NEURAL NETWORK BASED CONTROL OF MINERAL GRINDING PLANTS
F. FLAMENT §, J. THIBAULTt and D. HODOUIN §
§ Department of Mines and Metallurgy, Laval University, Sainte-Foy (Quebec) Canada G1K 7P4
t Department of Chemical Engineering, Laval University, Canada (Received 21 May 1992; accepted 11 August 1992)
ABSTRACT
This paper considers the identification o f the dynamics and the inverse dynamics o f a simulated grinding circuit, using feed forward neural networks. Various control strategies based on the plant and plant inverse neural models, with and without adaptation, are presented. Finally, the results o f some control strategies are evaluated and discussed.
Model based control has now gained sufficient notoriety to be accepted and implemented in traditional processes with relatively good success. Some processes offer greater difficulty for finding an acceptable plant model because they are highly nonlinear and time-varying. In addition, it is not always obvious to decide on a structure of a proper model. An industrial grinding circuit, where ore grindability may significantly vary over time and recycle streams are present, is indeed a difficult process to model and control. It is important to react as quickly as possible to changes in the process in order to alleviate upset in the downstream processes.
A promising alternative for the modelling of complex systems seems to be artificial neural networks which have the ability to capture the non linear dynamics of the process from the input/output data set. The network architecture that appears to offer more potential for the type of engineering problems encountered in identification and process control is the feed forward neural network. This network normally consists of several layers of processing units (or artificial neurons) where neuron connections occur only between adjacent layers as schematically shown in Figure 1 for a three-layer feedforward neural network. The squares simply indicate that each input is redistributed to the neurons of the next layer. The neurons, represented with circles, perform a simple task which consists of performing a weighted sum of all the inputs arriving at the neurons, and then applying a transfer function to this weighted sum. A single neuron performs very trivial tasks. However, artificial neural networks take their modelling power from the cooperative effort of individual neurons working in parallel in a similar fashion as computation is performed in the brain. The two most popular transfer functions for continuous systems are the sigmoid and hyperbolic tangent functions. These two functions are respectively bounded between 0 and 1, and -1 and 1 and they are differentiable. It is the addition of hidden layers with neurons using a differentiable non linear transfer function that gives multi-layer networks better representational abilities. Hidden layers act as layers of abstraction, extracting features from the learning data set [ 1 ]. In essence, a feedforward neural network can simply
235
236 F. FLAMENT et al.
be viewed as a nonlinear model and the parameters of the model are the weight connections between neurons of adjacent layers [2,3,4].
An experimental program has been set up to investigate the control of a simulated industrial grinding circuit using a number of control strategies based on feedforward neural networks. This paper briefly describes the main control strategies that were evaluated, and the results obtained with some of them are presented and discussed.
THE GRINDING DYNAMIC SIMULATOR
General Description
The dynamic simulator used is the PC version of the general dynamic grinding circuit simulator DYNAFRAG [5]. The simulator is written in APL, which compromises greater flexibility for slower execution (as it is an interpreted language). The choice lies in its interactive and modular structure, which both allow a rapid program development and an easy implementation of new features such as new modules.
The user accesses the various input modules through convenient menus and windows. These modules refer to the set-up of model parameters and definition of the control strategies and the possible addition of generated noise to simulate sensors and actuators. The unit models contained in DYNAFRAG are: rod mill, ball mill, fixed-separation curve classifiers, hydrocyclones, mixers, sump boxes, pumps, pipes and conveyor belts.
The dynamic model of the process basically consists of a set of mass balance equations for the pulp, the water and the particles of different mineral hardness. This implies a total of 50 to 100 simultaneous differential equations to be solved.
Simulated Plant Flowsheet
For this study, the units tisted in Table 1 were implemented in the simulator in an arrangement depicted in Figure 2. In addition to these major units, five actuators (u i) and
Neural network based control 237
eight sensors (mi) are part of the simulated circuit as they introduce dynamic components to the system response. These items are also listed in Table 1 and illustrated in Figure 2. Finally, five internal variables (Pi) can be manipulated by the user, in order to easily introduce realistic perturbations to the process (see Table l and Figure 2).
TABLE 1 Main features of DYNAFRAG simulated circuit
u n i t m o d e l s
Belt conveyor to rod mill Rod mill + water addition point Sump box + water addition point Variable speed pump Cluster of hydrocyclones Ball mill + water addition point Pipes
a c t u a t o r s
u l Fresh ore feed rate controller u2 Water addition valve to the rod mill u3 Pump speed controller u4 Water addition valve to the sump box u5 Water addition valve to the ball mill
s e n s o r s
ml Ore flowrate to the rod mill m2 Pulp level in the sump box m3 Volumetric pulp flowrate to the cyclones m4 Volumetric percent solid in cyclone feed m5 Volumetric pulp flowrate of cyclone overflow m6 Volumetric percent solid in cyclone overflow
m7 Percent passing 200 Mesh (75~m) in cyclone over- flow
m8 (not assigned yet) perturbations
pl Composition of the ore fed to the circuit p2 Size distribution of the ore fed to the circuit
p3 Specific gravity of the ore fed to the circuit
p4 Sump/pump behaviour p5 Hydrocyclone behaviour
Actuators (ui) and sensors (mi) are simulated using additive noises (a i or n i) to the desired actions (manipulated variables) or to the measured values. Various types of noise are provided within DYNAFRAG and more specific models or time series can be programmed by a user with some experi~nce in APL language. The available noise patterns are: white noise, step, ramp, AR, MA, ARMA models, PRBS and PRTS series.
238 F. FLAMENT et al.
ul pP~ U2===A g==U4 I
u3 m3 m4
Fig.2 DYNAFRAG simulator plant flowsheet.
The Unit Models
Ore description. The ore is assumed to be composed of two components, each having its own characteristics in what concerns flowrate, size distribution, hardness and specific gravity. Such a feed ore model permits the study of the influence of changes in hardness, size distribution and specific gravity (perturbations) on the quality of the final product and on the process behaviour. Both ore hardness and feed size distributions are categorized in three levels. These are hard, medium and soft for ore hardness, and coarse, medium and fine for feed particle size distribution.
Rod mill feed conveyor model. The conveyor is modelled using a pure delay of 35 seconds. At present, the simulator does not permit to modify this value interactively.
Rod mill model. The rod mill is modelled using two identical ball mills in series. A kinetic model is used for each ball mill. The values of model parameters (breakage matrix, selection function and residence time distribution) were obtained by retrofitting experimental size distribution data provided by a company. At present, these values cannot be entered or modified interactively. They must be introduced in the source code.
Pump sump box and pipe models. The pump model corresponds to the pump characteristic curves. The sump box is represented by a cubical open perfect mixer, with a maximum capacity of 10m 3 (2m x 5m2). The connecting pipes (suction and discharge ends) are modelled using variable pure delays.
Hydrocyclone model. A steady-state model is perfectly justified for the hydrocyclones as their response time is much shorter than that of the other main units (ball and rod mills). The model used by DYNAFRAG is Plitt's model, which implies the calculation of the cyclone pressure drop, the underflow/overflow pulp distribution, the classification cut-size (ds0c) , the solids separation efficiency and the water short circuiting. A different model for the fine particle short-circuiting to the underflow is also implemented in the simulator [6,7]. All calculations are based on the cyclone dimensions and operating conditions. Five adjustable coefficients permit the calibration of the model to the available grinding circuit data. The cyclone dimensions and the model parameters can be modified interactively.
Ball mill model. This model is the most important feature of the simulator, as it determines (through both the rod mill and the ball mill) most of the dynamic behaviour of the circuit. The dynamic model of the ball mill is based on the description of three particular phenomena [5]:
l) 2) 3)
the mill content mixing, the mill pulp volume variation and the grinding kinetics.
Neural network based control 239
The mixing properties are described by a series of two perfect mixers in the case of the ball mill and four in the case of the rod mill. The pulp volume variation within the mill is modelled by a series of interactive tanks and the grinding kinetics by the breakage and selection functions model.
The Control Strategy
The control strategy used in this study consists of three loops:
loop l:one ratio controller to control the rod mill pulp density by the water addition to the mill,
loop 2:one local PI loop to control the sump box level by the pump RPM and
loop 3:one neural network to control the cyclone overflow fineness by the water addition to the sump box.
In this study, the circulating load level is not controlled. Obviously, there is an interaction between the controllers. A water addition increase, applied to improve the product fineness, will result in an increase of the pulp level in the sump box. The PI loop will respond by increasing the pump speed to avoid overflowing. It is interesting to notice on Figure 3 that the pair of variables (water addition, product fineness) demonstrates an initial behaviour with a high gain and a final behaviour with a small gain. We have observed that such a behaviour cannot be controlled efficiently with a PI controller only. For the experiment reported in Figure 3, both loops 1 and 2 were closed.
Fig.3
3 I . . . . . . . . . i , , i , , , I , , , i
69 m7
6 7 ' , , , , , , , , , , , , , ,
0 1 2 Time (hours)
% passing 200 mesh f9llowing a step change of the water addition to the sump box.
NEURAL BASED CONTROL STRATEGIES
This section briefly describes the various control strategies that were evaluated in this investigation. However, only a few will be illustrated in the results and discussion section. All neural based control strategies rely strongly on the identification of an accurate neural transfer function. Therefore, before describing each of the control strategies, a brief account on the identification methodology is presented.
Identification Methodology
This is undoubtedly the most important aspect since the design of effective controllers depends greatly on how well the dynamics of the controlled process is known. The identification of neural models is akin to the identification of linear systems using ARMA models. In fact, traditional convolution and ARMA dynamic models are equivalent to a two-layered linear feedforward network model [8]. For the identification of the neural plant dynamics and its inverse, it is respectively assumed that the output and the manipulated variable can be reconstructed from a finite number of past values of the input
240 F. FLAMENT et al.
and output. A neural transfer function can be constructed with the feedforward neural network of Figure 1 with the input and output vectors defined in Table 2. For instance, the controlled output of the plant, at the next sampling instant, is predicted from the current and two past values of the output (m 7 - the percent passing 200 mesh in cyclone overflow), three values of the manipulated variables (u 4 - water addition to the sump box), sufficiently delayed and three values of an internal variable, the circulating load (CL). The circulating load can be calculated from~measured variables, it is a "measure" of the level of operation of the process. This neural transfer function was constructed from the first column of Table 2. The pure delay between the manipulated and controlled variables was found with experimentation and crosscorrelation function to be equal to one sampling period. When the structure of the neural network is selected, the identification process boils down in finding the values of the connection weights, Wij and Wjk, of the feedforward neural network that minimize the sum of squares of the errors between the predicted and target output, using an optimizing procedure. In this investigation, backpropagation and quasi-Newton were used as learning algorithms.
TABLE 2
Input Neurons
1 2 3 4 5 6 7 8 9 10 11
Output Neuron
Neurons in hidden
layer
Number of Parameters
Input/output information of neural models
DNC
roT(t) mT(t-1) m,(t-2)
u,(t) u,=(t-1) u4(t-2) CL(t)
CL(t-1) CL(t-2) 1 (Bias)
mT(t+l)
INC
mT(t+l) m7(t)
mT(t-1) mT(t-2) u4(t-1) u4(t-2) u4(t'3) CL(t)
CL(t-1) CL(t-2) 1 (Bias)
u,(t)
61 56
IDNC
AmT(t+l ) A~(t)
Am~(t-1) Au,(t-1) Au4(t-2) 1 (Bias)
Au,(t)
6
36
The model described in the previous paragraph is referred as direct plant and will be used with the direct neural controller. The other two columns of input and output variables in Table 2 are respectively used to determine the inverse plant dynamics model and the inverse differentiated plant dynamics model. All these three neural transfer function are used amongst others in various control strategies. These will be described in the following sections. All the input and output variables within the various models were scaled into the range of 0 to 1 (with a sigmoid function) and -1 to 1 (with a hyperbolic tangent function). The number of neurons in the hidden layer was set to six. Table 2 also provides the number of parameters to identify. The number of parameters is significantly larger than the number of parameters normally found in ARMA models.
Direct Neural Controller
Once a neural transfer function of the plant (Figure 1 and first column of Table 2) has been identified, it can be used as a one-step ahead predictive controller where at each sampling
Neural network based control 241
instant, a control move is determined in order that the estimated output of the plant equals to the desired setpoint [9]. The direct model can also be used recursively (the estimated future output values are used as inputs to the network to estimate the next future output values) in model based predictive control strategies where an optimization routine is used to determine the optimal sequence of future control moves to minimize an objective cost function, subject to some inequality constraints. However, only the first control move of the sequence is implemented. A new optimal sequence is then computed at the next sampling instant and so on. This is the basic configuration of a direct neural controller, denoted DNC. To avoid any misunderstanding, direct refers here to the neural model and not to the control strategy. The neural model is direct since it predicts the process output from the process input. The control strategy would rather be indirect in this ease since the controller (the neural network) does not computes the next control move. The next control move is determined by an optimization routine (see Figure 4): it is the control move which, when applied to the neural network model, gives a predicted process output (thT) as close as possible to the desired set-point (roT). In this study the following criterion is used:
J = ]C(thT-m-;)Z
The action (u4) applied to the process is the action which minimizes J. u 4 is searched on an interval around the action taken at the previous time lag.
+(--,L
t
m;
k(m-~ - m7) i i=O
• u / U4,corr ;iOPT'M'Z'NO ROUTINE 2[
FUTURE m7
I NEURAL ~ FUTURE U4,ne t
MODEL J
PLANT
Fig.4 Diagram of a DNC-I strategy.
m 7
A good neural transfer function contains the main features of the dynamics of the plant since it has learned from an unsteady state data set. However, there is no guarantee that there will be no offset under steady state conditions. To alleviate this problem, a pure integrator can be added in parallel to the DNC as presented in Figure 4. The lower portion of the diagram is the direct neural controller and the upper part is the parallel integration loop. The control move is then the additive contribution of the manipulated variable calculated with the neural transfer function and the output of an integrator as described by the following two equations:
u4(t) = u4,Network(t) + U4,Corr(t) (1)
U4,Corr(t) = U4,corr(t-1) + k[m~(t)-mz(t)] (2)
This controller is denoted as DNC-I (Direct Neural Controller with Integration). Similar results would be obtained if only the weight associated with the bias of the output neuron
242 F. FLAMENT et al.
was modified by backpropagation using the measured offset. Both correction schemes are excellent when it is believed that the dynamics of the system has not significantly changed from the dynamics that prevailed at the time of identification. Another alternative is to use
• • t . .
the predlct~on error of the controller (m r - m r) to directly adapt the neural transfer function of the plant. This has the advantage that both the dynamics and the offset are considered simultaneously in the adaptation of the model. However, if the process is nearly under steady state conditions, it is possible that the neural model will unlearn the dynamics of the plant trying to correct for the offset. Care must be exercised to make sure that the learning data are sufficiently informative about the dynamics of the system. This control scheme is denoted as DNC-A (Direct Neural Controller with Adaptation).
The online neural model adaptation can be performed in two different manners. In the first adaptation scheme, at each sampling instant, the current prediction error is used to correct the connection weights of rite neural model with a single backpropagation iteration. In the second adaptation scheme, data contained in a fixed length moving window are used to adapt the network by performing a number of iterations with one of the learning algorithm. The weighting of the data within the moving window can be uniform, triangular or exponential.
An identical control strategy can be used with a neural model that has learned with a data set containing the variations of the input/output variables, between two consecutive sampling instants, instead of the values of the variables. Therefore, rather than to evaluate the control move to give the target output, the optimizing routine calculates the change in the control move that will return the output of the process to its desired setpoint, provided no constraints are being violated. In other words, an incremental control move is calculated to predict a network output that is equal to the negative of the current error signal. This control scheme, denoted as DDNC (Direct Differential Neural Controller), has the disadvantage to learn the average dynamics over the full operating range of the process since the knowledge of the dynamics of the process, acquired by the network, is independent on the level of operation. This may result in a loss of performance during the transient behaviour of the process but may show an improvement under steady state conditions by reducing possible offsets. However, the addition of the level of operation as an input to the network would improve the dynamic performance. This control strategy could also be used in conjunction with adaptation.
Inverse Neural Controller (INC)
An important feature of neural networks is the possibility to generate the inverse plant dynamic model from input/output data sets, and to calculate explicitly the manipulated variables in order to bring the process output back to its setpoint value. There are no iterations involved. For the grinding circuit, the inverse plant dynamics was modelled with a feedforward neural network with the input and output variables listed in Table 2. The INC is a feedforward controller that anticipates the control action that will produce the desired output of the plant. Here inverse refers to the neural model which inverts the process dynamics: the process input is computed from the process output. The control strategy based on the inverse neural model would rather be direct since the controller computes directly the next control move.
The INC can also lead to an offset under steady state conditions and there is no way for the network to know if the correct control move was determined. A pure integrator, similar to the DNC-I can be added to correct the offset. This controller is denoted as INC-I. The inverse plant model can also be adapted based on the difference between the actual and the desired outputs of the plant (INC-A). However, with the inverse model, the plant is located between the neural model and the error signal of the plant output so that the learning rules, such as back-propagation, cannot be used directly to adapt the inverse neural model [10, 11]. The problem is in the evaluation of the error signal on the manipulated variable that corresponds to the error signal available at the output of the plant• Many schemes, to evaluate the error signal on the manipulated variables, have appeared in the literature [12]. The approach that was retained in this investigation relies on the evaluation of the Jacobian
Neural network based control 243
obtained analytically by differentiating the equations of the feedforward neural network. In order to adapt the weights of the inverse neural model, using the baekpropagation algorithm after each sampling, the estimated error on the control move (u 4 - u4),at the previous sampling instant has been determined from the error on the output (m.r- mr) determined at the current sampling instant with the following relation, using the nomenclature of both Figure 1 and Table 2:
The partial derivative can be calculated from the inverse neural model which has learned to give explicitly the control move u t. If the position of the target output value mr, t+ 1 in the input layer of the neural network is i=n, an estimate of the plant inverse Jacobian can be obtained by the following equation:
J J I 0u4, t /0mr, t+l = f'[ "~1Wj 1Hj][ . ~ Wj l f ' ( 5"2, W i iXi)Wnj](SJSm)
J= J=l i=1 " (4)
where s u and s m are the scaling factors applied respectively to u 4 and m r before being presented to the neural network. Indices i and j refer to the position of the neurons in the input and hidden layers which contain respectively I and J neurons. X and H are respectively the outputs of the input layer (scaled variables of Table 2) and of the hidden layer, f " is the derivative of the nonlinear transfer function. It is important to note that the correction of the network, performed at time t, considers the error on the manipulated variable at time t-1 because it is necessary to wait the number of sampling periods corresponding to the pure delay between the input and output of the process, in this case equal to one for a sampling period of 2 minutes.
Similar to a DDNC, an Inverse Differential Neural Controller (IDNC) can also be used where input/output variables, following a first order differentiation, are used for teaching the network. The main advantage of this strategy is the natural incorporation of the constraint on the control action. The list of variables used with this network are given in the last column of Table 2.
Another interesting control strategy, is to use both the direct and the inverse models of the plant dynamics in an internal model control (IMC) structure [8,13].
ILLUSTRATIONS AND DISCUSSION
Training Data Set
The training data set was generated using DYNAFRAG. After a steady state has been computed, the water addition to the sump box (u4) was manipulated at a sampling rate of 2 minutes according to a gaussian white noise. It was centred for a first experiment around 88m3/h and for a second experiment around 98m3/h. In both experiments, the noise standard deviation was 5m3/h. The various sensors signals were recorded in data files during 10 hours. Then, cross correlation studies have demonstrated high positive correlations at lag 1 between u 4 and m r (the final product fineness) and between u 4 and the circulating load CL (computed from the values of sensors m3, m4, ms, m 6 and the ore specific gravity). These results were used to test different patterns of neural networks for their applicability to control the final product fineness. When generating the training data set, both control loops 1 and 2 were closed.
Direct Neural Controller
Here, the objective of the neural network is to mimic the grinding circuit behaviour and to predict the future product fineness. Several input layer patterns were tested and the best
2 4 4 F . F L A M E N T et al.
compromise between a good prediction and a small number of input neurons was obtained using the past 3 values of m r, the past 3 values of u 4 and the past 3 values of CL (see Table 2 and Figure 1). Six intermediate neurons were found to be sufficient.
The network was then implemented in D Y N A F R A G as a controller. On Figure 5 is shown the response of the controller to a change of setpoint f rom 67.3% to 68% passing 200 mesh in the final product. As can be seen, the controller response is originally fast, but the new steady state obtained is not at the requested setpoint of 68%.
u4
104
96
88
Fig.5
m7
I I ' ' ' ' ' I ' ' ' ' ' I ' ' ' ' ' I ' ' ' ' ' I
68.2
67.6 ,..:?
, . . . . , . . . . . , . . . . . , 6 7 0 1 2 3 4
Time (hours) Variations of the controlled (m 7) and manipulated (u4) variables
for a setpoint change under DNC strategy.
To remedy to the problem, an integrator was introduced. A calibration of the integrator constant k (see Eq. 2) was~ then performed. On Figure 6, the sums, over 4 hours of processing, of the squared deviations to the setpoint are plotted for various values of the integrator constant. A value of 0.5 was retained as a good one. The corresponding controller response can be found in Figure 7. By comparison to the results of Figure 5, the improvement is drastic on a long term basis.
- i * , , t i a l , , . . , i . . , , , I , . , , . i
0 1 2 3 4 Time (hours)
m7
68.1
67.7
67.3
Variations of the controlled (m7) and manipulated (u 4) variables for a setpoint change under a DNC-I strategy (K=0.5).
Inverse Neural Controller
The neural network purpose is here to inverse the process dynamics and to predict which action should be taken to obtain the desired process output. After having tested several network patterns, a good compromise was obtained with the network described in Table 2. The past 3 values of the process output (mz), the past 3 values of the action (u 4) and the past 3 values of the circulating load (CL) are again used. But in addition the first neuron is fed, during training, with the value of m 7 resulting from action u 4, the value being learned at the network output layer. During prediction, the same neuron is fed with the desired setpoint value.
The network was implemented in DYNAFRAG as a controller. On Figure 8 is shown the response of the controller to a setpoint change of 67.3% to 68% passing 200 mesh in the final product. As can be seen, the controller response is good but again a slight bias exists at steady state.
Fig.8 Variations of the controlled (mr) and manipulated (u 4) variables for a setpoint change under INC strategy.
An integrator was implemented to remedy to the bias problem. For calibration, the same procedure as before was followed and the results are presented in Figure 9. The value of 0.5 was retained and the corresponding process output is given on Figure 10. By comparing Figure 10 to Figure 8, one can see that the improvement is mainly obtained during the first two hours after the change of setpoint.
Inverse Neural Controller with Weight Adaptation The following application is derived from the previous one. When a neural controller is used without any integration, a bias may be observed on the setpoint. In the present case, at least two reasons may explain this phenomenon. First, the new steady state does not
246 F . F L A M E N T et al .
correspond to a state learned by the network at training time. Second, during the training phase, the neural network seems to have learned only the high initial gain exhibited by the process (see Figure 3). When the new steady state is almost reached, the network is just not capable of providing the correct action which corresponds to a much smaller gain. There are two dynamical behaviours, only one of which was learned.
Fig.9 Sum of squared deviations to setpoint as a function of the integrator constant under an INC-I strategy.
u4 m7 I | I I | | I i n n ! u I i i l i l
10094 ."~~4" ........................ '""'"'"
88 / I ! I I I I I I I I i ~ I n n ! I I
0 1 2
Fig. 10
Time (hours)
I ! I ! | I I
• . . . . . . o o .
m7
68.2
6 7 . 6
, . . . . . , 67 3 4
Variations of the controlled (m r) and manipulated (u 4) variables for a setpoint change under an INC-I strategy (K---0.5).
To overcome such a difficulty, as well as any difficulty resulting from a change of state of the process, a possible solution consists in adapting on line the network weights. In Figure 11 is shown the response of the controller to a change of setpoint from 67.3% to 68% passing 200 mesh. The network used here was the same as in the previous section except that weight adaptation was performed at each control step. The adaptation coefficients were 0.1 for the hidden layer weights and 0.01 for the output layer weights. We have observed that high values have to be avoided, especially a t the output layer, to prevent oscillatory responses. In the present case, it can be seen that the response is very fast (less than 30 minutes) and stable, and that the setpoint bias is corrected.
Neural network based control 247
Fig. 11
u4
100
94
88
=| ! ! , , , i , , , , ! I , | , . ! I , , , , | I
. . . ° . ° . . . f . . . . . . . . .
m 7
"';;'4
0 1 2 3 4 T ime (hours)
m7
68.1
67.7
67.3
Variations of the controlled (m7) and manipulated (u 4) variables for a setpoint change under INC-A strategy.
Comparison of the INC-A Neural Controller to a Conventional PI Contoller
In order to compare the performance of a neural controller to more conventional technics, the same study was realized on a PI and an INC-A controller. The control strategy is the same as explained previously. In a first phase, the adaptation constants of the neural controller are tuned following a sytematic scanning between 0 (i.e. no adaptation) and an upper bound at which oscillations are observed in the response to a change of setpoint. The cri terium used to discrimate the controller performances is the sum of the squared deviations to the desired setpoint over a period of 4 hours following a change of setpoint f rom 67.34 to 68% passing 200 mesh in the cyclone overflow. The results are presented in Figure 12. The criterium value is reported on the Y axis, the adaptation coeff icient of the
¢ -
0
>
"13
ffl
0
E
, , I ) , I , ) ) ) ) ,
.................. ! ............... i ................................................. OLCOEF= 0.15
Fig.12 Influence of the values of the adaptation coefficients of the INC-A strategy onto the sum of squared-deviat ions to set point.
248 F. FLAMENT et al.
hidden layer (HLCOEF) is reported on the X axis and the adaptation coefficient of the output layer (OLCOEF) is used as a parameter. It can be seen that if low values of HLCOEF are used, high values of OLCOEF give low criterium values. On the contrary, for high values of HLCOEF, low values of OLCOEF should be prefered for good performance. The best performance (1.157) is obtained when there is no adaptation of the output layer weights. It can be seen also that for reasonable values of both coefficients (between 0 and 0.1) the performance is very stable which simplifies greatly the choice a priori of those coefficients.
In a second phase, a PI controller was implemented instead of the neural controller. The same sampling rate was used and again a systematic scanning of the PI parameter was performed between reasonnable bounds. The same performance criterium was used and the results are presented in Figure 13. The X axis reports the integral constant (Ti) while the proportional constant (Kp) is used as a parameter. It can be seen that the best performance (1.166) is obtained for low values of Ti (0.0075) and Kp (0.5). However, such a controller is not very stable. For more stability, higher values should be prefered (Ti=0.04 and Kp=2.5 for example) but at the detriment of the performance (1.290).
t,D t - ._o
>
" 0
" 0
"-!
tJ}
0
E -'-,i
( /3
4.5 I ~ c = : ~ { ~ : ~ i ~ : ~ . ~ : ~ . . ~ ; . ~ . ~ ! ~ -
4
3.5
3
2.5
2
1.5
0 0.01 0.02 0.03 0.04 0.05 'q
Fig.13 Influence of the values of the PI contoller parameters onto the sum of squared-deviations to set point.
By comparison to the neural controller, the PI is only slightly less performant, it has only two parameters to tune but the tuning itself is not straightforward for the type of process behaviour encountered here (see Figure 3). On the contrary, the neural controller has many parameters (all the connection weights plus the adaptation coefficients) which can be rather easily estimated provided the process dynamical behaviour can be well represented through many examples.
CONCLUSION
All model based control strategies require the availability of a good dynamic model. If the process is time-varying, it is necessary to adapt online the model for proper performance
Neural network based control 249
of the controller. Neural networks offer both ease of adaptability and plasticity in their structure to be used successfully for modelling the dynamic behaviour of complex processes. With neural networks, the model is able to self-organize to match the underlying dynamics of the process. This paper presents a series of control strategies, based on feedforward neural models, for the dynamics and the inverse dynamics of a simulated industrial grinding circuit. Some of them are illustrated and discussed.
It is shown that a neural network dynamic model of the plant and the inverse plant can serve as an efficient controller provided that it is coupled with some offset correction scheme such as a pure integrator in parallel to the neural controller or a neural network adaptation routine. It is believed that neural network will f ind wide use in process control and mineral processing is certainly one area that can greatly benefit from this new technology.
I .
2.
3.
4.
5.
6.
.
.
9.
10.
11.
12.
13.
REFERENCES
Bailey D. & Thompson D., How to Develop Neural Network Applications. AI expert, June, 38-47 (1990). Lippmann R.P., An Introduction to Computing With Neural Nets. IEEE ASSP Mag., April, 4-22 (1987). Wassermann P.D., Neural Computing: Theory and Practice. Van Nostrand Reinhold (1989). Widrow B. & Lehr M.A., 30 Years of Adaptive Neural Networks: Perceptron, Madaline, and Backpropagation. Proc. of the IEEE, 78, 9, 1415-1442 (1990). Dub6 Y., Lanthier R. & Hodouin D., Computer Aided Dynamic Analysis and Control Design for Grinding Circuits. CIM Bulletin, 80, 905, 65-70 (1987). Finch J.A., Laplante A.R. & del Villar R. Modelling cyclone performance curves with a size dependent correction factor. SME-AIME Annual Meeting, New York, (Feb. 1985). Hodouin D., Caron S. & Grand J.J., Modelling and Simulation of a Hydrocyclone Desliming Unit. First World Congress on Particle Technology, Ntirenberg, Fed. Rep. of Germany, April 16-18 (1986). Bhat N. & McAvoy T.J., Use of Neural Nets For Dynamic Modeling and Control of Chemical Process Systems. Computers Chem. Eng., 14, 4/5, 573-582 (1990). Ydstie B.E., Forecasting and Control Using Adaptive Connectionist Networks. Computers Chem. Eng., 14, 4/5, 583-599 (1990). Chen V.C. & Pao Y.H., Learning Control With Neural Networks. Proc. 1989 IEEE Int. Conf. Robot. Autom., 3, 1448-1453 (1989). Saerens M. & Soquet A. A Neural Controller Based On Back-Propagation Algorithm. Technical Report, IRIDIA-NN 005, Universit6 Libre de Bruxelles, 23 June (1989). Thibault J. & Grand jean B.P.A., Neural Networks in Process - A Survey. IFAC Syrup. ADCHEM, Toulouse, France, October 14-16 (1991). Ungar L.H., A Bioreactor Benchmark for Adaptive Network-Based Process Control. Chapt. 16 of Neural Networks for Control, W.T. Miller, R.S. Suthon and P.J. Werbos, Eds, 387-402 (1990).
