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Computer aided control system design applied to milk drying plants
Automatica, Vol. 17, No. 5, pp. 727-735
0005-1098/81/050727-09$02.00/0 PergamonPress Ltd © 1981InternationalFederationof AutomaticControl
Printed in Great Britain
Brief Paper Computer Aided Control System Design Applied to Milk Drying Plants* D . J. S A N D O Z t
and O. WONG:~
Key Words--Computer control; computer aided design; dynamic programming; multivariable control systems; identification. Abstract--This paper reviews a computer aided control system design facility that has been used to develop a set of control systems that have been implemented on a pilot scale industrial process. The facility caters for a broad range of control situations including those with interactions, time delays and disturbances. Online interactive graphics is used as a design aid for the identifmation of plant dynamics and for the assessment of control system performance. Control systems may be developed systematically to be structured in a hierarchical configuration on the plant. Particular applications to the plant, an evaporator and a spray drier, are discussed in detail,
Introduction
THIS PAPER reviews the features of a computer aided control system design facility that has been developed and applied in the laboratories of the New Zealand Dairy Research Institute, Palmerston North, New Zealand. An IBM System 7 computer has been used to control a Wiegand evaporator (Wiegand, 1971) and a De Laval tall form spray drier. Figure 1 shows the complete computer control system in schematic form. ~
~
Evaporator
Ins"l' rt~m@n't GonTr I~[~ ~ t I Interfoce I | ~ ~ System 7 computer I
¢~7"~
Grophlcs
FIG. 1. Computer control system, The evaporation processes are used for the preparation of milk powder. These are of pilot scale with a throughput capacity of approximately one-tenth that of a normal commercial production unit. The evaporator concentrates skimmed milk from 9 % to about 48 % total solids. This *Received 5 February 1980; revised 7 August 1980; revised 2 January 1981; The original version of this paper was presented at the IFAC Symposium on Computer Aided
concentrated milk is fed under pressure to the spray drier where it is atomised in a nozzle. A flow of hot air dries the resulting milk droplets as they fall under gravity within the drier chamber and form the powder product. The plant has been extensively instrumented. Upwards of 70 measurements are available to the computer. These include the usual temperatures, pressures and flow rates and also milk viscosity and density from the evaporator and air humidity from the spray drier. The purpose of this extensive range of measurements is not only for the implementation of effective control systems, but also to enable process engineers to gain further insight into the internal mechanisms of the evaporation processes. Ten output stations connect to the plant, giving the computer the capability for adjusting valves, pumps and fans directly. The computer system has a 64kbyte memory with two disks of 2.5 Mbyte storage capacity each. It also has a printer, a graphics vdu and a suitable interface range to permit connection to the instrumentation of the plant. Software has been developed for the computer with two purposes in mind: (a) to provide a real-time operating system to support the monitoring and control of the plant during normal production; and (b) to support, and assess the effectiveness of computer aided control system design procedures. These procedures are intended to assist the control engineer to establish good performance from the applied control systems. A major objective of the work described in this paper has been to progress development of a facility that has the potential for useful and wide industrial application. The design procedures are not specialized to be appropriate only to the milk evaporation processes to which application has been made. These processes do, however, reflect many of the control difficulties that are typical of industrial plant in general. They thus form a useful test-bed for the assessment and further development of the control system design and implementation procedures. The experience gained from these application studies has led to significant enhancement of the capabilities of the control system techniques that have been employed. The treatment of computer aided control system design in the literature is often fragmented and specialised. Many techniques presume the availability of a process model. For example, the inverse Nyquist methods (Munro, 1979) require the system transfer function matrix G(S). The identification of such a matrix is not straightforward but this aspect is often neglected as a consideration. CAD procedures for process modelling have also been widely investigated and a number of
728
Brief Paper
and used as a feature to aid the commissioning of multiple control systems, The work described in this paper integrates the aspects of identification, control systems design and simulation. The design techniques have been developed so that application to a wide range of industrial process control situations is valid. The parallel development of a software package for implementation of the designed control systems has permitted a thorough evaluation of the design procedures on the evaporation plant. The control system design problems associated with this plant involve, for example, aspects such as pure time delays, distribution, interactions and disturbances. These aspects have necessitated the development of a generalized representation for linear process dynamics which has the capability of approximating the behaviour of both the simple and the complex dynamic systems associated with the plant. On this basis, a uniform design procedure has been established. This caters for the modelling of dynamics using least squares techniques and for the design of suitable controls using dynamic programming. It involves interactive graphics and has been applied to a range of control problems from simple single-input-and-output to the more complex multivariable situations. The generalized representation and its use for modelling and control system design are reviewed in the paper. The implementation philosophy does not restrict to a single controller or to a single set of interacting controllers. The intention has been to develop a mechanism for implementing multiple controllers to control a complete plant, The overall design concept that has been applied, is to divide the plant into a number of sub-systems. Controllers are developed for each sub-system. The operation of these subsystems is then coordinated by other controllers operating within a structured hierarchy. This maintains a similarity with the conventional and common sense principles of cascade control. The overall hierarchy of control that has been implemented on the evaporation plant is described and two particular sub-systems are discussed in detail. One of the latter is multivariable and concerns the control of air flow and pressure in the spray drier. The other involves large delays and disturbances and is concerned with the control of milk density in the evaporator.
Each sub-system of the process is presumed to be of the form illustrated in Fig. 2, where u is an m x 1 vector of control inputs; v is a q x 1 vector of measurable disturbance inputs; and y is a p x 1 vector of measurable outputs. The inputs u and v may have pure time delays associated with any or all of their elements. Let m l = m + q , Linear process
=
dynamics --
I
FIG. 2. Sub-system representation, Process dynamics are represented by the generalized multivariable input and output equation (Sandoz and Wong, 1978) Yk=:tZk_~+/$k_~
r ]
Yk-c
I,
-7
Zk-c =
(3) ] Yk-(Kl-l~ I I1 Y2k-Rlc ,t _ _.J
Y2 represents the first n2 rows of Y so that as many elements are included in Y2 as are necessary to bring the size of Z to the required n l + m l , nl is > n, the order of the process dynamics. If h i > n , equation (1) generates a least squares filtered estimate to Yk~t,n4 × n l + m l is a matrix of constant coefficients RI+~ a~ +1 ~k o n4 x 1,= ~, pljUk_jc+ ~ yl~V k jc. (4) ~= ~ i=0 Uk, m x 1, is the control input difference vector with Uk=uk--Uk c
(5)
V k is the q x 1 disturbance input difference vector Vk=Vk--Vk-c
(6)
,81j, n4 x m, and ~,lj, n4 x q, are constant coefficient matrices. If there are pure time delays associated with the inputs, equation (1) remains valid provided the interval c is greater than any of the delays. If any delay is greater than c, then the equation must be adjusted to accommodate the delay. Thus, if an input u (or v) has an associated delay of d intervals (i.e. dc seconds) with d > c such that (7)
d=ic+dl
with i an integer > 0 and c > d l , then the associated element in equation (5) [or (6)] is redefined as Uk=uk-~c--Uk-"+ ~
(8)
[or Vk = Vk_i~-- Vk-,+ 1~]"
Review of process representation
•
sl,s2...ss_ t prior to k(c>sR_l). The vector Z k c, ~ × is compounded of a sequence of R I samples of Y
k=O,c, 2c,....
(1)
If the interval k - - . k + l is ~ seconds, then the update interval of equation (1) is cx seconds. The vector Y, n4 x 1, is co.mPounded . .of . a . number . . . of discrete output measurements
The structure of equation (1) is general for the representation of any linear and multivariable process dynamics, subject to the constraints that (a) the control inputs u must be constant across interval k--*k+c (this presents no difficulty since this interval becomes that for update of the control signal, which is implemented from a computer); and (b) the disturbance inputs v are measurable and may be approximated as piecewise steps or alternatively as piecewise ramps across the interval k ~ k + c. The structure is convenient for control system design. Since in steady state ~=0, it follows that Yk may be redefined as Ii k Yk =
] (9)
k-s~_
with error term ek=yk--y~; where y~, is a p × l set point vector that defines the origin of the new system. A controller designed on the basis of equation (1) is incremental and incorporates error feedback, two necessary aspects for industrial aovlication. The control obiective becomes to drive
Brief Paper with I YI k, n4 × 1 =
-~
Yk--Yk-c i l Lyk_s~___yk_ c
and I!
--1 k-c-s~- Yk-c ~
: l~,lk_2 _ ~1 Zlk_c,nl + m l - - p x 1,= k-c-~R t - - Y k - l • j
atl may be derived directly from ~t. The structure of equation (10) requires the identification of p×n4 fewer parameters. The output differencing provides greater tolerance to drifting which, for example might arise from aspects that are not measured, To model a process in terms of equation (10), the following must be selected or established, given definition of outputs y and inputs u (a) control interval c; (b) R, the number of samples per control interval and the intervals s I ~s~_ 1 ; (c) the measurable disturbance inputs v that impact upon the system; (d) the delays associated with both control and disturbance inputs; and (e) the process order n, or the minimum effective value of nl. The choice of the control interval c, is subject to the rate of the process dynamics, to the disturbance signal characteristics (with respect to the validity of piecewise linear approximations) and to time delays. The choice of the sampling pattern influences the number of terms R1 that need to be incorporated within the vector lSk-~ [equation (4)]. For example, if n l = n4 so that all samples are collected within one interval c, then R I = I and the structure of Pk-, is a minimum. Aspects associated with delays influence the choice of sampling. If c~s~_~>dl>O, where dl is the largest delay element in the system [accounting for equation (7)] then pR~ + and ),1~+~ are zero. This condition implies that measurements taken in the interval k ~ k + c are collected after the control action of Uk-~ can be seen to be influencing the process. This necessarily applies if samples are taken only at the control instants (i.e. k-jc, j=l--*R1), The above aspects invite a range of options to be considered in the selection of a structure for the process model. Software has been developed to provide the following facilities (1) The injection of sequences of random step changes into the control inputs and the monitoring of the process responses directly using graphics trend displays. The interval between steps is a direct multiple of the control interval c. At this stage, the designer establishes by inspection, the presence and approximate magnitude of delays. It is also possible to establish if the initial choice for the control interval c, the amplitude of the injected perturbations, and the defined time span for collection of data are realistic given consideration of the observed process dynamics and the delays. This experiment must continue until a satisfactory sequence of data is established, (2) The analysis of data, using reeursive least squares
729
and disturbance sequences that perturbed the process. The data generated is then compared with the original. The mean difference and mean square difference between the two sets of data provide numerical figures of merit for the model. Visual inspection and comparison of the model and original data trends is also very informative and gives a valuable subjective interpretation of the quality of the model. Initially, the designer will not know the model structure that gives rise to the best identification of the plant dynamics, unless there is helpful process engineering knowledge at hand. It is therefore usually necessary to apply the analysis a number of times before an acceptable identification is obtained. It is common sense to begin with the most simple structure that is appropriate to the input and output signals that have been selected to relate to the model. Model dimensions and assumed time delays can then be increased systematically until a satisfactory result arises. The graphics displays and the figures of merit gi~.e the designer a feel for the improvements that arise from these systematic adjustments to the structure. If a reasonable model cannot be obtained, then this may point to a need for a retrial of the initial data collection experiment, or to a need for the inclusion of other signals within the mode/ description. The way in which the regenerated data from the model differs from the process data can point to more effective model structures. For example, disturbance effects are suggested if the process and model follow closely and then suddenly deviate.
Control system design Successive manipulation and iteration of equation (1) permits the structure of (11) to be obtained t'-
----~
IVk+~Rl-l~ Zj+l =~t3Zj+/~31 Wj+/~32Wj_ a +r3 ]:1. /} (11) Ix[.Vk_~R~+t~j | with ] Uk-2e Wk-2,= [ i
/"
Z~=Zk-c
Lu~-tRI+~J and the interval j ~ j + 1, R 1 'c of the intervals k--, k + 1. Software has been developed to support dynamic programming (Kuo, 1970; Sandoz, 1973) to minimize the quadratic performance criterion I=
~..
{ZTQZj + W~PW~}. (12) J= ~ This technique is well suited to be applied with the model structure of equation (I 1). The controller that results has the form V~_, 1 Uk-~=GIZ~-c+G2Wk-2~ +G31 i
J
.
(13)
Vk-~R~÷t)~ The parameters of the gain matrices G1, and G2 and G3 define the controller. The disturbance elements are only incorporated in the dynamic oro~rammin~ for the ~ta~,~ ~= t
730
Brief P a p e r
only a single input and output, then it reduces to
Uk--Uk_~=gl(yk--ys~)+g2(yk_~--yss), C>S l.
(14)
Control system design software has been developed to provide for (a) specification of the elements of the weighting matrices Q and P and the number of stages M; (b) computation of the controller gains; (c) simulation of the resulting controller and the graphical display of its response in application to the derived process model. Disturbances are included at this stage as random sequences. If response is unsatisfactory the designer repeats the procedure from stage (a) until he is satisfied with the control performance. The weighting matrices Q and P are thus re-adjusted in a successive manner. A criticism often levelled at controllers that are based upon minimization of a quadratic cost criterion is that the selection of the elements of the weighting matrices to achieve particular control system performance is a black art. In the context of the structure described here, the following considerations are relevant (1) The vector Z in equations (12) and (13) is compounded of successive samples of error (measurement less set point). The vector W is compounded of successive increments in the input signals. (2) The interpretation of off diagonal elements in Q and P is difficult. It is reasonable to restrict these matrices to a diagonal form. (3) Given the diagonal restriction, the relative magnitude of the diagonal elements in Q reflects the urgency with which the measurement errors are to be zeroed relative to each other, e.g. a large weight relating to one error, in comparison to a small weight relating to another, indicates that the former is to be zeroed more quickly, (4) The inclusion of diagonal elements in P introduces a constraint on the amounts that the associated inputs change and therefore give rise to a slower overall response, On the basis of these and other aspects, the designer quickly establishes a feel for the impact of various elements and is able to home in on a satisfactory combination. The control parameters are then passed forward for implementation and the final test online,
Generalized facility for design and implementation A complete facility has been developed, incorporating the computer aided design aspects already described, with the means for implementation of the control systems online in a structured hierarchical form. The conventional approach for the implementation of industrial process control systems, is to consider the plant that is to be controlled as a number of sub-systems. At the most simple level, these might be flow or temperature loops with the control actuation signal driving some physical aspect of the plant, such as a valve. More complex sub-systems incorporate these simple loops and the controllers (which will now regulate parameters more remote from the plant inputs or with longer time constants), cascade set points to actuate the simple loops. This philosophy has been maintained in the approach described in this paper. The object is not to derive an overall dynamic model to define the plant characteristics, It is to obtain a set of models for sub-systems and to incorporate controllers with each before proceeding to consider the next sub-system. Thus the identification and control application advances in a systematic fashion until the total olant complex is incorporated within the structured
consideration has been to make the software as flexible as possible, so that, by straight forward specification of data, valid application can be made to a wide variety of plant control situations. The real time system provides for (a) plant control and the application of perturbation trials to collect data for analysis by the CAD programmes; (b) plant operation with facilities for data logging either to terminals or to disk files; start up and shut down of plant operations; alarm detection and reporting; definition of control requirements, set points etc; and trend graphics; (c) interfacing with the CAD programmes via disk file. The offline system supports the least-squares, dynamic programming and simulation software that integrates with the interactive graphics to provide the full CAD facility. Overall, therefore, the designer is provided with the facilities to investigate a wide variety of control system options that are appropriate for application. The appendix briefly overviews the main stages associated with the CAD procedures. A flow diagram is presented to emphasize the coordination of the design phases described above. Using the CAD facilities, the designer may build a complete structure of control systems to cater for total plant control.
Examples ofapplicati,m The control systems that have been implemented on the milk powder plant are listed in Table 1. The first six systems have been applied to the evaporator and the remainder to the spray drier. A brief description of the milk powder plant is presented so that the control systems may be appreciated. A schematic illustration of the evaporator is shown in Fig. 3. Skimmed milk is pumped to the evaporator at a particular flow rate and passes through preliminary pre-heat stages. At the main pre-heater, steam is injected directly into the milk to raise its temperature to a required value. The milk then feeds to the first evaporation effect. The concentrated product emerges from the third effect. Steam is supplied to a steam jacket that surrounds the first effect, providing the energy for the initial evaporation. Steam evaporated from the milk provides the energy for subsequent effects. Steam from the third effect is condensed to provide the pressure differential across the plant. The milk takes between two and three minutes to propagate through the plant. The product density and flow rate vary according to the density and flow rate of the supplied milk and also according to the steam supply. The temperature differential across the plant influences the quality of the fmal powder product. A more detailed description of the multiple evaporation plant is available (Sandoz and Wong, 1978). With reference to Table 1, systems 1 to 4 regulate the steam, milk and water supplies to the evaporator. Each of these systems can be designed independently since there is little interaction between them. Note, however, that there is interaction within system 1 that necessitates a multi-variable solution. The order of design and implementation is not important. These systems constitute a base level of control designed to minimize variations in the supplies and thereby reduce disturbance to the plant. Systems 5 and 6 cascade set points to the base level and constitute the second level. These latter systems control aspects associated with the production end of the evaporator. Concentrated milk from the evaporator is pumped to the spray drier at a controlled rate. A large fan maintains an air flow through the drier. This air is heated by a gas burner and its temperature may be regulated by adjusting the flow of gas.
Brief Paper
731
TABLE 1. LIST OF CONTROLSYSTEMSIMPLEMENTED System 1
Measurements
Controls
Rate of flow of milk to evaporator
Pump in milk feed line
Milk pre-heat temperature
Valve in steam injection line
2
Steam flow to steam jacket of evaporator
Valve in steam line
3
Condenser water flow rate
Valve in water line
4
Interstage ejector temperature (condenser)
Valve in water line
5
Pressure in terminal evaporation stage
Set point to controller of system 3
6
Milk density
Set point to controller of system 2
7
Milk flow to spray drier
Pump in milk feed line
8
Inlet air temperature to spray drier
Valve in gas line
9
Spray drier chamber pressure spray drier air flow
Dampers in inlet and exhaust air lines
Features Multivariable system with 2 inputs and 2 outputs Time delay of 4 s associated with temperature measurement Disturbance due to variation in pressure in steam main
Time delay of 30 s
Disturbances due to rate of milk flow and supplied milk density Time delay of 2-3 rain
Multivariable system with 2 inputs and 2 outputs
Condenser water in
1 Milk in
in
_J
] BarometriCcondenser
L
Co¢~enser wafer out our out M i l ; out Main prB-h*~er I
A
i~
i,
I"--I
Concentrated product
I " - - I ~I,o_
I
732
Brief P a p e r
evaporator and the humidity of exhaust air from the spray drier. The major problem associated with these aspects is the generation of consistent and reliable measurement rather than one of process control. In summary of the control systems, the controllers associated with systems 3, 5, 7, and 8 are straightforward, with the minimal structure of equation 14. Systems 1 and 9 require multivariable controllers, involving 2 inputs and 2 outputs because of interaction within the plant. The remaining systems are single input and output but involve time delays and disturbances. Two of these sub-systems are now discussed in detail to demonstrate the features of the design procedures. These are system 9, air flow and pressure control for the spray drier, and system 6, milk density control for the evaporator. These systems are chosen because the complications of interaction, time delay and disturbance associated with them, make it difficult to establish effective control system performance by conventional industrial means, Spray drier system (Control system 9). It is desirable, for the production of milk powder of consistent quality, to have both the rate of flow of air through the chamber and the pressure within the chamber closely regulated. These two quantities interact and the problem must be treated as a multivariable one. Figure 4 illustrates a perturbation experiment carried out on this system of the spray drier. Both the inlet and exhaust air dampers (parameters 3 and 4) are stepped with randomly varying amplitudes at intervals of 48 s. These amplitudes of variation cover about 25 ~o of the full actuation range of the dampers. Superimposed upon the airflow and pressure characteristics in Fig. 4 (parameters 1 and 2) are the characteristics obtained by subjecting the derived least squares model to the same disturbing sequences. This model is established for a control interval c of 8s and a single sampling interval s, of 4 s. It represents the best characteristic that could be established via the interactive modelling procedure. The model has second order dynamics (n=2), with R = 1 and n4=4. It is evident from Fig. 4 that nonlinear and/or time varying influences are present, but that the model is still reasonably representative of process behaviour. Equation (15) details the controller derived via the interactive design procedure, with ul and u2 the inlet and exhaust damper positions, yl the inlet air flow and y2 the chamber pressure, yl~., and y2~ define the set points associated with yl and y2, respectively
][
15.7
LU2k --U2k-8 =
9.1
ul k
--Ulk_ 8
[-ylkr [ y2k
--9
ylk_ 4
[__y2k 4
--4.9
09]
--2.5
1.1
--yl,~|
/
_y2s ~
×
(15)
--yl,,|'
--y2s,
/
Figure 5 illustrates online control. A sequence of changes to both the pressure and the air flow set points is introduced. The controller compensates for the interactions and follows the set points effectively. The short-comings in the model because of the non-linear influences are of no apparent significance. These arise mainly because of stiction and hysteresis in the dampers. Inspection of Fig. 5 clearly indicates the interaction in this system. Both dampers have to adjust significantly and simultaneously to effect the set point changes. Evaporator system (control system 6). It is desirable to have the density of the milk produced by the evaporator closely regulated to be consistent with the needs of the spray drier. The spray drier requires that the flow of milk from the evaporator be adjusted occasionally, but with density unchanged. There are three main factors that influence the density of the milk produced by the evaporator. These are of the flow of steam to the first evaporation stage, the inlet flow rate of milk to the evaporator and finally, the density of the milk supplied to the evaporator. Figure 6 illustrates an experiment carried out on the evaporator. Perturbations are injected from three sources. The set points to lower level controllers for the milk inflow rate (+ 301/h around 17501/h) and the steam inflow rate (+ 10 kg/h around 440kg/h) are adjusted at 2min intervals (parameters 5 and 7). The density of the incoming milk (parameter 8) is adjusted less frequently by adding either milk of higher concentration or water. The variations in milk density and the superimposed model characteristic (parameter 6) are also illustrated in Fig. 6. Again, the model is not perfect but it does demonstrate enough similarity to give confidence that an effective controller can be obtained. The model is based upon a
I 8 kg Imin High
2 Z5 m bar a. and model
l
Exhaust air
damper
I
8.1
I
25%1 f . s . d
Brief Paper
733
Air flow rate and set point High
yl A
A
25 kg / min /
=
A
~.~~.Chamber
A
I~.I-
pressure and set point
2- ul
25% f.s.d
/
2
2I% f.s.d. position
Low
Time,
I 500
s
FIG. 5. Spray drier, set point control Low 87 kg/min 0.987 bar a 40 % f.s.d. - 2 5 ~o
1. Air flow rate 2. Chamber pressure 3. Exhaust damper position 4. Inlet damper position
Milk inflow rote
~
High
High 97 kg/min 1.007 bar a 140 ~ f.s.d. 75 ~o f.s.d.
l /
5 75 I / h r ~
~
~
Product density_
//~
.
t
50 kg/h
~ Low 0
~
~
~ J ~ Milk input density Time, S
8 I!kg/m 3 I 4800
FIG. 6. 5. 6. 7. 8.
Milk inflow rate (set point) Product density Steam flow rate (set point) Milk input density
control interval of 60s, with intermediate intervals si =20s
Low 14501/h l140kg/m 3 400kg/h 1030kg/m 3
High 17501/h 1200kg/m 3 520kg/h 1070kg/m 3
the steam has to be adjusted to compensate for changes in
734
Brief Paper
High
/
\
\
t
F--"
Milk inflow rote
.__/
60 I / h r
/
5 1
•
. ~//("
1 2 . 5 kg / m
set point
m flow rate
3
25 kg/hr , , .
LOW
I
180
Time, s
FIG. 7, Simulation of evaporator control Low 5 Milk inflow rate (set point) 6. Product density 7. Steam flow rate (set point)
Milk inflow rate
High
1500 l/h ll50kg/m 3 400kg/h
1750 l/h 1200kg/m 3 500kg/h
/
/
High
60II/h 5
t t
' l 25 I / h
~
Low
-~
_ _
~,_
~
8
I0 kg
/m 3
input density
Milk
0
Time,
I 6500
s
FIG. 8 Evaporator, set point control 5. 6. 7. 8.
Milk inflow rate (set point) Product density Steam flow rate Milk input density
discrepancies observed at the modelling stage (Fig. 6) and is caused by unmonitored factors that influence the process (such as steam supply pressure variations), Conclusions and discussion The design of controllers for 8 of the 9 subsystems associated
Low 14001/h 1140 kg/m 3 400 kg/h 1035 kg/m 3
High 17501/h 1200 kg/m 3 500 kg/h 1075 kg/m 3
Fig. 6 lasted for over 2 h. It was difficult to establish perturbation ranges for signals 5 and 7 that resulted in the milk density remaining within an acceptable operating region throughout the course of the experiment. The model as illustrated in Fig. 6 was obtained quickly using the interactive procedure once acceptable data had been established.
Brief Paper designs rely upon trial and error associated with simulation. Aids to prompt the designer to a realistic choice of options would be valuable, this particularly so in establishing the most effective structure for the process model. The dynamic programming method may not be the most appropriate for control system design. It would be advantageous to utilize some design procedure that leads the designer via a more direct route to the desired response characteristics. A problem with evaporators is that their characteristics slowly change (a) in the short term because of milk burning on to the interior tubes thereby altering heat transfer coefficients; and (b) in the long term because the properties of the milk supply (viscosity etc.) alter throughout the dairy season. Such difficulties are associated with many industrial processes. Similar effects occur with plant that is nonlinear when the plant is required to adjust from one operating point to another. These problems suggest a need for periodic re-identification and upgrading of controls to keep them in tune with the plant or for an adaptive/self-tuning mechanism so that the controllers are always set correctly. These aspects, together with a need for a more straightforward control system design procedure, provide interesting possibilities for further application studies,
Acknowledgements--The authors are grateful to the New Zealand Dairy Research Institute, IBM (NZ) Limited, The New Zealand Department of Scientific and Industrial
735
Research and Massey University for supporting this project. They also wish to thank Professor J. K. Scott for his consistent support for this work.
References Batey, D. J., M. J. H. Sterling, D. J. Antcliffe and S. A. Billings (1975). The design and implementation of an interactive data analysis package for a process computer. Comp. Aided Design 7, 265. Hasting-James, R. and M. W. Sage (1969). Recursive generalised least-squares procedure for online identification of process parameters. Proc. lEE 116, 2057. Kuo, B. C. (1970). Discrete Data Control Systems. Prentice Hal/. Munro, N. (1979). The UMIST control system design and synthesis suites. IFAC Symposium on Computer Aided Design of Control Systems, Zurich, pp. 343-348. Sandoz, D. J. (1973). Optimal Control of linear multivariable systems based on discrete output feedback. Proc. lEE 12,0, 1439. Sandoz, D. J. and O. Wong (1978). Design of hierarchical computer control system for industrial plant. Proc. lEE 125, 1290. Wiegand, J. (1971). Falling film evaporators and their application in the food industry. J. Appl. Chem. and Biotechnol 21,000. Young, P. and R. Jakeman (1979). The development of captain: a computer aided programme for time-series analysis and the identification of noisy systems. IFAC
Symposium on Computer Aided Design of Control Systems, Zurich, pp. 391-400.
Flow diagram of CAD procedures
A
B
C
Select £irst/next sub-system ~- of the plant that is to be controlled Define the measurements, actuations -----4~and disturbances associated with the sub-system Perturb~and/or monitor the plant to get data No Check if data suitable ~--- {C)
t~e Yes Poatula the characteristics of the D --'-"4~model (order, intervals, delays etc. )
Identify the model parameters
No
Check if model is satisfactory
I~
Yes
E
S e l e c t elements of weighting - - ~ " m a t r i c e s for control system design
Calcula/e controller gains Simulate~ the controller (working on the model) and inspect the performance
Have all options re c h a r a c t e r i s t i c s been tried? No (D)
(B)
0005-1098/81/050727-09$02.00/0 PergamonPress Ltd © 1981InternationalFederationof AutomaticControl
Printed in Great Britain
Brief Paper Computer Aided Control System Design Applied to Milk Drying Plants* D . J. S A N D O Z t
and O. WONG:~
Key Words--Computer control; computer aided design; dynamic programming; multivariable control systems; identification. Abstract--This paper reviews a computer aided control system design facility that has been used to develop a set of control systems that have been implemented on a pilot scale industrial process. The facility caters for a broad range of control situations including those with interactions, time delays and disturbances. Online interactive graphics is used as a design aid for the identifmation of plant dynamics and for the assessment of control system performance. Control systems may be developed systematically to be structured in a hierarchical configuration on the plant. Particular applications to the plant, an evaporator and a spray drier, are discussed in detail,
Introduction
THIS PAPER reviews the features of a computer aided control system design facility that has been developed and applied in the laboratories of the New Zealand Dairy Research Institute, Palmerston North, New Zealand. An IBM System 7 computer has been used to control a Wiegand evaporator (Wiegand, 1971) and a De Laval tall form spray drier. Figure 1 shows the complete computer control system in schematic form. ~
~
Evaporator
Ins"l' rt~m@n't GonTr I~[~ ~ t I Interfoce I | ~ ~ System 7 computer I
¢~7"~
Grophlcs
FIG. 1. Computer control system, The evaporation processes are used for the preparation of milk powder. These are of pilot scale with a throughput capacity of approximately one-tenth that of a normal commercial production unit. The evaporator concentrates skimmed milk from 9 % to about 48 % total solids. This *Received 5 February 1980; revised 7 August 1980; revised 2 January 1981; The original version of this paper was presented at the IFAC Symposium on Computer Aided
concentrated milk is fed under pressure to the spray drier where it is atomised in a nozzle. A flow of hot air dries the resulting milk droplets as they fall under gravity within the drier chamber and form the powder product. The plant has been extensively instrumented. Upwards of 70 measurements are available to the computer. These include the usual temperatures, pressures and flow rates and also milk viscosity and density from the evaporator and air humidity from the spray drier. The purpose of this extensive range of measurements is not only for the implementation of effective control systems, but also to enable process engineers to gain further insight into the internal mechanisms of the evaporation processes. Ten output stations connect to the plant, giving the computer the capability for adjusting valves, pumps and fans directly. The computer system has a 64kbyte memory with two disks of 2.5 Mbyte storage capacity each. It also has a printer, a graphics vdu and a suitable interface range to permit connection to the instrumentation of the plant. Software has been developed for the computer with two purposes in mind: (a) to provide a real-time operating system to support the monitoring and control of the plant during normal production; and (b) to support, and assess the effectiveness of computer aided control system design procedures. These procedures are intended to assist the control engineer to establish good performance from the applied control systems. A major objective of the work described in this paper has been to progress development of a facility that has the potential for useful and wide industrial application. The design procedures are not specialized to be appropriate only to the milk evaporation processes to which application has been made. These processes do, however, reflect many of the control difficulties that are typical of industrial plant in general. They thus form a useful test-bed for the assessment and further development of the control system design and implementation procedures. The experience gained from these application studies has led to significant enhancement of the capabilities of the control system techniques that have been employed. The treatment of computer aided control system design in the literature is often fragmented and specialised. Many techniques presume the availability of a process model. For example, the inverse Nyquist methods (Munro, 1979) require the system transfer function matrix G(S). The identification of such a matrix is not straightforward but this aspect is often neglected as a consideration. CAD procedures for process modelling have also been widely investigated and a number of
728
Brief Paper
and used as a feature to aid the commissioning of multiple control systems, The work described in this paper integrates the aspects of identification, control systems design and simulation. The design techniques have been developed so that application to a wide range of industrial process control situations is valid. The parallel development of a software package for implementation of the designed control systems has permitted a thorough evaluation of the design procedures on the evaporation plant. The control system design problems associated with this plant involve, for example, aspects such as pure time delays, distribution, interactions and disturbances. These aspects have necessitated the development of a generalized representation for linear process dynamics which has the capability of approximating the behaviour of both the simple and the complex dynamic systems associated with the plant. On this basis, a uniform design procedure has been established. This caters for the modelling of dynamics using least squares techniques and for the design of suitable controls using dynamic programming. It involves interactive graphics and has been applied to a range of control problems from simple single-input-and-output to the more complex multivariable situations. The generalized representation and its use for modelling and control system design are reviewed in the paper. The implementation philosophy does not restrict to a single controller or to a single set of interacting controllers. The intention has been to develop a mechanism for implementing multiple controllers to control a complete plant, The overall design concept that has been applied, is to divide the plant into a number of sub-systems. Controllers are developed for each sub-system. The operation of these subsystems is then coordinated by other controllers operating within a structured hierarchy. This maintains a similarity with the conventional and common sense principles of cascade control. The overall hierarchy of control that has been implemented on the evaporation plant is described and two particular sub-systems are discussed in detail. One of the latter is multivariable and concerns the control of air flow and pressure in the spray drier. The other involves large delays and disturbances and is concerned with the control of milk density in the evaporator.
Each sub-system of the process is presumed to be of the form illustrated in Fig. 2, where u is an m x 1 vector of control inputs; v is a q x 1 vector of measurable disturbance inputs; and y is a p x 1 vector of measurable outputs. The inputs u and v may have pure time delays associated with any or all of their elements. Let m l = m + q , Linear process
=
dynamics --
I
FIG. 2. Sub-system representation, Process dynamics are represented by the generalized multivariable input and output equation (Sandoz and Wong, 1978) Yk=:tZk_~+/$k_~
r ]
Yk-c
I,
-7
Zk-c =
(3) ] Yk-(Kl-l~ I I1 Y2k-Rlc ,t _ _.J
Y2 represents the first n2 rows of Y so that as many elements are included in Y2 as are necessary to bring the size of Z to the required n l + m l , nl is > n, the order of the process dynamics. If h i > n , equation (1) generates a least squares filtered estimate to Yk~t,n4 × n l + m l is a matrix of constant coefficients RI+~ a~ +1 ~k o n4 x 1,= ~, pljUk_jc+ ~ yl~V k jc. (4) ~= ~ i=0 Uk, m x 1, is the control input difference vector with Uk=uk--Uk c
(5)
V k is the q x 1 disturbance input difference vector Vk=Vk--Vk-c
(6)
,81j, n4 x m, and ~,lj, n4 x q, are constant coefficient matrices. If there are pure time delays associated with the inputs, equation (1) remains valid provided the interval c is greater than any of the delays. If any delay is greater than c, then the equation must be adjusted to accommodate the delay. Thus, if an input u (or v) has an associated delay of d intervals (i.e. dc seconds) with d > c such that (7)
d=ic+dl
with i an integer > 0 and c > d l , then the associated element in equation (5) [or (6)] is redefined as Uk=uk-~c--Uk-"+ ~
(8)
[or Vk = Vk_i~-- Vk-,+ 1~]"
Review of process representation
•
sl,s2...ss_ t prior to k(c>sR_l). The vector Z k c, ~ × is compounded of a sequence of R I samples of Y
k=O,c, 2c,....
(1)
If the interval k - - . k + l is ~ seconds, then the update interval of equation (1) is cx seconds. The vector Y, n4 x 1, is co.mPounded . .of . a . number . . . of discrete output measurements
The structure of equation (1) is general for the representation of any linear and multivariable process dynamics, subject to the constraints that (a) the control inputs u must be constant across interval k--*k+c (this presents no difficulty since this interval becomes that for update of the control signal, which is implemented from a computer); and (b) the disturbance inputs v are measurable and may be approximated as piecewise steps or alternatively as piecewise ramps across the interval k ~ k + c. The structure is convenient for control system design. Since in steady state ~=0, it follows that Yk may be redefined as Ii k Yk =
] (9)
k-s~_
with error term ek=yk--y~; where y~, is a p × l set point vector that defines the origin of the new system. A controller designed on the basis of equation (1) is incremental and incorporates error feedback, two necessary aspects for industrial aovlication. The control obiective becomes to drive
Brief Paper with I YI k, n4 × 1 =
-~
Yk--Yk-c i l Lyk_s~___yk_ c
and I!
--1 k-c-s~- Yk-c ~
: l~,lk_2 _ ~1 Zlk_c,nl + m l - - p x 1,= k-c-~R t - - Y k - l • j
atl may be derived directly from ~t. The structure of equation (10) requires the identification of p×n4 fewer parameters. The output differencing provides greater tolerance to drifting which, for example might arise from aspects that are not measured, To model a process in terms of equation (10), the following must be selected or established, given definition of outputs y and inputs u (a) control interval c; (b) R, the number of samples per control interval and the intervals s I ~s~_ 1 ; (c) the measurable disturbance inputs v that impact upon the system; (d) the delays associated with both control and disturbance inputs; and (e) the process order n, or the minimum effective value of nl. The choice of the control interval c, is subject to the rate of the process dynamics, to the disturbance signal characteristics (with respect to the validity of piecewise linear approximations) and to time delays. The choice of the sampling pattern influences the number of terms R1 that need to be incorporated within the vector lSk-~ [equation (4)]. For example, if n l = n4 so that all samples are collected within one interval c, then R I = I and the structure of Pk-, is a minimum. Aspects associated with delays influence the choice of sampling. If c~s~_~>dl>O, where dl is the largest delay element in the system [accounting for equation (7)] then pR~ + and ),1~+~ are zero. This condition implies that measurements taken in the interval k ~ k + c are collected after the control action of Uk-~ can be seen to be influencing the process. This necessarily applies if samples are taken only at the control instants (i.e. k-jc, j=l--*R1), The above aspects invite a range of options to be considered in the selection of a structure for the process model. Software has been developed to provide the following facilities (1) The injection of sequences of random step changes into the control inputs and the monitoring of the process responses directly using graphics trend displays. The interval between steps is a direct multiple of the control interval c. At this stage, the designer establishes by inspection, the presence and approximate magnitude of delays. It is also possible to establish if the initial choice for the control interval c, the amplitude of the injected perturbations, and the defined time span for collection of data are realistic given consideration of the observed process dynamics and the delays. This experiment must continue until a satisfactory sequence of data is established, (2) The analysis of data, using reeursive least squares
729
and disturbance sequences that perturbed the process. The data generated is then compared with the original. The mean difference and mean square difference between the two sets of data provide numerical figures of merit for the model. Visual inspection and comparison of the model and original data trends is also very informative and gives a valuable subjective interpretation of the quality of the model. Initially, the designer will not know the model structure that gives rise to the best identification of the plant dynamics, unless there is helpful process engineering knowledge at hand. It is therefore usually necessary to apply the analysis a number of times before an acceptable identification is obtained. It is common sense to begin with the most simple structure that is appropriate to the input and output signals that have been selected to relate to the model. Model dimensions and assumed time delays can then be increased systematically until a satisfactory result arises. The graphics displays and the figures of merit gi~.e the designer a feel for the improvements that arise from these systematic adjustments to the structure. If a reasonable model cannot be obtained, then this may point to a need for a retrial of the initial data collection experiment, or to a need for the inclusion of other signals within the mode/ description. The way in which the regenerated data from the model differs from the process data can point to more effective model structures. For example, disturbance effects are suggested if the process and model follow closely and then suddenly deviate.
Control system design Successive manipulation and iteration of equation (1) permits the structure of (11) to be obtained t'-
----~
IVk+~Rl-l~ Zj+l =~t3Zj+/~31 Wj+/~32Wj_ a +r3 ]:1. /} (11) Ix[.Vk_~R~+t~j | with ] Uk-2e Wk-2,= [ i
/"
Z~=Zk-c
Lu~-tRI+~J and the interval j ~ j + 1, R 1 'c of the intervals k--, k + 1. Software has been developed to support dynamic programming (Kuo, 1970; Sandoz, 1973) to minimize the quadratic performance criterion I=
~..
{ZTQZj + W~PW~}. (12) J= ~ This technique is well suited to be applied with the model structure of equation (I 1). The controller that results has the form V~_, 1 Uk-~=GIZ~-c+G2Wk-2~ +G31 i
J
.
(13)
Vk-~R~÷t)~ The parameters of the gain matrices G1, and G2 and G3 define the controller. The disturbance elements are only incorporated in the dynamic oro~rammin~ for the ~ta~,~ ~= t
730
Brief P a p e r
only a single input and output, then it reduces to
Uk--Uk_~=gl(yk--ys~)+g2(yk_~--yss), C>S l.
(14)
Control system design software has been developed to provide for (a) specification of the elements of the weighting matrices Q and P and the number of stages M; (b) computation of the controller gains; (c) simulation of the resulting controller and the graphical display of its response in application to the derived process model. Disturbances are included at this stage as random sequences. If response is unsatisfactory the designer repeats the procedure from stage (a) until he is satisfied with the control performance. The weighting matrices Q and P are thus re-adjusted in a successive manner. A criticism often levelled at controllers that are based upon minimization of a quadratic cost criterion is that the selection of the elements of the weighting matrices to achieve particular control system performance is a black art. In the context of the structure described here, the following considerations are relevant (1) The vector Z in equations (12) and (13) is compounded of successive samples of error (measurement less set point). The vector W is compounded of successive increments in the input signals. (2) The interpretation of off diagonal elements in Q and P is difficult. It is reasonable to restrict these matrices to a diagonal form. (3) Given the diagonal restriction, the relative magnitude of the diagonal elements in Q reflects the urgency with which the measurement errors are to be zeroed relative to each other, e.g. a large weight relating to one error, in comparison to a small weight relating to another, indicates that the former is to be zeroed more quickly, (4) The inclusion of diagonal elements in P introduces a constraint on the amounts that the associated inputs change and therefore give rise to a slower overall response, On the basis of these and other aspects, the designer quickly establishes a feel for the impact of various elements and is able to home in on a satisfactory combination. The control parameters are then passed forward for implementation and the final test online,
Generalized facility for design and implementation A complete facility has been developed, incorporating the computer aided design aspects already described, with the means for implementation of the control systems online in a structured hierarchical form. The conventional approach for the implementation of industrial process control systems, is to consider the plant that is to be controlled as a number of sub-systems. At the most simple level, these might be flow or temperature loops with the control actuation signal driving some physical aspect of the plant, such as a valve. More complex sub-systems incorporate these simple loops and the controllers (which will now regulate parameters more remote from the plant inputs or with longer time constants), cascade set points to actuate the simple loops. This philosophy has been maintained in the approach described in this paper. The object is not to derive an overall dynamic model to define the plant characteristics, It is to obtain a set of models for sub-systems and to incorporate controllers with each before proceeding to consider the next sub-system. Thus the identification and control application advances in a systematic fashion until the total olant complex is incorporated within the structured
consideration has been to make the software as flexible as possible, so that, by straight forward specification of data, valid application can be made to a wide variety of plant control situations. The real time system provides for (a) plant control and the application of perturbation trials to collect data for analysis by the CAD programmes; (b) plant operation with facilities for data logging either to terminals or to disk files; start up and shut down of plant operations; alarm detection and reporting; definition of control requirements, set points etc; and trend graphics; (c) interfacing with the CAD programmes via disk file. The offline system supports the least-squares, dynamic programming and simulation software that integrates with the interactive graphics to provide the full CAD facility. Overall, therefore, the designer is provided with the facilities to investigate a wide variety of control system options that are appropriate for application. The appendix briefly overviews the main stages associated with the CAD procedures. A flow diagram is presented to emphasize the coordination of the design phases described above. Using the CAD facilities, the designer may build a complete structure of control systems to cater for total plant control.
Examples ofapplicati,m The control systems that have been implemented on the milk powder plant are listed in Table 1. The first six systems have been applied to the evaporator and the remainder to the spray drier. A brief description of the milk powder plant is presented so that the control systems may be appreciated. A schematic illustration of the evaporator is shown in Fig. 3. Skimmed milk is pumped to the evaporator at a particular flow rate and passes through preliminary pre-heat stages. At the main pre-heater, steam is injected directly into the milk to raise its temperature to a required value. The milk then feeds to the first evaporation effect. The concentrated product emerges from the third effect. Steam is supplied to a steam jacket that surrounds the first effect, providing the energy for the initial evaporation. Steam evaporated from the milk provides the energy for subsequent effects. Steam from the third effect is condensed to provide the pressure differential across the plant. The milk takes between two and three minutes to propagate through the plant. The product density and flow rate vary according to the density and flow rate of the supplied milk and also according to the steam supply. The temperature differential across the plant influences the quality of the fmal powder product. A more detailed description of the multiple evaporation plant is available (Sandoz and Wong, 1978). With reference to Table 1, systems 1 to 4 regulate the steam, milk and water supplies to the evaporator. Each of these systems can be designed independently since there is little interaction between them. Note, however, that there is interaction within system 1 that necessitates a multi-variable solution. The order of design and implementation is not important. These systems constitute a base level of control designed to minimize variations in the supplies and thereby reduce disturbance to the plant. Systems 5 and 6 cascade set points to the base level and constitute the second level. These latter systems control aspects associated with the production end of the evaporator. Concentrated milk from the evaporator is pumped to the spray drier at a controlled rate. A large fan maintains an air flow through the drier. This air is heated by a gas burner and its temperature may be regulated by adjusting the flow of gas.
Brief Paper
731
TABLE 1. LIST OF CONTROLSYSTEMSIMPLEMENTED System 1
Measurements
Controls
Rate of flow of milk to evaporator
Pump in milk feed line
Milk pre-heat temperature
Valve in steam injection line
2
Steam flow to steam jacket of evaporator
Valve in steam line
3
Condenser water flow rate
Valve in water line
4
Interstage ejector temperature (condenser)
Valve in water line
5
Pressure in terminal evaporation stage
Set point to controller of system 3
6
Milk density
Set point to controller of system 2
7
Milk flow to spray drier
Pump in milk feed line
8
Inlet air temperature to spray drier
Valve in gas line
9
Spray drier chamber pressure spray drier air flow
Dampers in inlet and exhaust air lines
Features Multivariable system with 2 inputs and 2 outputs Time delay of 4 s associated with temperature measurement Disturbance due to variation in pressure in steam main
Time delay of 30 s
Disturbances due to rate of milk flow and supplied milk density Time delay of 2-3 rain
Multivariable system with 2 inputs and 2 outputs
Condenser water in
1 Milk in
in
_J
] BarometriCcondenser
L
Co¢~enser wafer out our out M i l ; out Main prB-h*~er I
A
i~
i,
I"--I
Concentrated product
I " - - I ~I,o_
I
732
Brief P a p e r
evaporator and the humidity of exhaust air from the spray drier. The major problem associated with these aspects is the generation of consistent and reliable measurement rather than one of process control. In summary of the control systems, the controllers associated with systems 3, 5, 7, and 8 are straightforward, with the minimal structure of equation 14. Systems 1 and 9 require multivariable controllers, involving 2 inputs and 2 outputs because of interaction within the plant. The remaining systems are single input and output but involve time delays and disturbances. Two of these sub-systems are now discussed in detail to demonstrate the features of the design procedures. These are system 9, air flow and pressure control for the spray drier, and system 6, milk density control for the evaporator. These systems are chosen because the complications of interaction, time delay and disturbance associated with them, make it difficult to establish effective control system performance by conventional industrial means, Spray drier system (Control system 9). It is desirable, for the production of milk powder of consistent quality, to have both the rate of flow of air through the chamber and the pressure within the chamber closely regulated. These two quantities interact and the problem must be treated as a multivariable one. Figure 4 illustrates a perturbation experiment carried out on this system of the spray drier. Both the inlet and exhaust air dampers (parameters 3 and 4) are stepped with randomly varying amplitudes at intervals of 48 s. These amplitudes of variation cover about 25 ~o of the full actuation range of the dampers. Superimposed upon the airflow and pressure characteristics in Fig. 4 (parameters 1 and 2) are the characteristics obtained by subjecting the derived least squares model to the same disturbing sequences. This model is established for a control interval c of 8s and a single sampling interval s, of 4 s. It represents the best characteristic that could be established via the interactive modelling procedure. The model has second order dynamics (n=2), with R = 1 and n4=4. It is evident from Fig. 4 that nonlinear and/or time varying influences are present, but that the model is still reasonably representative of process behaviour. Equation (15) details the controller derived via the interactive design procedure, with ul and u2 the inlet and exhaust damper positions, yl the inlet air flow and y2 the chamber pressure, yl~., and y2~ define the set points associated with yl and y2, respectively
][
15.7
LU2k --U2k-8 =
9.1
ul k
--Ulk_ 8
[-ylkr [ y2k
--9
ylk_ 4
[__y2k 4
--4.9
09]
--2.5
1.1
--yl,~|
/
_y2s ~
×
(15)
--yl,,|'
--y2s,
/
Figure 5 illustrates online control. A sequence of changes to both the pressure and the air flow set points is introduced. The controller compensates for the interactions and follows the set points effectively. The short-comings in the model because of the non-linear influences are of no apparent significance. These arise mainly because of stiction and hysteresis in the dampers. Inspection of Fig. 5 clearly indicates the interaction in this system. Both dampers have to adjust significantly and simultaneously to effect the set point changes. Evaporator system (control system 6). It is desirable to have the density of the milk produced by the evaporator closely regulated to be consistent with the needs of the spray drier. The spray drier requires that the flow of milk from the evaporator be adjusted occasionally, but with density unchanged. There are three main factors that influence the density of the milk produced by the evaporator. These are of the flow of steam to the first evaporation stage, the inlet flow rate of milk to the evaporator and finally, the density of the milk supplied to the evaporator. Figure 6 illustrates an experiment carried out on the evaporator. Perturbations are injected from three sources. The set points to lower level controllers for the milk inflow rate (+ 301/h around 17501/h) and the steam inflow rate (+ 10 kg/h around 440kg/h) are adjusted at 2min intervals (parameters 5 and 7). The density of the incoming milk (parameter 8) is adjusted less frequently by adding either milk of higher concentration or water. The variations in milk density and the superimposed model characteristic (parameter 6) are also illustrated in Fig. 6. Again, the model is not perfect but it does demonstrate enough similarity to give confidence that an effective controller can be obtained. The model is based upon a
I 8 kg Imin High
2 Z5 m bar a. and model
l
Exhaust air
damper
I
8.1
I
25%1 f . s . d
Brief Paper
733
Air flow rate and set point High
yl A
A
25 kg / min /
=
A
~.~~.Chamber
A
I~.I-
pressure and set point
2- ul
25% f.s.d
/
2
2I% f.s.d. position
Low
Time,
I 500
s
FIG. 5. Spray drier, set point control Low 87 kg/min 0.987 bar a 40 % f.s.d. - 2 5 ~o
1. Air flow rate 2. Chamber pressure 3. Exhaust damper position 4. Inlet damper position
Milk inflow rote
~
High
High 97 kg/min 1.007 bar a 140 ~ f.s.d. 75 ~o f.s.d.
l /
5 75 I / h r ~
~
~
Product density_
//~
.
t
50 kg/h
~ Low 0
~
~
~ J ~ Milk input density Time, S
8 I!kg/m 3 I 4800
FIG. 6. 5. 6. 7. 8.
Milk inflow rate (set point) Product density Steam flow rate (set point) Milk input density
control interval of 60s, with intermediate intervals si =20s
Low 14501/h l140kg/m 3 400kg/h 1030kg/m 3
High 17501/h 1200kg/m 3 520kg/h 1070kg/m 3
the steam has to be adjusted to compensate for changes in
734
Brief Paper
High
/
\
\
t
F--"
Milk inflow rote
.__/
60 I / h r
/
5 1
•
. ~//("
1 2 . 5 kg / m
set point
m flow rate
3
25 kg/hr , , .
LOW
I
180
Time, s
FIG. 7, Simulation of evaporator control Low 5 Milk inflow rate (set point) 6. Product density 7. Steam flow rate (set point)
Milk inflow rate
High
1500 l/h ll50kg/m 3 400kg/h
1750 l/h 1200kg/m 3 500kg/h
/
/
High
60II/h 5
t t
' l 25 I / h
~
Low
-~
_ _
~,_
~
8
I0 kg
/m 3
input density
Milk
0
Time,
I 6500
s
FIG. 8 Evaporator, set point control 5. 6. 7. 8.
Milk inflow rate (set point) Product density Steam flow rate Milk input density
discrepancies observed at the modelling stage (Fig. 6) and is caused by unmonitored factors that influence the process (such as steam supply pressure variations), Conclusions and discussion The design of controllers for 8 of the 9 subsystems associated
Low 14001/h 1140 kg/m 3 400 kg/h 1035 kg/m 3
High 17501/h 1200 kg/m 3 500 kg/h 1075 kg/m 3
Fig. 6 lasted for over 2 h. It was difficult to establish perturbation ranges for signals 5 and 7 that resulted in the milk density remaining within an acceptable operating region throughout the course of the experiment. The model as illustrated in Fig. 6 was obtained quickly using the interactive procedure once acceptable data had been established.
Brief Paper designs rely upon trial and error associated with simulation. Aids to prompt the designer to a realistic choice of options would be valuable, this particularly so in establishing the most effective structure for the process model. The dynamic programming method may not be the most appropriate for control system design. It would be advantageous to utilize some design procedure that leads the designer via a more direct route to the desired response characteristics. A problem with evaporators is that their characteristics slowly change (a) in the short term because of milk burning on to the interior tubes thereby altering heat transfer coefficients; and (b) in the long term because the properties of the milk supply (viscosity etc.) alter throughout the dairy season. Such difficulties are associated with many industrial processes. Similar effects occur with plant that is nonlinear when the plant is required to adjust from one operating point to another. These problems suggest a need for periodic re-identification and upgrading of controls to keep them in tune with the plant or for an adaptive/self-tuning mechanism so that the controllers are always set correctly. These aspects, together with a need for a more straightforward control system design procedure, provide interesting possibilities for further application studies,
Acknowledgements--The authors are grateful to the New Zealand Dairy Research Institute, IBM (NZ) Limited, The New Zealand Department of Scientific and Industrial
735
Research and Massey University for supporting this project. They also wish to thank Professor J. K. Scott for his consistent support for this work.
References Batey, D. J., M. J. H. Sterling, D. J. Antcliffe and S. A. Billings (1975). The design and implementation of an interactive data analysis package for a process computer. Comp. Aided Design 7, 265. Hasting-James, R. and M. W. Sage (1969). Recursive generalised least-squares procedure for online identification of process parameters. Proc. lEE 116, 2057. Kuo, B. C. (1970). Discrete Data Control Systems. Prentice Hal/. Munro, N. (1979). The UMIST control system design and synthesis suites. IFAC Symposium on Computer Aided Design of Control Systems, Zurich, pp. 343-348. Sandoz, D. J. (1973). Optimal Control of linear multivariable systems based on discrete output feedback. Proc. lEE 12,0, 1439. Sandoz, D. J. and O. Wong (1978). Design of hierarchical computer control system for industrial plant. Proc. lEE 125, 1290. Wiegand, J. (1971). Falling film evaporators and their application in the food industry. J. Appl. Chem. and Biotechnol 21,000. Young, P. and R. Jakeman (1979). The development of captain: a computer aided programme for time-series analysis and the identification of noisy systems. IFAC
Symposium on Computer Aided Design of Control Systems, Zurich, pp. 391-400.
Flow diagram of CAD procedures
A
B
C
Select £irst/next sub-system ~- of the plant that is to be controlled Define the measurements, actuations -----4~and disturbances associated with the sub-system Perturb~and/or monitor the plant to get data No Check if data suitable ~--- {C)
t~e Yes Poatula the characteristics of the D --'-"4~model (order, intervals, delays etc. )
Identify the model parameters
No
Check if model is satisfactory
I~
Yes
E
S e l e c t elements of weighting - - ~ " m a t r i c e s for control system design
Calcula/e controller gains Simulate~ the controller (working on the model) and inspect the performance
Have all options re c h a r a c t e r i s t i c s been tried? No (D)
(B)