AUTOMATIC, CASCADE, REMOTE), control error (4 LED-s per loop), process variable alarms (Hi gh, Low) are continuousl y displayed f or all control loops . Moreover, the serial number and the most important da ta of a sel ec t ed contr ol-l oop (set-p oint, ac tua t or position, pr oces s vari abl e, deviati on,r a ti o and PID parameters, range and limit data) are displayed and the parameters can be changed by the operator. The four separate character displays belonging to the four sequences continuously display the step serial number of the batch process under control. Dedicated panel-mounted push buttons enabl e simple supervision and manual c ontr ol to be achieved. INTELLICON has special hardware and software -to run a continous self-test. In case of an error detected by the system an alarm is sounded and the cause of the error is displayed. Fatal errors result in automatic switch-over of all control loops to the stand-by Manual Control Panel. (The INTELLICON has pro cess control local area networking capabilities, too .) The most important techni cal data are: 16 analo gue inputs (0-5, 0-10, 0-20, 4-20 mA) 32 discrete inputs 8 pulse inputs (0-50 Hz max.) 32 discrete outputs } out ut to 16 analogue outputs (4-20 mA) 8x2 contact outputs for motor tP t control ac ua ors manual control panel with analogue instruments (optional) number of control loops: 8-16 closed loop control (depending on the actuator type); 2 discrete control; 4 batch control sequences. INTELLICON's ada?tive tunin g capability enables the loop t uning to be automati cally adjusted to match the variations of the process. CONCEPTION OF THE APPLIED ADAPTIVE STRATEGY At the design and the realization of the adaptive regulator some serious r e stri c tions had to be taken into considerati on. The software of the ada ptive regulator had to be implemented on a given hardware and on this hardware the software o f the INTELLICON realizes seve ral other functi ons (see the Introducti on) .
The front-panel makes all the important inform-
12li7
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L. Ke\'irzk\', I. \ 'aik and.J. J-1etthess\
The most important constraints were the following: - the available code memory for the adaptive regulator was not more than 5 kbyte EROM; - the INTELLICON uses only 3 byte precision software floating point arithmetic routines; the adaptive algorithm has to tune the parameters of the INTELLICON's PID regulators; - the man/machine hardware interface is given by the INTELLICON's front panel, The available memory size did not give the possibility to estimate the delay time of the process, The low precision of the arithmetics required to reduce the number of the estimated parameters. At tl.e can be linear can be y (t)
design phase it was assumed that the process well approximated by a second order, stable, lumped parameter system with dead time. It written schematically that k/Kls
e- TDS u(t) + net),
(1)
where yet), u(t), net) are the measured process output, the process input variables and the additive noise, respectively. K, Kl, Tl, TT2 are the parameters of the second order process model and TD is the delay time. The spectrum of the noise is considered wider than that of the noiseless process output. The realized self-tuning PID regulator is a robust explicit parameter adaptive controller. The scheme of the regulator is shown in Fig. 2. The algorithm estimates the process parameters and on the basis of the estimation it designs the parameter of the controller, tunes the parameters of a PID regulator. It might happen that the identification gives an unrealistic parameter estimation, in this case the regulator design is based on the apriori process parameters. The sampling time hr of the PID regulator is fixed (2 sec). But the sampling time of the identification hi is chosen using the apriori information of the process parameters, it is the integer multiple of the control sampling time. (We should mention here that the apriori information can be overwritten by the aposteriori information using the RESET key, se e later, and at the same time a new sampling time for identification will be automatically redesi gne d.)
sampling time of the regulator. It is used in the shadow system which generates the instrumental variables and partly applied for the regulator design; 3. discrete time process model obtained by the
sampling time of the identification. This description form is used by the estimator. The exact transformation between the different process descriptions is difficult to realize without hardware arithmetics because the execution time of the calculations is very long (think the exponential transformation, e.g.). Therefore, we applied a modified version of bilinear approximation for the transformation. The classical bilinear approximation may result transfer without time delay which is unrealistic in a controlled process. In order to eliminate this disadvantage, the following approximation is used between the system descriptions : W(z
-1
2 -1 ) = _z_ _ l+z-l
.r
2 l_z-l (s = -h ~l) l+z
(2)
where .r(s) is the transfer function of the continuous process without holding unit, W(z-l) is the discrete model of the process.Here s is the Laplace operator, z-l is the backward shift operator and h is the sampling time. PARAMETER ESTIMATION In an adaptive controller the direct application of the maximum likelihood estimation is very complicated. However, it is useful to apply such a method which does not estimate the parameters of the noise in order to decrease the number of the estimated parameters and which only requires that the expected value of the noise is zero. (The slow drift can be eliminated by a high pass filter.) The instrumental variable (IV) method can satisfy these requirements. Let assume that the discrete process is described by
b~+b~Z-l
-d.
y (k) = "':"-1":':......1-1.,-·--"""2 z
l+al z
1
u(k) + n(k)
(3)
+a 2z
where d is the discrete delay time. This model can also be i given in another form (4)
For the generation of the parameter estimation database the primary variables are averaged and filtered by a high pass filter designed on the apriori data to eliminate the working point. The adaptation is automatically suspended if the database of the estimation is not informative enough. The algorithm checks the set point (reference) value Yr(t) in closed loop case and the input signal u(t) in open loop case. If in a longer period there is no change, the identification is stopped. This strategy guarantees the elimination of burst phenomena if the input is not persistently exciting and eliminates the effect of disturbances which is not simultaneously accompanied by changes in the set value in closed loop and in the input signal in open loop case. Since the sampling time of the regulator and the identification are different, the adaptive controller uses three dif f erent system descriptions. These
where T stands for the transposition furthermore (5)
r (k)
and
Ei
i
i
i
i T
[ b ,b l ,a l ,a 2 J o
=
i(k)
=
[ u(k-d i ), u(k-di-l), -y(k-l),-y(k-2)J
(8)
where
'L F
the communication between the operator and the INTELLICON and partly for the regulator design; 2. discrete time process model obtained by the
(7)
Here the index i refers to identification. Eq. (6) can be written in a vector form
= [y (l) , .•• ,y (N) ) J T
are: 1. Continuous time process model (see Eq. (1)) for
(6) T
(9 )
T
(10)
[ r(l), ... ,r(N) J T
(11)
[ i(l) , ... ,i(N) J
assuming N processed observations.
Industrial \Iultiloop ;\d;qJliH' [{q.:llbtnr
l:ztiy
The IV estimator for the parameter vector .Ri is ( T )-1 Q_T .Ri = ~ ~ . 'i.
REGULATOR DESIGN
(12)
where
The design of the regulator is based on the estimated second order process model with delay using the sampling time hr of the regulator:
b~ + b~z-l
(13)
The method gives unbiased parameter estimation if the IV (£(k) and the equation error (r(k» in (4) are uncorrelated (i.e., E{~ ) = Q). The expected value of the estimation is independent from the noise, but the variance of the estimated parameters is determined by the noise characteristics. The best selection of the instrumental variables is
~
=
(1 ~
(14)
where ~ is the covariance matrix of the noise. It is difficult to choose the instrumental variables according to (14) in a corresponding on-line strategy. It is better to use the filtered values ~F = ~
-1/2
~; 'i.F = ~
-1/2
'i.; ~F
~
-1/2
~
In the adaptive controller the recursive version of the IV method (RIV) is useful to apply: -i 1 T -' .Rk = .R k- l + ~ .!l.(k)Cy(k)-! (k).R~_lJ
(16) {R
=k-l
-
~_l.!l.(k) !T(k)~_l 2 w +
It is well known that the above naive programming form of the recursive least-squares like estimation can exhibit numerical difficulties. The problem may be very serious if a number representation of low precision is used. To make the algorithm numerically less sensitive the UDV factorization is used instead of (16) and (17). The FORTRAN subroutine UDVFLT realizing the UDV factorization is given on Fig. 3. (The program is based on the UD factorization published by Clarke (1979.) The prefiltering formulated by (15) is easy to perform by introducing the filtered 1 ~
Ai (z
~F(k)
u(k) ; /(k)
)
1 ~ Ai (z )
The INTELLICON realizes the discrete PID regulator by the following equation: U(k)=(K + p l-z-l
(l-a) ----1 y(k)
::---=yAi (z
Zi(k); ?(k)
As Eq. (19) shows the set value avoids the derivative term of the regulator and the differential action can be smoothed by a time lag. At a=O the elimination of the process poles can be reached, if the regulator parameters satisfy the equations
1
r
= h _---".2_ _
P
r
(20)
r
l+a l +a.z . (21)
h
These equations indicate that the pole elimination of a stable second order system can be performed if a~ > O. The parameter Kp can be determined in such a way that the phase margin ~ of the control system is to reach a prescribed value. (See this teChnique in Banyasz, Hetthessy and Keviczky If the derivative term of the regulator has to be limited (i.e. a # 0) because the designed T is too large, the direct pole cancellation cangot be applied. The parameter space (ar, a~) projected by the three-term controller is signif1cantly reduc~d with respect to the parameter a. This can be seen on Fig. 4. However, the Bode plot of the PID regulator explains that the time lag part of the controller hardly influences the low frequency characteristics. So Eqs (20) and (21) can be used, as well, if a # O. If at least one of the time constants of the process is larger than the sampling time h , the transfer function of the open loop control ~ystem can be approximated by
W,,(s) where
y(k)
)
1
( 0
(18)
-
~y(k)
Ai (z
l-a
T.K
)
'1
variables in !(k) and £(k) instead of the original ones.
(19)
l-az
(1985).)
!T(k)~_l£(k)
where w is the forgetting factor and
F u (k)
(18)
where K , ~i' Td and a are the regulator parameters and yr(~) 1S the reference signal (set point value).
In a elosed loop system the noise and the input signal of the process are correlated. So the usually applied choice of the IV results in unbiased estimation, if there is no additional delay in the controller, but the delay makes the control worse. A good selection of the instrumental variables is based on the model of the entire closed loop system. The auxiliary model can be based on the knowledge of the controller and the apriori or aposteriori estimation of the process parameters. The apriori or aposteriori information of the noise characteristic can be used for filtering the variables to improve the estimation. The construction of the database for the IV estimation can also be seen on Fig. 2.
1
r
The process is assumed to be controlled by the most widely used proportional - integral - derivative (PID) regulator, the parameters of which are adapted at each parameter estimation step.
(15)
easier to calculate.
2' w
-d
1 r -2 z r l+a z +a z l 2
and
l:::/b[J
else
(23)
I~,II
I.. Kc\ iuh. I. Vajk andl. Henhess\
= -h I lna
T
(24)
r
At th e ga in crossover frequency
(22) can be
separated to
.r
Having initialized Ec(O) and TO the system is ready for adaptation both in open- and closed loop mode which modes can be selected by the M&~UAL AUTOMATIC switch, if the operator enables the adap tation by ryressin~ a ~ISC START seauence (ADAPTATION O~). The tuning nrocedure can be stopned by pressing a MISC STOP sequence (ADAPTATION OFF). Any of the INTELLICON's PlO regulator can be switched on for adaptation, however, only one loop can be self-tuned continuously at the same time.
- 2~
i. l+( ~ c : l)
\~-Zc 1 )2 and - )[
+
The time lag part of the derivative action is determined in such a way that the following inequality is satisfied: Td
11
Kp +
(1-a) < MAX
I-a
K
(27)
p
r
where MAX is a control ler design constant. Eqs (25), (26) and (27) give the possibility to design the gain K and the lag term parameter a. In the INTELLICON ~h e regulator is designed on the basis of the approximation of the nonlinear Eqs (25) and (26). OPERATION OF THE INTELLICON ADAPTATION
e
2
-sTD
(28)
l+sTl+s TT2 As a matter of fact there is no hope to get particular knowl~dge about Kl, however, the steady-state ga in K, the time constants Tl and TT2, as well as the pure time delay TO might be approximated evaluating a step response of the process. It is noted that in the course of the identification procedure the continuous process parameters ~=
[ K,Kl,Tl,TT2 J
T
(29)
will on l y be updated, while TO remains to be fixed. The identification step looks like: based on ~ c( O) a samp lin g time hi is designed
carefully to set up a second order discrete time model ~
h.
~
~ (0) -2:..- Ei (0) - evaluating the process~control input and process vari~ble measurements Ei is updated using the on-l,ne IV method. To generate instrumental variables, a s~adow system is run using the actual set point and PlO regulator in closed loop and the actual process input in open loop case. The shadow process model works with a samplin g time of h . Just for the regulator desi gn step, the tra~sformation
\
~
E.i (k)
-
Finally we can summarize that for the normal operation of the adaptive regulator the following apriori information is required - the time delay (TO) - the steady-state gain (K) - at least one of the time constants (Tl or TT2) of the process and the operation of the regulator can be controlled by the following switches: - RESET - MANUAL-AUTOMATIC - MISC-START, STOP (ADAPTATION-ON, OFF). Examples
It has been shown so far that the adaptive PlO regulator implemented in the INTELLICON means an explicit design method, i.e . , the regulator parameters are always determined as functions of a second order process model with time-delay. As a consequence, to start up a set of parameters corresponding to the following second order apriori model should be defined first: K +Kls
pc(O), and a new, better value for h. will be 1 computed.
~
£C (t)
is also performed in every step. It ~s seen ~hat in this way hi is only a function of ~(O) WhlCh could actually be a rough estimation. The sampling time h . has an importance to improve the identification performance, so a RESET function has been elaborat~d. If the operator gene rat es RESET, the updated ~(t) is loaded into
The operation of a self-tuning regulator of the INTELLICON will be illustrated by some simple examples. Let the continuous process be . -4s e (1+103) (1+20s) where the time constants and delay are in seconds. Fig. 5. shows the input (u{t», the output (yet»~ of the process and the square wave like reference ~ignal (Yr{t» excitation. First the system works ln open loop, then the loop is closed. The identification, running continuously, ensured good regulator design for the second phase which is already a normal operation mode. Here the design parameter MAXs 2 was chosen. This procedure can be considered a general approach in the practice. The selection of MAX influences the closed loop transient. A faster step reponse can be reached by greater value of MAX, however, the actuator output will be much higher. This is the price, the designer should pay for the result. The application of different values of MAX (MAX~lO, 1.5 and 0.75) can be seen on Fig. 6. The operation of the adaptive regulator under complex conditions can be seen on Fig. 7. Here the apriori parameter estimation is quite bad using 2 e- 4s 1+20s as a first guess. This explains the poor transient at the beginning of the experiment. It can be well seen that after switching the adaptation on the transient process became very nice. Lateron a step-like output disturbance appeared in the system which did not disturb the parameter estimation and the closed loop eliminated this unwanted effect using the latest optimal regulator parameters. Here MAX~1.5 was applied. CONCLUSION In spite of the many successful applications of the self-tuning regulators with more complex structure, our experience is that industry people prefer PlO regulators. More exactly, the industrial practice has almost no OPPOSltlon against the implementation of PlO regulators, even if they
Illdustri a l \fllitil()()p .\daptill· Rq.\uLl i()1 are adaptive. Starting fr om this phil os opy , we think that the developed industrial multilo op adaptive regulator INTELLICON will be a substantial contributio~ to the introduction of the adaptive control techniques into the process control practice.
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" U"'~L ' ';F:' .' r "· r F"£F' ", rH ! . l ~ T; ' " f:' C F C~,':oET Fc"c~r;!';'~ r .~;::·_'-
Young, P.C. (1960) . An instrumental variable method for real-time identification of a noisy process. IFAC Journ. Automatica, 6, 271-287 . Steiglitz, K., and L.E . Mc.BrIde (1965). A technique for the identification of linear systems. IEEE Trans. on Aut. Control, AC-10, 461-464. Clarke, D.W., and P.J. Gawthrop (1979). Implementation and application of microprocessor-based self-tuners. 5th IFAC Symp. on System Identification and Process Parameter Estimation, Darmstadt, 197-208. Wittenmark, B. (1979). Self-tuning PID controllers based on pole-placement. Departm. of Automatic Control, Lund Institute of Technology, Sweden. Orteg~1982). On PID self-tuners. SOCOCO'82, Madrid, 239-244. Cameron, F., and D.E. Seborg (1983). A self-tuning co~roller with a PID structure . IFAC/IFIP Symp. on Real-Time Digital Control Applications, Guadalajara, Mexico, 461-470. Rbzsa, L., A. Szigeti, Gy. Varrb and F . Zald (1984). An intelligent multiloop digital controller. IECON'84, Tokyo . B!ny!sz, Cs., J. Hetthessy, and L. Keviczky (1985). An adaptive PID regulator dedicated for microprocessor-based compact controllers. 7th IFAC Syrnp. on System Identification and Process Parameter Estimation, York.
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REFERENCES
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DO ::'OI""'ld - 1 w:-vn.U '.') +':I'!JI(I) - :O;'.'JA 'J!lU!
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0 !.)'.') ' 1J ~ ..!" . " ' I'l' '.1) X'}[:U ( I J - t'!~'t! ( I ) • ~'!:, o IJ '.', 'J'.'l U (t,U'.')" 1.1 CONTlr'U( r Ef., R-f DO 50 I" i. t/F"I'.R F'[ I'.:R ""' f"Ef..R- f,·,kII) ' Y,( I l DO no I - I .U'()!,; r,; R (I ) -f' AR ( I ~ . ~ "- RE • '! ,.1Il (! ) /0;; J J([TUHI H ID
Fig. 3. FORTRAN list of SUBROUTINE UDVFLT
Fig. 1. Front-panel of the INTELLICON
IS VOL 2 -F*
1.. Kc\iczky. I. Vajk and
J.
H e llhcssy
- -- " - - .- - - - - - - 1
,
u
o
. ,
~
c
~
.
<
.
Fig. 2. Block-scheme of the adaptive control strategy
" 'r"'· o
100
Fig. 5. Illustration of the design step of the adaptive regulator r
r
Fig. 4 . Parameter plane of a ,a l 2
'''':I/~-______C~',,<~=''_l~: ON~_____ _L~ W_'' ' _"''__'_.'_'~_b-j
~~=====:==::??4= ======~
''''::=: 1
""l'~o
Fig. 6. Influence of the parameter MAX
100
L
2"~
Fig. 7. Operation of the INTELLICON under complex conditions
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INTELLICON: AN INDUSTRIAL MULTILOOP ADAPTIVE REGULATOR L. Keviczky*, I. Vajk** and
J.
Hetthessy**
* /) " /JIII"IIIII' 1I1 of Pro!!'ss C (JII l ro/. CO III/wln ({ /I(/ ,~ II I {Jlllfl l i{J 1I / lIl l i l lllf'. 1-llIlIg al"iflll Amill'lll.\' Sr i(' II I'1'.I. 8//(/({/lnl. 1IIIIIgal"Y
01
** DI'/)(II"IIIII' 1I1
ul
Alllolllalioll . Tn/lllim/ L 'lIi l'l'nily
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8 11 iIlI/)n I. 811r1I1/N' II.ll lllI g a n
Abstract. The paper des c ribes the design conception of an industrial multi loop adaptive regulat or and th e prac ti c al approach of the implementation of a hi ghly r e liable adaptive control strate gy . Keywords . Ada pt i ve contro l; multiloop regulator; PID regulator. INTRODUCTION In the iast few years some adaptive controllers appeared on the market. Two years ago a project was started to develop a multiloop intelligent re gulator with adaptive fa c ilities in Hungary, too. The project has successfully been finished and now this equipment, called INTELLICON, is already a factory produc t. The key features of INTELLICON are the very high level man/machine communication (the very flexible configuration and "softwiring" possibilities) and the adaptively tunable PID loops. A general description of IN TELL ICON has already released by Rbzsa and co-workers (1984) and this paper will concentrate only f or the adaptation. Therefore a very short in f ormation will be only given on the sp ec ifi c da ta of the equipment here -inb e low . INTELLICON is a microcomputer-based pre-programmed digital controller, whose capabilities meet the most up-to-date requirements. (The front-panel can be seen on Fig. 1.) . INTELLICON continuously accepts, measures and processes - in a way selected by the user to solve the control problem at hand - all information coming from the proc ess and computes and outputs those signa ls which are required to keep it under its control, to the actuators . Moreover it makes all information required by the process operator available and displays them using character displays and LED-s. There are over 50 pre-programmed FUNCTIONS (program blocks desi gned to implement a welldefined function) permanently stored in EPROM memory. They provide alarm generation, integration, counting, limiting, PID ratio, cascade and feedforward control, mathematical operations, set-point generation, timing and logical functions, and more. In order to solve a control problem, the user s elects and references ("wires") the required functions from the function library in the same way as he should do it if they were not implemented by a computer program, but by an analogue electrical equipment. This opera tion is the CONFIGURATION of INTELLICON, which can be made by using the displ ays and push-buttons mounted on the controller's front panel. Neither computer-programming expertise nor knowledge of a programmin g language are required for the on the-spot configuration of the controller. Once configured, the c ontro l problem is stored in battery-backed up CMOS RAM memory and can be activated without delay.
ation, required by the proc ess operator, easil y available. The chosen operating mode (MANUAL, AUTOMATIC, CASCADE, REMOTE), control error (4 LED-s per loop), process variable alarms (Hi gh, Low) are continuousl y displayed f or all control loops . Moreover, the serial number and the most important da ta of a sel ec t ed contr ol-l oop (set-p oint, ac tua t or position, pr oces s vari abl e, deviati on,r a ti o and PID parameters, range and limit data) are displayed and the parameters can be changed by the operator. The four separate character displays belonging to the four sequences continuously display the step serial number of the batch process under control. Dedicated panel-mounted push buttons enabl e simple supervision and manual c ontr ol to be achieved. INTELLICON has special hardware and software -to run a continous self-test. In case of an error detected by the system an alarm is sounded and the cause of the error is displayed. Fatal errors result in automatic switch-over of all control loops to the stand-by Manual Control Panel. (The INTELLICON has pro cess control local area networking capabilities, too .) The most important techni cal data are: 16 analo gue inputs (0-5, 0-10, 0-20, 4-20 mA) 32 discrete inputs 8 pulse inputs (0-50 Hz max.) 32 discrete outputs } out ut to 16 analogue outputs (4-20 mA) 8x2 contact outputs for motor tP t control ac ua ors manual control panel with analogue instruments (optional) number of control loops: 8-16 closed loop control (depending on the actuator type); 2 discrete control; 4 batch control sequences. INTELLICON's ada?tive tunin g capability enables the loop t uning to be automati cally adjusted to match the variations of the process. CONCEPTION OF THE APPLIED ADAPTIVE STRATEGY At the design and the realization of the adaptive regulator some serious r e stri c tions had to be taken into considerati on. The software of the ada ptive regulator had to be implemented on a given hardware and on this hardware the software o f the INTELLICON realizes seve ral other functi ons (see the Introducti on) .
The front-panel makes all the important inform-
12li7
1~(iH
L. Ke\'irzk\', I. \ 'aik and.J. J-1etthess\
The most important constraints were the following: - the available code memory for the adaptive regulator was not more than 5 kbyte EROM; - the INTELLICON uses only 3 byte precision software floating point arithmetic routines; the adaptive algorithm has to tune the parameters of the INTELLICON's PID regulators; - the man/machine hardware interface is given by the INTELLICON's front panel, The available memory size did not give the possibility to estimate the delay time of the process, The low precision of the arithmetics required to reduce the number of the estimated parameters. At tl.e can be linear can be y (t)
design phase it was assumed that the process well approximated by a second order, stable, lumped parameter system with dead time. It written schematically that k/Kls
e- TDS u(t) + net),
(1)
where yet), u(t), net) are the measured process output, the process input variables and the additive noise, respectively. K, Kl, Tl, TT2 are the parameters of the second order process model and TD is the delay time. The spectrum of the noise is considered wider than that of the noiseless process output. The realized self-tuning PID regulator is a robust explicit parameter adaptive controller. The scheme of the regulator is shown in Fig. 2. The algorithm estimates the process parameters and on the basis of the estimation it designs the parameter of the controller, tunes the parameters of a PID regulator. It might happen that the identification gives an unrealistic parameter estimation, in this case the regulator design is based on the apriori process parameters. The sampling time hr of the PID regulator is fixed (2 sec). But the sampling time of the identification hi is chosen using the apriori information of the process parameters, it is the integer multiple of the control sampling time. (We should mention here that the apriori information can be overwritten by the aposteriori information using the RESET key, se e later, and at the same time a new sampling time for identification will be automatically redesi gne d.)
sampling time of the regulator. It is used in the shadow system which generates the instrumental variables and partly applied for the regulator design; 3. discrete time process model obtained by the
sampling time of the identification. This description form is used by the estimator. The exact transformation between the different process descriptions is difficult to realize without hardware arithmetics because the execution time of the calculations is very long (think the exponential transformation, e.g.). Therefore, we applied a modified version of bilinear approximation for the transformation. The classical bilinear approximation may result transfer without time delay which is unrealistic in a controlled process. In order to eliminate this disadvantage, the following approximation is used between the system descriptions : W(z
-1
2 -1 ) = _z_ _ l+z-l
.r
2 l_z-l (s = -h ~l) l+z
(2)
where .r(s) is the transfer function of the continuous process without holding unit, W(z-l) is the discrete model of the process.Here s is the Laplace operator, z-l is the backward shift operator and h is the sampling time. PARAMETER ESTIMATION In an adaptive controller the direct application of the maximum likelihood estimation is very complicated. However, it is useful to apply such a method which does not estimate the parameters of the noise in order to decrease the number of the estimated parameters and which only requires that the expected value of the noise is zero. (The slow drift can be eliminated by a high pass filter.) The instrumental variable (IV) method can satisfy these requirements. Let assume that the discrete process is described by
b~+b~Z-l
-d.
y (k) = "':"-1":':......1-1.,-·--"""2 z
l+al z
1
u(k) + n(k)
(3)
+a 2z
where d is the discrete delay time. This model can also be i given in another form (4)
For the generation of the parameter estimation database the primary variables are averaged and filtered by a high pass filter designed on the apriori data to eliminate the working point. The adaptation is automatically suspended if the database of the estimation is not informative enough. The algorithm checks the set point (reference) value Yr(t) in closed loop case and the input signal u(t) in open loop case. If in a longer period there is no change, the identification is stopped. This strategy guarantees the elimination of burst phenomena if the input is not persistently exciting and eliminates the effect of disturbances which is not simultaneously accompanied by changes in the set value in closed loop and in the input signal in open loop case. Since the sampling time of the regulator and the identification are different, the adaptive controller uses three dif f erent system descriptions. These
where T stands for the transposition furthermore (5)
r (k)
and
Ei
i
i
i
i T
[ b ,b l ,a l ,a 2 J o
=
i(k)
=
[ u(k-d i ), u(k-di-l), -y(k-l),-y(k-2)J
(8)
where
'L F
the communication between the operator and the INTELLICON and partly for the regulator design; 2. discrete time process model obtained by the
(7)
Here the index i refers to identification. Eq. (6) can be written in a vector form
= [y (l) , .•• ,y (N) ) J T
are: 1. Continuous time process model (see Eq. (1)) for
(6) T
(9 )
T
(10)
[ r(l), ... ,r(N) J T
(11)
[ i(l) , ... ,i(N) J
assuming N processed observations.
Industrial \Iultiloop ;\d;qJliH' [{q.:llbtnr
l:ztiy
The IV estimator for the parameter vector .Ri is ( T )-1 Q_T .Ri = ~ ~ . 'i.
REGULATOR DESIGN
(12)
where
The design of the regulator is based on the estimated second order process model with delay using the sampling time hr of the regulator:
b~ + b~z-l
(13)
The method gives unbiased parameter estimation if the IV (£(k) and the equation error (r(k» in (4) are uncorrelated (i.e., E{~ ) = Q). The expected value of the estimation is independent from the noise, but the variance of the estimated parameters is determined by the noise characteristics. The best selection of the instrumental variables is
~
=
(1 ~
(14)
where ~ is the covariance matrix of the noise. It is difficult to choose the instrumental variables according to (14) in a corresponding on-line strategy. It is better to use the filtered values ~F = ~
-1/2
~; 'i.F = ~
-1/2
'i.; ~F
~
-1/2
~
In the adaptive controller the recursive version of the IV method (RIV) is useful to apply: -i 1 T -' .Rk = .R k- l + ~ .!l.(k)Cy(k)-! (k).R~_lJ
(16) {R
=k-l
-
~_l.!l.(k) !T(k)~_l 2 w +
It is well known that the above naive programming form of the recursive least-squares like estimation can exhibit numerical difficulties. The problem may be very serious if a number representation of low precision is used. To make the algorithm numerically less sensitive the UDV factorization is used instead of (16) and (17). The FORTRAN subroutine UDVFLT realizing the UDV factorization is given on Fig. 3. (The program is based on the UD factorization published by Clarke (1979.) The prefiltering formulated by (15) is easy to perform by introducing the filtered 1 ~
Ai (z
~F(k)
u(k) ; /(k)
)
1 ~ Ai (z )
The INTELLICON realizes the discrete PID regulator by the following equation: U(k)=(K + p l-z-l
(l-a) ----1 y(k)
::---=yAi (z
Zi(k); ?(k)
As Eq. (19) shows the set value avoids the derivative term of the regulator and the differential action can be smoothed by a time lag. At a=O the elimination of the process poles can be reached, if the regulator parameters satisfy the equations
1
r
= h _---".2_ _
P
r
(20)
r
l+a l +a.z . (21)
h
These equations indicate that the pole elimination of a stable second order system can be performed if a~ > O. The parameter Kp can be determined in such a way that the phase margin ~ of the control system is to reach a prescribed value. (See this teChnique in Banyasz, Hetthessy and Keviczky If the derivative term of the regulator has to be limited (i.e. a # 0) because the designed T is too large, the direct pole cancellation cangot be applied. The parameter space (ar, a~) projected by the three-term controller is signif1cantly reduc~d with respect to the parameter a. This can be seen on Fig. 4. However, the Bode plot of the PID regulator explains that the time lag part of the controller hardly influences the low frequency characteristics. So Eqs (20) and (21) can be used, as well, if a # O. If at least one of the time constants of the process is larger than the sampling time h , the transfer function of the open loop control ~ystem can be approximated by
W,,(s) where
y(k)
)
1
( 0
(18)
-
~y(k)
Ai (z
l-a
T.K
)
'1
variables in !(k) and £(k) instead of the original ones.
(19)
l-az
(1985).)
!T(k)~_l£(k)
where w is the forgetting factor and
F u (k)
(18)
where K , ~i' Td and a are the regulator parameters and yr(~) 1S the reference signal (set point value).
In a elosed loop system the noise and the input signal of the process are correlated. So the usually applied choice of the IV results in unbiased estimation, if there is no additional delay in the controller, but the delay makes the control worse. A good selection of the instrumental variables is based on the model of the entire closed loop system. The auxiliary model can be based on the knowledge of the controller and the apriori or aposteriori estimation of the process parameters. The apriori or aposteriori information of the noise characteristic can be used for filtering the variables to improve the estimation. The construction of the database for the IV estimation can also be seen on Fig. 2.
1
r
The process is assumed to be controlled by the most widely used proportional - integral - derivative (PID) regulator, the parameters of which are adapted at each parameter estimation step.
(15)
easier to calculate.
2' w
-d
1 r -2 z r l+a z +a z l 2
and
l:::/b[J
else
(23)
I~,II
I.. Kc\ iuh. I. Vajk andl. Henhess\
= -h I lna
T
(24)
r
At th e ga in crossover frequency
(22) can be
separated to
.r
Having initialized Ec(O) and TO the system is ready for adaptation both in open- and closed loop mode which modes can be selected by the M&~UAL AUTOMATIC switch, if the operator enables the adap tation by ryressin~ a ~ISC START seauence (ADAPTATION O~). The tuning nrocedure can be stopned by pressing a MISC STOP sequence (ADAPTATION OFF). Any of the INTELLICON's PlO regulator can be switched on for adaptation, however, only one loop can be self-tuned continuously at the same time.
- 2~
i. l+( ~ c : l)
\~-Zc 1 )2 and - )[
+
The time lag part of the derivative action is determined in such a way that the following inequality is satisfied: Td
11
Kp +
(1-a) < MAX
I-a
K
(27)
p
r
where MAX is a control ler design constant. Eqs (25), (26) and (27) give the possibility to design the gain K and the lag term parameter a. In the INTELLICON ~h e regulator is designed on the basis of the approximation of the nonlinear Eqs (25) and (26). OPERATION OF THE INTELLICON ADAPTATION
e
2
-sTD
(28)
l+sTl+s TT2 As a matter of fact there is no hope to get particular knowl~dge about Kl, however, the steady-state ga in K, the time constants Tl and TT2, as well as the pure time delay TO might be approximated evaluating a step response of the process. It is noted that in the course of the identification procedure the continuous process parameters ~=
[ K,Kl,Tl,TT2 J
T
(29)
will on l y be updated, while TO remains to be fixed. The identification step looks like: based on ~ c( O) a samp lin g time hi is designed
carefully to set up a second order discrete time model ~
h.
~
~ (0) -2:..- Ei (0) - evaluating the process~control input and process vari~ble measurements Ei is updated using the on-l,ne IV method. To generate instrumental variables, a s~adow system is run using the actual set point and PlO regulator in closed loop and the actual process input in open loop case. The shadow process model works with a samplin g time of h . Just for the regulator desi gn step, the tra~sformation
\
~
E.i (k)
-
Finally we can summarize that for the normal operation of the adaptive regulator the following apriori information is required - the time delay (TO) - the steady-state gain (K) - at least one of the time constants (Tl or TT2) of the process and the operation of the regulator can be controlled by the following switches: - RESET - MANUAL-AUTOMATIC - MISC-START, STOP (ADAPTATION-ON, OFF). Examples
It has been shown so far that the adaptive PlO regulator implemented in the INTELLICON means an explicit design method, i.e . , the regulator parameters are always determined as functions of a second order process model with time-delay. As a consequence, to start up a set of parameters corresponding to the following second order apriori model should be defined first: K +Kls
pc(O), and a new, better value for h. will be 1 computed.
~
£C (t)
is also performed in every step. It ~s seen ~hat in this way hi is only a function of ~(O) WhlCh could actually be a rough estimation. The sampling time h . has an importance to improve the identification performance, so a RESET function has been elaborat~d. If the operator gene rat es RESET, the updated ~(t) is loaded into
The operation of a self-tuning regulator of the INTELLICON will be illustrated by some simple examples. Let the continuous process be . -4s e (1+103) (1+20s) where the time constants and delay are in seconds. Fig. 5. shows the input (u{t», the output (yet»~ of the process and the square wave like reference ~ignal (Yr{t» excitation. First the system works ln open loop, then the loop is closed. The identification, running continuously, ensured good regulator design for the second phase which is already a normal operation mode. Here the design parameter MAXs 2 was chosen. This procedure can be considered a general approach in the practice. The selection of MAX influences the closed loop transient. A faster step reponse can be reached by greater value of MAX, however, the actuator output will be much higher. This is the price, the designer should pay for the result. The application of different values of MAX (MAX~lO, 1.5 and 0.75) can be seen on Fig. 6. The operation of the adaptive regulator under complex conditions can be seen on Fig. 7. Here the apriori parameter estimation is quite bad using 2 e- 4s 1+20s as a first guess. This explains the poor transient at the beginning of the experiment. It can be well seen that after switching the adaptation on the transient process became very nice. Lateron a step-like output disturbance appeared in the system which did not disturb the parameter estimation and the closed loop eliminated this unwanted effect using the latest optimal regulator parameters. Here MAX~1.5 was applied. CONCLUSION In spite of the many successful applications of the self-tuning regulators with more complex structure, our experience is that industry people prefer PlO regulators. More exactly, the industrial practice has almost no OPPOSltlon against the implementation of PlO regulators, even if they
Illdustri a l \fllitil()()p .\daptill· Rq.\uLl i()1 are adaptive. Starting fr om this phil os opy , we think that the developed industrial multilo op adaptive regulator INTELLICON will be a substantial contributio~ to the introduction of the adaptive control techniques into the process control practice.
1:!71 ' ::J :
-c . ' . ' - , -~" ~-.
,. C 1 C'\
~ 1" 1 [, " '. ~ f' " 51:;::"1 :''l",T
C Z C F.:. .
SH.H"JoJ
~ ''' l ,>
r:' ...... :::,;.
" U"'~L ' ';F:' .' r "· r F"£F' ", rH ! . l ~ T; ' " f:' C F C~,':oET Fc"c~r;!';'~ r .~;::·_'-
Young, P.C. (1960) . An instrumental variable method for real-time identification of a noisy process. IFAC Journ. Automatica, 6, 271-287 . Steiglitz, K., and L.E . Mc.BrIde (1965). A technique for the identification of linear systems. IEEE Trans. on Aut. Control, AC-10, 461-464. Clarke, D.W., and P.J. Gawthrop (1979). Implementation and application of microprocessor-based self-tuners. 5th IFAC Symp. on System Identification and Process Parameter Estimation, Darmstadt, 197-208. Wittenmark, B. (1979). Self-tuning PID controllers based on pole-placement. Departm. of Automatic Control, Lund Institute of Technology, Sweden. Orteg~1982). On PID self-tuners. SOCOCO'82, Madrid, 239-244. Cameron, F., and D.E. Seborg (1983). A self-tuning co~roller with a PID structure . IFAC/IFIP Symp. on Real-Time Digital Control Applications, Guadalajara, Mexico, 461-470. Rbzsa, L., A. Szigeti, Gy. Varrb and F . Zald (1984). An intelligent multiloop digital controller. IECON'84, Tokyo . B!ny!sz, Cs., J. Hetthessy, and L. Keviczky (1985). An adaptive PID regulator dedicated for microprocessor-based compact controllers. 7th IFAC Syrnp. on System Identification and Process Parameter Estimation, York.
!
=. ~ -,.
' : ,.'-
C tFP'
REFERENCES
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(':',
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DU! - [I ~ J) ~U IJ XV[lU\J ) - Y'.'I· V1JUI ( JpvU! SJI - $J SJ",C;J II '/.'JJ * lI\J: D( J ) -[I(J) 0': .'!/SJ/fCo:.G(T Y.'JJI'. ~- ~VJ.'": J l U lj;,~ - UU'SJI
DO ::'OI""'ld - 1 w:-vn.U '.') +':I'!JI(I) - :O;'.'JA 'J!lU!
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20 30 40 :;0
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0 !.)'.') ' 1J ~ ..!" . " ' I'l' '.1) X'}[:U ( I J - t'!~'t! ( I ) • ~'!:, o IJ '.', 'J'.'l U (t,U'.')" 1.1 CONTlr'U( r Ef., R-f DO 50 I" i. t/F"I'.R F'[ I'.:R ""' f"Ef..R- f,·,kII) ' Y,( I l DO no I - I .U'()!,; r,; R (I ) -f' AR ( I ~ . ~ "- RE • '! ,.1Il (! ) /0;; J J([TUHI H ID
Fig. 3. FORTRAN list of SUBROUTINE UDVFLT
Fig. 1. Front-panel of the INTELLICON
IS VOL 2 -F*
1.. Kc\iczky. I. Vajk and
J.
H e llhcssy
- -- " - - .- - - - - - - 1
,
u
o
. ,
~
c
~
.
<
.
Fig. 2. Block-scheme of the adaptive control strategy
" 'r"'· o
100
Fig. 5. Illustration of the design step of the adaptive regulator r
r
Fig. 4 . Parameter plane of a ,a l 2
'''':I/~-______C~',,<~=''_l~: ON~_____ _L~ W_'' ' _"''__'_.'_'~_b-j
~~=====:==::??4= ======~
''''::=: 1
""l'~o
Fig. 6. Influence of the parameter MAX
100
L
2"~
Fig. 7. Operation of the INTELLICON under complex conditions