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Multivariable Control of a Steam Generator Characteristics and Results
MULTIVARIABLE CONTROL OF A STEAM GENERATOR. CHARACTERISTICS AND RESULTS M. Lecrique*, M. Tessier*, A. Rault** andJ. L. Testud** *Electr£cite de France, Research & Development Department, 6 Quai Watier, F78400 Chatou, France **ADERSA IGERBIOS, 53 avenue de [,Europe, F78140 Velizy, France
Abstract. Control at varying load of the steam pressure and the steam temperatures delivered by the steam generator has been performed by a multivariable numerical control technique IDCOM on a thermal power plant (250 MW) l ocated in Martigues-Ponteau. The paper describes the plant characteristics, interactions between variables, controlability difficulties, actuator saturation, various non-linearities ; the general principles of the method are given. Operating since April 1976, IDCOM has been tested at various operating regimes to which a power plant is submitted (programmed load changes, step variation, tele-regulated working). The paper makes a comparative analysis of the numerical control performances and those obtained by the analog control. The noted improvement is obtained without increasing constraints on regUlating components, essentially through the multivariable and predictive control. Such a technique, whose implementation is particularly easy, will allow an improveme nt of the thermal power plants flexibility as well as a reduction of stresses undergone by the nuclear power plants equipment.
INTRODUCTION
control variables, all the the main effects, direct and crossed, between the different inputs and outputs of a system.
Generally, industrial processes are complex physical or physico-chemical phenomena. From the point of view of a control engineer it results in static and dynamic behaviours with pronounced non-linearities and sometimes very close couplings between the main variables. The thermal electric power production units present many non-linearities (actuators characteristics, operat ing regimes effect). The heat-exchange phenomena entail very important cross - couplings, that may be complicated by those due to the fluids dynamics (forced circulation boilers) or by an operation in closed loop of the heat in nuclear reactors. The classical one input one output regulation techniques can deal with non-linear phenomena and take them into account. Basically, these techniques are extended in the multivariable context and no multivariable control is actually performed. Although the performances obtained in such a way are considered at present time as satisfactory in operation (maybe because there is a lack of data for comparison), it seemed to us useful to implement a multivariable technique, which would take into account, by a single computation of the
Such a control algorithm is operating on a natural circulation boiler of a MartiguesPonteau oi l power plant 250 MW unit. It controls the superheated and reheated steam temperatures as well as the steam pressure . This recent unit was chosen to allow a good comparison of the performances with respect to the existing modern analog regUlation equipned with adaptation factors function of the load and feed forward actions. The practical organiz ation is such that at every moment, regulation can be switched from one mode to the other . PLANT CHARACTERISTICS The functional block diagram of the plant is given on Fig. 1 . For the steam generator, the steam flow Qv cal led up by the turbine constitutes the m~in disturbance. Available control variables. Variables to be controlled are the steam pressure PV, the superheated temperatur Ta and the reheated one TR' The avallable control variables on the plant are :
7
73
M. Lecrique et al .
74
QF
QD
RY
QV
Figure 1
- the reference input of the fuel-oil flow Qf' that brings forward the totality of calories, - the reference input of gas recirculation R that withdraws the gas from the gas outlet Y of the economiser and discharges into the bottom of the furnace in order to reduce exchanges by radiation (favourable to the vaporization) on behalf of convective exchanges (boosting the temperatures), - the reference input of the spray-water flow Qd ' entailing an additional vaporization to the prejudice of the temperatures. Plant interactive character. As the three control variables influence at the same time the global vaporization as well as exchanges, the interactions are important. This is particularly the case for the steam temperatures, as it is shown in Fig. 2a and 2b, responses of positive steps of gas recirculation, spray-water flow, pressure set-point and steam flow.
"" r"'.'.""'"
~ (~o:)r-Ste -p----ron-Q-D-=-Q.'5rV-:(2,-4-tl-hT,-6""-: . ,- . - - - ,
4
input and output
Power plant description
100~--+---~~L-~--~-~
signals
The maln effect on the pressure is due to the fuel flow; therefore it is used for the steam pressure control. In such a manner, it yields an important disturbing action on temperatures, which must be corrected by gas recirculation and spray-water flow. These two variables (Fig. 2a) act on both temperatures in the same direction, similar gain-factors and dynamic behaviour, and differ only in response to the spray-water flow. This is almost a non-controllability situation. Non-linear behaviour. The operating regime, that reflects the instantaneous power called up by the network, constitutes the main cause of non-linearity in a steam generator. Convection dynamics are approximately, inversely proportional to the steam flow. Gains depend also on it ; so, the spraywater flow has a gain inversely proportional to the steam flow. On the contrary, exchanges by radiation are
·c (mV) 200 r---r----t-~~t_~~*=~
•
41100~_++_+-~r_4_1-~_+--~-~
I I
o
Or I
i ·4 -100r---+------'ld---+-----F===1
o
i I
-4 -lOO t---t---+---+----r>-.....--i
;
on PVC step on QV
Step
Figure 2a
Identification - Step responses TS/QD , TS/RY , TR/QD , TR/RY
Figure 2b
=0,3 V (5 bars' =0,' V ( 10 till)
Identification - Step responses TS/PVC , TS/QV , TR/PVC , TR/QV
Multivariable Control of a Steam Generator
practically insensitive to that ; so, the steam pressure behaviour doesn 't depend on the load. There is an important difference with respect to the temperatures behaviour. Other non-linearities are due to actuators saturation ; thus, actions due to the gas recirculation have an S-type static characteristic. In addition, gas recirculation and spray-water flow, that control temperatures are frequently saturated. CHARACTERISTICS OF THE CONTROL ALGORITHM Outline of the method. The Model Algorithmic Control strategy (MAC) implemented thr ough the software IDCOM will be explained very simply . Longer mathematical developments can be found in previous publications (1), (2) and (3).
75
The method reli es on three principles : - the process to be controlled is represented by its impulse responses that constitute the "internal model", its outputs are computed in real time by discrete "convolution" ; - the controlling strategy 1S established through the "reference model" which defines the close-loop behavi our of the system. The reference model is chosen as to satisfy the overall stability and performances - the controls to be applied are computed at each sampling period either by a oneshot operator , or by an iterative proce dure whose principles rest upon the duality of the identification and control . The internal model, determined by identification, is used to compute the future c ontrols of the process such that the variables to be controlled fit to the trajectory deli vered by the reference mo~el (see Fig . 3) .
-t;_-_-_-_-_-_-
C = De.ired output _ _ _ _ _
_p_r_'_d_ic_ti_O"_ _-=--=--=--=-::::::::=:~L--=-==
-----
MeaJllred output
/L
Pa.t4l-~-_Futurl
Figure 3 The internal model formulation
1S
as follows
N L
SOJ(n)
Hk(i) Pvc(n-i)
i=l N +
L
i=l
~+l(i) Qd(n-i)
N
+
+ where
and
80 (n) 1
L Hk +2 (i) Ry(n-i) i=l N L H + (i) ~(n-i) k 3 i=l Pv(n)
S02(n)
T (n) 8
80 (n) 3
TR ( n)
k
=
(J-1) x 4 +
Predicted output LReference traj1tctory
Control scheme The control variables are P v ,Qd and R (see Fig.4). The steam flow agts both as y a state and a structural disturbance. In the vicinity of an operation point Qvo the signal QV is taken into account as a measurable state disturbance. When there are important load variations, the internal model is adapted through the sampling time. In the case an actuator has a non-linear characteristic , and provided it has previously been identified, it can be taken into account by the algor i thm (for example : input reference o f gas recirculation Ry ). The impulse response type of representation is particularly well suited to industrial processes in which phenomena are, in general, distributed. Its non-minimality is widely compensated by the r esulting increase in robustness. The linearity hypothesis is valid around an operating point, as it is shown by the results obtained during the identificati on
76
M. Lecrique et al.
Pv ref TS ref
Figure 4
Control implementation
stage. The control computation is eased by using the notion of reference trajectory initialized at each sample time on the actual measured output. At each sample time, the computed control is a predictivecne,such
Identification
that the predictive output computed through the internal model satisfy the desired reference trajectory (see Fig.3). The controls computation method proceeds directly from the duality principle established hereafter :
SO(n)
!
measure
Control
ET . H
SO(n)
t
I +
past
future
measure
reference model
.---l-,ii,ntificatinn past
Constraints on the control variables, to the extent that they may be expressed as linear and non-linear combinations of input variables, are easily taken into account. In this application, constraints on the absolute values and on the speed of variat i ons on each control variable are used in the control seQuences computation. Implementation. The pressure dynamics are not affected by load variations. Therefore, control on the pressure is performed by the fuel flow in a single loop using as feed forward variables Qd and Ry . The temperatures are controlled in a multi variable fashion, self adapted to load variations and using the pressure set point as feed forward variable. a) Implementation scheme. A block diagram of the IDCOM control is reproduced on Fig.4 . The pressure control is carried out as follows: a P.I. monovariable regulator regulates the pressure
~
measure
future
~
computed
permanently ; its set point is driven every 20 s by the I DCOM algorithm, that takes into account the disturbing actions of the steam flow and the actions carried out on gas recirculation and spray-water flow. Despite the difficulty of such a control, the adjustment of both temperatures is carried out only by the IDCOM algorithm, in a rigour ously multivariable way (by a single computation of both control variables) and taking into account the effects of the steam flow and of the action determined by the pressure control. The sampling rate is 20 s, at the nominal regime. In order to obtain a better control of the actuators saturation, the algorithm controls directly the corresponding variables either in a direct digital control fashion, or in addition to the existing analog control, that secures then the average regime and may be simplified. Both types of implementation are being tested.
Multivariable Control of a Steam Generator
b) Adaptation to non-linearities. Because of no servo control on the gas recirculation Ry ' i~s static characteristic had to be taken lnto account. The steam flow affects the temperature dynamics in a ratio one to three. Adaptation to the load is thus necessary. It is performed through a variable sampling rate in such a way that,viewed from the computer,the dynamics of the heat exchange appear as constant. Gains are adapted either througP a precompiled set of static gains or using a self adaptive procedure which however necessitatES the use of external signals in order to identify. Such a procedure presen~the additional advantage to make the reference model variable in the same ratio, preserving thus a constant ratio between the natural system dynamics and the specified performances, at every load. c) Action in case of saturation. When one temperature actuator is saturated, safety imperatives require that the control deterioratedout on the other actuator is not deteriored. Consequently, when the multivariable computation brings to or maintain an actuator saturated, the action applied to the other results from an additional monovariable computation that takes the saturation into account. The same monovariable computation is also used when one of the actuators is excluded from the multi variable control (manual action or analog control). Equipment used. The operator, responsible for the control unit has at his disposal a "manual control relay" with three positions for each actuator manual control, analog control and digital control. The last one is the only innovation ; in particular, it preserves the previous setting of the three input references (pressure, superheated and reheated temperatures) . A minicomputer (Mitra 15 - from the French Manufactor CII) is being used for the experiment. It is connected to an inputoutput system (analog-digital interface), safety devices (particularly a "watch-dog" system) and a teleprinter. The real time monitor has been improved for operating in a multitask scheme ; it needs 8 K-words of 16 bits. In this set up, most programs are written in Fortran, which facilitates the adjustment, but doesn't optimize the holding in memory, which reaches 16 K-words. Programs are divided into two tasks. The first task, acti vated every 2,5 s, carries out the digital (10) and analog (16) input acquirings, the digital (3) and analog (3) outputs, the transposed P.I. computation of
77
the pressure loop and the signals likeli.l-.cod test. The second task, activated every 20 s for the pressure and at a variable rate for both temperatures, carries out the totality of the functions connected with the IDCOM algorithm (eventual identification, gain adaptation, control computation) as well as the parameters change in real time and the different messages printing. In addition, the system manages certain safety devices in connection with the equipment reliability. In particular, it automatically and smoothly assures the transition between numerical and analog control in case of failure. RESULTS This scheme was implemented in April 1976 and has been operating since at the Martigues-Ponteau thermal power plant. The first tests allowed the results to be compared with respect to the performances obtained with the analog control (4), whose characteristics are the following : - the P.I. regulation has parameters identical to those in the numerical transparent solution (the set-point is then driven by IDCOM algorithm) ; - the superheated temperature control is performing fairly well. The main P.I.D. regulator, with actions adapted to the load, works out the set-point of an intermediate temperature control, whose P.I. regulator is also adapted to the load and controls the spray-water flow, to which are added feed-forward actions proceeding from the fuel flow, steam flow as well as gas recirculation flow ; - similarly the reheated temperature control has three P.I.D. actions. Tests description. The tests presented herein were carried out in order to test the described regulation in the most significant working conditions, such as : - large amplitude load variations, characterized by the test nO 1, that shows a regular decrease of the load, 40 % in 19 min, followed by a stabilization, and the test nO 2 (Fig.5) corresponding to the increase of the load accomplished in identical conditions ; - fast load variations, of a reduced amplitude, represented by the test nO 3, that shows a load decrease of 10 % in 30 s , followed by a stabilization, and by the test nO 4 (Fig.6), where the increase of load was accomplished at a gradient to 4 % per min, in order to avoid the blowing fans disconnecting ;
M. Lecrique et al.
78
line curves correspond to the rDCOM control tests and dotted line curves "to the analog control.
- tele-adjusting operation, schematized by the test nO 5 (Fig.7), that shows a V load variation (immediate decrease followed by the upward motion) of 16 % accomplished with a gradient of 3 % per min.
Results. The main results are shown in Table 1, where appear the maximum deviations with respect to the first three overshoots of cont ro l led out puts ( cll, d;; and d3) and the peak to p e~ amplitude lA) of their variations.
These figures reproduce, in addition t o the load evolution, the evolution of the controlled outputs (Pv , TS and TR) as well as the control variables l Qf, Qd and Ry )' The f ull
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Load rise from 140 to 240 MW at a rate of 5 MW/min
Figure 5
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6
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Digital control
25 MW load rise at a rate of 10 MW/min
Multivariable Cont rol of a Steam Generator
Ba r
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PV
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Figure 7 Triangular load variation (45 MW at a rate of 7 , 5 MW/min ) The improvement brought by the IDCOM regula~ tion is c lear in general. Indeed, as well as To the overshoot improvement is often assothe analog control it is not able to mainciated a shorter time tain the reheated temperature at small load response to the stabilization of both (test N° 1); this is due to the under dimentemperatures , the third overshoot being elisioning of the gas recirculation. The improminated (in analog control, it is often vement is the most sensitive with respect to larger than the first) . the most constraining tests (test nO 5, Fig. 7), where the temperatures maximum deviations These results have been obtained with cons are reduced in a ratio larger than 1,6 . traints on control variables of the same It results also in a gradient reduction; nature as with the analog control (very this constitutes an interesting aspect for the equipment behaviour . Table Results Ste= Pressure (bar) ANA. IDCOM
Test 1st Test Decrease of load : 40 % 1n 19 min
------------------------nd 2
Test
Increase of l oad : 40 % in 19 m1n
------------------------rd 3
Test
Decrease of load : 10 % in 30 s
d1 d2 d3
+ 1, 6
+ 1 ,1
+ 1,6
+ 3,2
-
-
-
-
- 6,8
- 2 ,0 -
1,6
1,1
/';
---- -------d 1 d 2 d /'; 3 ---d 1 d 2 d /'; 3
-
1,5
Increase of l oad : 10 % in 150 s
d 1 d 2 d /'; 3
---------------------------th 5
Test
Triangular load varia tion : 16 % in 11 min
d 1 d 2 d /'; 3
---------
0, 8
-
-
1, 5
0 ,8
--------
+ 2,0
-
-
-
2,0
2,0
-
1, 5
-
1,5 -------+ 1,8 - 1,5
+ 2,0 8,4
1,1 -
1,1
--------+ 1,3 - 0 ,7
-
-
3,3
2,0
+ 0,5 -25,3 -
+ 2,0 +23 , 0
-
25, 8
25,5 --------
- 1,6 + 5,6 - 3,2 7,2
- 4,0 + 0 ,8
+ 1,0
-
-
-
-
+ 4 ,0 - 5,2 + 2,4 9,2
+ 4,0 - 4,4
------------ ----------- --------
--------- ------------
Reheated Tempera:ture (OC) IDCOM ANA.
5,2
4,8
--------- ------------ -----------
+ 2,0
---- -------------------------------4th Test
Superheated Temperature (OC) ANA . IDCOM
-
-
8,4
-----------
+ 5,6 - 3,6 9,2
+ 2,8 - 2,4 5,2
+ 4,0 - 7,6 + 7,6 15,2
+ 6,0 - 2 ,8
------------ -----------
8,8
1,0 -------- -------+ 2 ,0 + 2 ,0 - 9, 0 -12, 0 -
-
11,0 14 , 0 -------- --------
-
+ 5 ,0 + 0,5 - 0,5 - 2, 0 5,5 3,5 - ------- -------+ 2,4 - 2 ,8 - 6,8 -1 0. 0 + 4,8 14, 8 9 ,6
80
M. Lecrique et aZ.
similar in amplitudes and gradients). This proves that the reference model time constants are not very severe : 60 s on pressure and 120 s on temperatures. The difference is essentially due to the anticipative action of the IDCOM regulation. This anticipation varies from two minutes on fuel flow to six minutes on gas recirculation. The multivariable character is difficult to bring out on test results. However it is possible to reveal it in the test nO 4 (Fig.6\ where gas recirculation was temporarily requested at the beginning of the test (while in simi lar situation the analog control kept its action constant) and reached its final value only at the end of the transient regime. Performances persistency. After an eight months internal, tests were again carried out in the same conditions. Despite the steam generator evolution (clogging,etc), no visible alteration of performances was discovered, the curves remaining practically identical. This indicates the robustness of the algorithm and validates the impulse response representation of the steam generator. It thus seems sensible not to have recourse to on line identification and selfadaptation. Statistical analysis. It is interesting to complete the preceding results by a statistical analysis of the control behaviour in normal exploiting conditions. Temperatures histograms for both types of regulation will be presented. In order to have a statistical validity and a similarity in nature, tests have to be long enough and are not completed at this time. CONCLUSION The detailed favourable results stated above put forward the advantages that may be acquired from multivariable control (IDCOM) in the case of a steam generator. These results are more especially significant as they are obtained without increasing the constraints with respect to the analog control behaviour. With the present increase of the number of nuclear power plants producing electric power two ways are opened to the development of such a technique : - with constant constraints on the control variables and identical performances on the controlled outputs, this method will allow an improvement of the conventional thermal power plants exploiting flexibility. Indeed in the near future, these power plants will be asked to provide the network with the rapid transient variations ; - to reduce in nuclear power plants the constraints connected with the primary loop behaviour (pressure, average temperature deviations, etc) or the secondary loop behaviour (steam pressure, etc) ;
The IDCOM method (aChieving multivariable predictive control) limits at best temporary deviations of the other controlled outputs during an action aiming at zeroing the deviation on one of them. It carries out, thanks to the knowledge of the foreseeable natural evolution (due to the residual effec1 of "Oast inDuts). a deliberate ad.iusting control action (at a convenient moment, with a just suitable amplitude minimizing the controlling work). In addition, such a technique adapts itself to various means of action : as direct digital control or as superposition to an elementary control. In the last case, the technological basic level may consist of individual regulators with a simplified structure, without adaptations or feed forward actions, securing the average operating regime. The IDCOM regulation acts then in addition to bring the multi variable character that is absolutely necessary to the dynamical performances improvement. Therefore, the simultaneous operation of both levels brings an interesting redundancy and provides the permanent proof that each level is able to replace the other in case of failure. The stated method facilitates also the takiq into account of constraints : gradients limitation, safety conditions, control variables saturation, reduction of the number of contrc elements without multi variable control (without changing the algorithm, it is sufficient to limit correspondingly the outputs to be controlled in multivariable technique) Finally, such a method has proved to be easily implemented on a thermal power plant. As a matter of fact, the aforestated advantage allows a progressive implementation of a loop by loop type well known by analog regulation technicians. Without any previous computation, operators display reference model time constants of the controlled output and eventually modify them to refine performances as the unit is starting. It is only necessary to estimate the main static gains ; the dynamics of the impulse responses can be obtained from simplified models (well known as well for the classical thermal power plants as for the nuclear power plants steam generators, which are subject to a systematic modeling) . REFERENCES (1) Richalet, J., Rault,A., Testud, J.L., Papon, J., (1976). Algorithmic control of industrial processes. 4th IFAC Symposium, Tbilissi, USSR. (2) Richalet, J., ana Rault, A., (1977). Model algorithmic control of industrial processes. 5th IFAC Symposium, The Hague (3) IDCOM Proceedings of a seminar on industrial process control (1976). ADERSA. (4) Tessier, M., (1977). Experience of IDCOM regulation; tests results. Electricite de France internal paper, p 44/19.
Abstract. Control at varying load of the steam pressure and the steam temperatures delivered by the steam generator has been performed by a multivariable numerical control technique IDCOM on a thermal power plant (250 MW) l ocated in Martigues-Ponteau. The paper describes the plant characteristics, interactions between variables, controlability difficulties, actuator saturation, various non-linearities ; the general principles of the method are given. Operating since April 1976, IDCOM has been tested at various operating regimes to which a power plant is submitted (programmed load changes, step variation, tele-regulated working). The paper makes a comparative analysis of the numerical control performances and those obtained by the analog control. The noted improvement is obtained without increasing constraints on regUlating components, essentially through the multivariable and predictive control. Such a technique, whose implementation is particularly easy, will allow an improveme nt of the thermal power plants flexibility as well as a reduction of stresses undergone by the nuclear power plants equipment.
INTRODUCTION
control variables, all the the main effects, direct and crossed, between the different inputs and outputs of a system.
Generally, industrial processes are complex physical or physico-chemical phenomena. From the point of view of a control engineer it results in static and dynamic behaviours with pronounced non-linearities and sometimes very close couplings between the main variables. The thermal electric power production units present many non-linearities (actuators characteristics, operat ing regimes effect). The heat-exchange phenomena entail very important cross - couplings, that may be complicated by those due to the fluids dynamics (forced circulation boilers) or by an operation in closed loop of the heat in nuclear reactors. The classical one input one output regulation techniques can deal with non-linear phenomena and take them into account. Basically, these techniques are extended in the multivariable context and no multivariable control is actually performed. Although the performances obtained in such a way are considered at present time as satisfactory in operation (maybe because there is a lack of data for comparison), it seemed to us useful to implement a multivariable technique, which would take into account, by a single computation of the
Such a control algorithm is operating on a natural circulation boiler of a MartiguesPonteau oi l power plant 250 MW unit. It controls the superheated and reheated steam temperatures as well as the steam pressure . This recent unit was chosen to allow a good comparison of the performances with respect to the existing modern analog regUlation equipned with adaptation factors function of the load and feed forward actions. The practical organiz ation is such that at every moment, regulation can be switched from one mode to the other . PLANT CHARACTERISTICS The functional block diagram of the plant is given on Fig. 1 . For the steam generator, the steam flow Qv cal led up by the turbine constitutes the m~in disturbance. Available control variables. Variables to be controlled are the steam pressure PV, the superheated temperatur Ta and the reheated one TR' The avallable control variables on the plant are :
7
73
M. Lecrique et al .
74
QF
QD
RY
QV
Figure 1
- the reference input of the fuel-oil flow Qf' that brings forward the totality of calories, - the reference input of gas recirculation R that withdraws the gas from the gas outlet Y of the economiser and discharges into the bottom of the furnace in order to reduce exchanges by radiation (favourable to the vaporization) on behalf of convective exchanges (boosting the temperatures), - the reference input of the spray-water flow Qd ' entailing an additional vaporization to the prejudice of the temperatures. Plant interactive character. As the three control variables influence at the same time the global vaporization as well as exchanges, the interactions are important. This is particularly the case for the steam temperatures, as it is shown in Fig. 2a and 2b, responses of positive steps of gas recirculation, spray-water flow, pressure set-point and steam flow.
"" r"'.'.""'"
~ (~o:)r-Ste -p----ron-Q-D-=-Q.'5rV-:(2,-4-tl-hT,-6""-: . ,- . - - - ,
4
input and output
Power plant description
100~--+---~~L-~--~-~
signals
The maln effect on the pressure is due to the fuel flow; therefore it is used for the steam pressure control. In such a manner, it yields an important disturbing action on temperatures, which must be corrected by gas recirculation and spray-water flow. These two variables (Fig. 2a) act on both temperatures in the same direction, similar gain-factors and dynamic behaviour, and differ only in response to the spray-water flow. This is almost a non-controllability situation. Non-linear behaviour. The operating regime, that reflects the instantaneous power called up by the network, constitutes the main cause of non-linearity in a steam generator. Convection dynamics are approximately, inversely proportional to the steam flow. Gains depend also on it ; so, the spraywater flow has a gain inversely proportional to the steam flow. On the contrary, exchanges by radiation are
·c (mV) 200 r---r----t-~~t_~~*=~
•
41100~_++_+-~r_4_1-~_+--~-~
I I
o
Or I
i ·4 -100r---+------'ld---+-----F===1
o
i I
-4 -lOO t---t---+---+----r>-.....--i
;
on PVC step on QV
Step
Figure 2a
Identification - Step responses TS/QD , TS/RY , TR/QD , TR/RY
Figure 2b
=0,3 V (5 bars' =0,' V ( 10 till)
Identification - Step responses TS/PVC , TS/QV , TR/PVC , TR/QV
Multivariable Control of a Steam Generator
practically insensitive to that ; so, the steam pressure behaviour doesn 't depend on the load. There is an important difference with respect to the temperatures behaviour. Other non-linearities are due to actuators saturation ; thus, actions due to the gas recirculation have an S-type static characteristic. In addition, gas recirculation and spray-water flow, that control temperatures are frequently saturated. CHARACTERISTICS OF THE CONTROL ALGORITHM Outline of the method. The Model Algorithmic Control strategy (MAC) implemented thr ough the software IDCOM will be explained very simply . Longer mathematical developments can be found in previous publications (1), (2) and (3).
75
The method reli es on three principles : - the process to be controlled is represented by its impulse responses that constitute the "internal model", its outputs are computed in real time by discrete "convolution" ; - the controlling strategy 1S established through the "reference model" which defines the close-loop behavi our of the system. The reference model is chosen as to satisfy the overall stability and performances - the controls to be applied are computed at each sampling period either by a oneshot operator , or by an iterative proce dure whose principles rest upon the duality of the identification and control . The internal model, determined by identification, is used to compute the future c ontrols of the process such that the variables to be controlled fit to the trajectory deli vered by the reference mo~el (see Fig . 3) .
-t;_-_-_-_-_-_-
C = De.ired output _ _ _ _ _
_p_r_'_d_ic_ti_O"_ _-=--=--=--=-::::::::=:~L--=-==
-----
MeaJllred output
/L
Pa.t4l-~-_Futurl
Figure 3 The internal model formulation
1S
as follows
N L
SOJ(n)
Hk(i) Pvc(n-i)
i=l N +
L
i=l
~+l(i) Qd(n-i)
N
+
+ where
and
80 (n) 1
L Hk +2 (i) Ry(n-i) i=l N L H + (i) ~(n-i) k 3 i=l Pv(n)
S02(n)
T (n) 8
80 (n) 3
TR ( n)
k
=
(J-1) x 4 +
Predicted output LReference traj1tctory
Control scheme The control variables are P v ,Qd and R (see Fig.4). The steam flow agts both as y a state and a structural disturbance. In the vicinity of an operation point Qvo the signal QV is taken into account as a measurable state disturbance. When there are important load variations, the internal model is adapted through the sampling time. In the case an actuator has a non-linear characteristic , and provided it has previously been identified, it can be taken into account by the algor i thm (for example : input reference o f gas recirculation Ry ). The impulse response type of representation is particularly well suited to industrial processes in which phenomena are, in general, distributed. Its non-minimality is widely compensated by the r esulting increase in robustness. The linearity hypothesis is valid around an operating point, as it is shown by the results obtained during the identificati on
76
M. Lecrique et al.
Pv ref TS ref
Figure 4
Control implementation
stage. The control computation is eased by using the notion of reference trajectory initialized at each sample time on the actual measured output. At each sample time, the computed control is a predictivecne,such
Identification
that the predictive output computed through the internal model satisfy the desired reference trajectory (see Fig.3). The controls computation method proceeds directly from the duality principle established hereafter :
SO(n)
!
measure
Control
ET . H
SO(n)
t
I +
past
future
measure
reference model
.---l-,ii,ntificatinn past
Constraints on the control variables, to the extent that they may be expressed as linear and non-linear combinations of input variables, are easily taken into account. In this application, constraints on the absolute values and on the speed of variat i ons on each control variable are used in the control seQuences computation. Implementation. The pressure dynamics are not affected by load variations. Therefore, control on the pressure is performed by the fuel flow in a single loop using as feed forward variables Qd and Ry . The temperatures are controlled in a multi variable fashion, self adapted to load variations and using the pressure set point as feed forward variable. a) Implementation scheme. A block diagram of the IDCOM control is reproduced on Fig.4 . The pressure control is carried out as follows: a P.I. monovariable regulator regulates the pressure
~
measure
future
~
computed
permanently ; its set point is driven every 20 s by the I DCOM algorithm, that takes into account the disturbing actions of the steam flow and the actions carried out on gas recirculation and spray-water flow. Despite the difficulty of such a control, the adjustment of both temperatures is carried out only by the IDCOM algorithm, in a rigour ously multivariable way (by a single computation of both control variables) and taking into account the effects of the steam flow and of the action determined by the pressure control. The sampling rate is 20 s, at the nominal regime. In order to obtain a better control of the actuators saturation, the algorithm controls directly the corresponding variables either in a direct digital control fashion, or in addition to the existing analog control, that secures then the average regime and may be simplified. Both types of implementation are being tested.
Multivariable Control of a Steam Generator
b) Adaptation to non-linearities. Because of no servo control on the gas recirculation Ry ' i~s static characteristic had to be taken lnto account. The steam flow affects the temperature dynamics in a ratio one to three. Adaptation to the load is thus necessary. It is performed through a variable sampling rate in such a way that,viewed from the computer,the dynamics of the heat exchange appear as constant. Gains are adapted either througP a precompiled set of static gains or using a self adaptive procedure which however necessitatES the use of external signals in order to identify. Such a procedure presen~the additional advantage to make the reference model variable in the same ratio, preserving thus a constant ratio between the natural system dynamics and the specified performances, at every load. c) Action in case of saturation. When one temperature actuator is saturated, safety imperatives require that the control deterioratedout on the other actuator is not deteriored. Consequently, when the multivariable computation brings to or maintain an actuator saturated, the action applied to the other results from an additional monovariable computation that takes the saturation into account. The same monovariable computation is also used when one of the actuators is excluded from the multi variable control (manual action or analog control). Equipment used. The operator, responsible for the control unit has at his disposal a "manual control relay" with three positions for each actuator manual control, analog control and digital control. The last one is the only innovation ; in particular, it preserves the previous setting of the three input references (pressure, superheated and reheated temperatures) . A minicomputer (Mitra 15 - from the French Manufactor CII) is being used for the experiment. It is connected to an inputoutput system (analog-digital interface), safety devices (particularly a "watch-dog" system) and a teleprinter. The real time monitor has been improved for operating in a multitask scheme ; it needs 8 K-words of 16 bits. In this set up, most programs are written in Fortran, which facilitates the adjustment, but doesn't optimize the holding in memory, which reaches 16 K-words. Programs are divided into two tasks. The first task, acti vated every 2,5 s, carries out the digital (10) and analog (16) input acquirings, the digital (3) and analog (3) outputs, the transposed P.I. computation of
77
the pressure loop and the signals likeli.l-.cod test. The second task, activated every 20 s for the pressure and at a variable rate for both temperatures, carries out the totality of the functions connected with the IDCOM algorithm (eventual identification, gain adaptation, control computation) as well as the parameters change in real time and the different messages printing. In addition, the system manages certain safety devices in connection with the equipment reliability. In particular, it automatically and smoothly assures the transition between numerical and analog control in case of failure. RESULTS This scheme was implemented in April 1976 and has been operating since at the Martigues-Ponteau thermal power plant. The first tests allowed the results to be compared with respect to the performances obtained with the analog control (4), whose characteristics are the following : - the P.I. regulation has parameters identical to those in the numerical transparent solution (the set-point is then driven by IDCOM algorithm) ; - the superheated temperature control is performing fairly well. The main P.I.D. regulator, with actions adapted to the load, works out the set-point of an intermediate temperature control, whose P.I. regulator is also adapted to the load and controls the spray-water flow, to which are added feed-forward actions proceeding from the fuel flow, steam flow as well as gas recirculation flow ; - similarly the reheated temperature control has three P.I.D. actions. Tests description. The tests presented herein were carried out in order to test the described regulation in the most significant working conditions, such as : - large amplitude load variations, characterized by the test nO 1, that shows a regular decrease of the load, 40 % in 19 min, followed by a stabilization, and the test nO 2 (Fig.5) corresponding to the increase of the load accomplished in identical conditions ; - fast load variations, of a reduced amplitude, represented by the test nO 3, that shows a load decrease of 10 % in 30 s , followed by a stabilization, and by the test nO 4 (Fig.6), where the increase of load was accomplished at a gradient to 4 % per min, in order to avoid the blowing fans disconnecting ;
M. Lecrique et al.
78
line curves correspond to the rDCOM control tests and dotted line curves "to the analog control.
- tele-adjusting operation, schematized by the test nO 5 (Fig.7), that shows a V load variation (immediate decrease followed by the upward motion) of 16 % accomplished with a gradient of 3 % per min.
Results. The main results are shown in Table 1, where appear the maximum deviations with respect to the first three overshoots of cont ro l led out puts ( cll, d;; and d3) and the peak to p e~ amplitude lA) of their variations.
These figures reproduce, in addition t o the load evolution, the evolution of the controlled outputs (Pv , TS and TR) as well as the control variables l Qf, Qd and Ry )' The f ull
2';0 /
/
190 165
--- -
--
A--
Qy 215
J ~
/
lLl1
·1.
,
80
QF
~
72
//
64
51 .,~
-
-
/l
f'
V
/
.
C
- ...
TR 5 65
/'
/
5 61 557 553 549 S4S
I I
~
--,,"-
/ /
/
/V ,.t/
54,~,
5
0~--~1~0----~m~--~~~----~~-t~lrm~n
-
....
0
10
Analog co'lltrol
20
30
Digital control
40 tTmn
Load rise from 140 to 240 MW at a rate of 5 MW/min
Figure 5
II '~k'*i I tl ~~- I I ':vi19JJJ ::~j' ~~~ ~ t IJ
~[r t --1 .
lOO .t. RV 80
~-
---
40 0
I
-
--:+1--..::>-
V'...
&0
~~~ll1j _ ~
f~=t=tld ,L -t=r 553
1
20
~
Analog control
Figure
6
40
tlmn
o
10
20
__ ___ _ 40 t (mn)
~
Digital control
25 MW load rise at a rate of 10 MW/min
Multivariable Cont rol of a Steam Generator
Ba r
hll
'\
PV
,/V\'.
164
/ 163 IJ
I
~~~~Lf1~1"--,------,I1 ~:~--T'j-----f= .. ~ 10
- - - - -
20
30
Analog control
I
I
1
100
t
I mn
._.-
I!
---
-- -
-- -----
'(
_\- LL - - -r'/ __r-- - -
16 2f---- -\
I
- - *- -
16I
·c
:'\
TS 5&9
~:§4ft-+ff
79
\
/\
r. \
565/ 56I
I
....--..,
\\ \
I 1 \ I!
~
....,~
;"
'.
55
ltWl-t1 0
10
20
30
Digital control
j
100 t
Imnl
Figure 7 Triangular load variation (45 MW at a rate of 7 , 5 MW/min ) The improvement brought by the IDCOM regula~ tion is c lear in general. Indeed, as well as To the overshoot improvement is often assothe analog control it is not able to mainciated a shorter time tain the reheated temperature at small load response to the stabilization of both (test N° 1); this is due to the under dimentemperatures , the third overshoot being elisioning of the gas recirculation. The improminated (in analog control, it is often vement is the most sensitive with respect to larger than the first) . the most constraining tests (test nO 5, Fig. 7), where the temperatures maximum deviations These results have been obtained with cons are reduced in a ratio larger than 1,6 . traints on control variables of the same It results also in a gradient reduction; nature as with the analog control (very this constitutes an interesting aspect for the equipment behaviour . Table Results Ste= Pressure (bar) ANA. IDCOM
Test 1st Test Decrease of load : 40 % 1n 19 min
------------------------nd 2
Test
Increase of l oad : 40 % in 19 m1n
------------------------rd 3
Test
Decrease of load : 10 % in 30 s
d1 d2 d3
+ 1, 6
+ 1 ,1
+ 1,6
+ 3,2
-
-
-
-
- 6,8
- 2 ,0 -
1,6
1,1
/';
---- -------d 1 d 2 d /'; 3 ---d 1 d 2 d /'; 3
-
1,5
Increase of l oad : 10 % in 150 s
d 1 d 2 d /'; 3
---------------------------th 5
Test
Triangular load varia tion : 16 % in 11 min
d 1 d 2 d /'; 3
---------
0, 8
-
-
1, 5
0 ,8
--------
+ 2,0
-
-
-
2,0
2,0
-
1, 5
-
1,5 -------+ 1,8 - 1,5
+ 2,0 8,4
1,1 -
1,1
--------+ 1,3 - 0 ,7
-
-
3,3
2,0
+ 0,5 -25,3 -
+ 2,0 +23 , 0
-
25, 8
25,5 --------
- 1,6 + 5,6 - 3,2 7,2
- 4,0 + 0 ,8
+ 1,0
-
-
-
-
+ 4 ,0 - 5,2 + 2,4 9,2
+ 4,0 - 4,4
------------ ----------- --------
--------- ------------
Reheated Tempera:ture (OC) IDCOM ANA.
5,2
4,8
--------- ------------ -----------
+ 2,0
---- -------------------------------4th Test
Superheated Temperature (OC) ANA . IDCOM
-
-
8,4
-----------
+ 5,6 - 3,6 9,2
+ 2,8 - 2,4 5,2
+ 4,0 - 7,6 + 7,6 15,2
+ 6,0 - 2 ,8
------------ -----------
8,8
1,0 -------- -------+ 2 ,0 + 2 ,0 - 9, 0 -12, 0 -
-
11,0 14 , 0 -------- --------
-
+ 5 ,0 + 0,5 - 0,5 - 2, 0 5,5 3,5 - ------- -------+ 2,4 - 2 ,8 - 6,8 -1 0. 0 + 4,8 14, 8 9 ,6
80
M. Lecrique et aZ.
similar in amplitudes and gradients). This proves that the reference model time constants are not very severe : 60 s on pressure and 120 s on temperatures. The difference is essentially due to the anticipative action of the IDCOM regulation. This anticipation varies from two minutes on fuel flow to six minutes on gas recirculation. The multivariable character is difficult to bring out on test results. However it is possible to reveal it in the test nO 4 (Fig.6\ where gas recirculation was temporarily requested at the beginning of the test (while in simi lar situation the analog control kept its action constant) and reached its final value only at the end of the transient regime. Performances persistency. After an eight months internal, tests were again carried out in the same conditions. Despite the steam generator evolution (clogging,etc), no visible alteration of performances was discovered, the curves remaining practically identical. This indicates the robustness of the algorithm and validates the impulse response representation of the steam generator. It thus seems sensible not to have recourse to on line identification and selfadaptation. Statistical analysis. It is interesting to complete the preceding results by a statistical analysis of the control behaviour in normal exploiting conditions. Temperatures histograms for both types of regulation will be presented. In order to have a statistical validity and a similarity in nature, tests have to be long enough and are not completed at this time. CONCLUSION The detailed favourable results stated above put forward the advantages that may be acquired from multivariable control (IDCOM) in the case of a steam generator. These results are more especially significant as they are obtained without increasing the constraints with respect to the analog control behaviour. With the present increase of the number of nuclear power plants producing electric power two ways are opened to the development of such a technique : - with constant constraints on the control variables and identical performances on the controlled outputs, this method will allow an improvement of the conventional thermal power plants exploiting flexibility. Indeed in the near future, these power plants will be asked to provide the network with the rapid transient variations ; - to reduce in nuclear power plants the constraints connected with the primary loop behaviour (pressure, average temperature deviations, etc) or the secondary loop behaviour (steam pressure, etc) ;
The IDCOM method (aChieving multivariable predictive control) limits at best temporary deviations of the other controlled outputs during an action aiming at zeroing the deviation on one of them. It carries out, thanks to the knowledge of the foreseeable natural evolution (due to the residual effec1 of "Oast inDuts). a deliberate ad.iusting control action (at a convenient moment, with a just suitable amplitude minimizing the controlling work). In addition, such a technique adapts itself to various means of action : as direct digital control or as superposition to an elementary control. In the last case, the technological basic level may consist of individual regulators with a simplified structure, without adaptations or feed forward actions, securing the average operating regime. The IDCOM regulation acts then in addition to bring the multi variable character that is absolutely necessary to the dynamical performances improvement. Therefore, the simultaneous operation of both levels brings an interesting redundancy and provides the permanent proof that each level is able to replace the other in case of failure. The stated method facilitates also the takiq into account of constraints : gradients limitation, safety conditions, control variables saturation, reduction of the number of contrc elements without multi variable control (without changing the algorithm, it is sufficient to limit correspondingly the outputs to be controlled in multivariable technique) Finally, such a method has proved to be easily implemented on a thermal power plant. As a matter of fact, the aforestated advantage allows a progressive implementation of a loop by loop type well known by analog regulation technicians. Without any previous computation, operators display reference model time constants of the controlled output and eventually modify them to refine performances as the unit is starting. It is only necessary to estimate the main static gains ; the dynamics of the impulse responses can be obtained from simplified models (well known as well for the classical thermal power plants as for the nuclear power plants steam generators, which are subject to a systematic modeling) . REFERENCES (1) Richalet, J., Rault,A., Testud, J.L., Papon, J., (1976). Algorithmic control of industrial processes. 4th IFAC Symposium, Tbilissi, USSR. (2) Richalet, J., ana Rault, A., (1977). Model algorithmic control of industrial processes. 5th IFAC Symposium, The Hague (3) IDCOM Proceedings of a seminar on industrial process control (1976). ADERSA. (4) Tessier, M., (1977). Experience of IDCOM regulation; tests results. Electricite de France internal paper, p 44/19.