- Email: [email protected]
Artificial Neural Network Control Design for Continuous Flow Stirred Tank Reactor
Copyright © IFAC New Trends in Design of Control Systems, Smolenice, Slovak Republic, 1997
ARTIFICIAL NEURAL NETWORK CONTROL DESIGN FOR CONTINUOUS FLOW STIRRED TANK REACTOR
Vladimir Popardovsky
Institute of Control Theory and Robotics, Slovak Academy of Sciences Dubravska cesta 9, 842 37 Bratislava, Slovak Republic E-mail: [email protected]
Abstract: This contribution shows artificial neural network (ANN) approach in system identification and control of the continuous flow stirred tank reactor (CSTR). The internal model control (IMC) strategy was used. Some simulation results are included. Keywords: inverse model , forward model, backpropagation, IMC, CSTR.
1 INTRODUCTION Chemical reactors are commonly used in the chemical industry. The reactor is a nonlinear process. In paper proposed approach to the CSTR control is based on using of ANN. The controlled object is a CSTR with first order exothermic reaction. Only the reactant temperature is measured and this variable represents the controlled output of the system.
There was used following transfer function of the process (CSTR) for simulation experiments F CITR
0.09265s + 0.085839 (s ) = -:J2;-+-0.-83-9-8-2s-+-0.-17-2-8-98-8
The reactor is assumed as SISO system with one input (Tc) and one output (T).
2 PROCESS DESCRIPTION 3 ARTIFICIAL NEURAL NETWORK CONTROLER DESIGN
We consider a CSTR in which an irreversible k
decomposition A ~ B proceeds. Assume that conversion is manipulated by adjusting the reactor temperature. The reaction temperature is controlled by the coolant temperature. Nonlinear model reactor is described by the following diferential equations of mass and heat balances.
3. J Brief introduction to the theory of neural networks. Neural networks, originaly inspirated by their biologicaly namesakes, are composed many intercomunicating elements (neurons), working a parallel to solve a problem.What makes them interesting is the fact that once a network has been set up, it can learn in a self-organizing way. In this sens, the internal behavior of a network is not designed - it grows as the network learns to operate properly based on a set of training data provided by the user. Once it has mastered the training data it can be turned loose on problems where the answers are not known. Because neural
Transfer function for linearizing model of CSTR is
397
networks can be trained to respond in parallel to the inputs presented to them, they often can be much faster than more conventional methods. Basic functional unit of the artificial neural network is neuron. Neuron can be considered as a processor with n-inputs (synapses) and one output (axon), which performs relatively complicated mathematical operation. Input signals are mUltiplied by the positive or negative value (synaptic weight) in the synapses .. Then they are summed and the sum comes to a non-linearity (or linearity) which determines the intensity of the output signal. If the weighted sum of the inputs exceeds the threshold, neuron sends a signal which is close one. In the opposite case, output signal approaches to zero. Artificial neural networks are created via compiling the neurons into large integrates. Learning is performed on the so called training set, in which the input-otput relation for each element is known. Neural network can be understood as a function y = T(x) adapted by weight and bias parameters for the training set. A neural network can have any number of layers, but networks with more than three are uncommon.
3.2 Control structure based on a model of the inverse dynamics.
u(k) = F(y(k
+ 1); y(k); ..... ;y(k -n);u(k -l); ..... ;u(k -m)]
The model obtained for the inverse dynamics will represent a generalized right inverse of the process.
3.3 Internal model control strategy. The Internal Model Control (lMC) structure will be introduced as an alternative to the classic feedback structure. Because to the controller C it includes the plant model M explicitly, we refer to this feedback configuration as Internal Model Control.
~ _ d
Fig.3. Internal model control The feedback signal is
A model of the inverse dynamics of the same process can be identified directly as shown in following figure.
M)u
+d
= 0) then the model
output y and
the process output y are the same and the feedback signal d is zero. Thus, the control system is openloop when there is no uncertainty - no model uncertainty and no unknown inputs d. If a process and all its inputs are known perfectly, there is no need for feedback control. The feedback signal d expresses the uncertainty about the process. Control objective can be written in the dead-beat form as y(k+l) = w(k). The resulting nonlinear IMC controller can be written Q - CF. Objective at each iteration is y(k+ 1) = w(k). Control system output y( k + 1) can be expressed as y( k + 1) = PCw(k). We have P = M and therefore can written y(k+l) = MCw(k) . Problem y(k+l) = w(k) can be reformulated as choosing C such that (1MC)w(k)=O. Eqn. y(k+l) = PCw(k) is achieved by choosing the controller C to be the right inverse of the model C = M ; 1. The feedback signal represents
Fig.i. Direct identification of the inverse model If the input to the ANN for the identification is now taken to be + 1); y(k); ..... ; y(k -
d =(P -
If the model is exact (P = M) and there are no disturbances (d
1= [y(k
- +
M
n);u(k -I) ; ..... ;u(k -m)f
the error between the system output and the model output
and the output is u(k) then identified mapping F represents the inverse dynamics of the process.
d(k) = y(k) - /( k) / (k+l) = w(k) - d(k) y(kJ y(Ic-1J y(lc-nJ y(k+1J u(k-1J
We obtain the close-loop relation u(kJ
/( k+l) - /(k) = w(k) - y(k)
u(k-mJ --~_---.J
Fig.2. Inverse model
398
3.4 Relationship with "classicfeedback".
IMC controller was used. Structure of inverse and forward models was 4-8-1.
We transform IMC control structure in FigA. on the form in Fig.5. T [K]
C'
700 600
j
i'
500 1\ 400 300
FigA. Equivalent feedback structure
200 100
u=Cv
50
u=C(e+ y )
100
150
200
250
' - - - - - -- - - - - - - T i m e [min]
u=Ce+C y =Ce+CMu u( 1-CM)=Ce C e Fc - = - - u 1- CM
Fig.6. Controlled output of CSTR for cx=O.7 T[K]
Fig.5. Alternative feedback scheme of IMC Equivalent classic feedback (FigA,5) is stable because the internal signal u and y are unaffected by the transformation.
50
100
150
200
250
' - - - - - - - - - - - - - - Time [min]
Fig.7. Control actions of CSTR for cx=0.7
3.5 Filter design.
T [K]
400
Inverse model as feedback controller can produce large control actions which can lead to a unstability. Therefore a robust filter is added as a precompensator to the ANN controller. A common choice for the filter is a exponential filter with following transfer function
300 200 100 50
100
150
200
250
' - - - - - - - - - - - - - - Time [min]
Fig.8. Controlled output of CSTR for cx=O.9
where ex is time constant of the filter. In this time domain the filter can be represented recursively as v(k)=av(k-l)+(l-ex)[w(k)-d(k)}. The pole of the filter ex is used as tuning parameter. ex is chosen such that 0< cx< 1.
T[K]
400 /~ -.
.....
i
/
300
........ -
i '
4 SIMULA nON RESULTS 200 Inverse and forward models of IMC controller was identified by the off-line direct identification. There was obtained 200 inputoutput pairs for each of the models with sampling time equal 5. For training phase of IMC controller was used adaptiv backpropagation algorithm. The linear transfer function of the inverse and forward models of
100
'-------------~
50
100
150
200
250
' - - - - - - - - - - - - - - Time [min]
Fig.9. Control actions of CSTR for cx=0.9
399
5 CONCLUSION
Henson M . A., Seborg D. E. (1991). An internal model control strategy for nonlinear systems. AIChE 1., 37, 1065-1081.
An application of a IMC controller is given . The paper presents the ANN approach to chemical reactor control. The simulation results clearly show the advantages of this approach .
Hunt K. 1., Sbarbaro D., Zbikowski R. (1992). Neural Network for Control Systems-A survey . Automatica, Vol. 28, No. 6, 1083- 1112. Thibault l ., Grandjean B. P. A. (1992). Process Control Using Feedforward Neural Networks . 1. of Systems Engineering, 2, 199-212.
6 REFERENCES Hertz l ., A. Krogh, R. Palmer (1991). Introduction to the theory of neural computation. Addison-Wesley Publishing Company.
400
ARTIFICIAL NEURAL NETWORK CONTROL DESIGN FOR CONTINUOUS FLOW STIRRED TANK REACTOR
Vladimir Popardovsky
Institute of Control Theory and Robotics, Slovak Academy of Sciences Dubravska cesta 9, 842 37 Bratislava, Slovak Republic E-mail: [email protected]
Abstract: This contribution shows artificial neural network (ANN) approach in system identification and control of the continuous flow stirred tank reactor (CSTR). The internal model control (IMC) strategy was used. Some simulation results are included. Keywords: inverse model , forward model, backpropagation, IMC, CSTR.
1 INTRODUCTION Chemical reactors are commonly used in the chemical industry. The reactor is a nonlinear process. In paper proposed approach to the CSTR control is based on using of ANN. The controlled object is a CSTR with first order exothermic reaction. Only the reactant temperature is measured and this variable represents the controlled output of the system.
There was used following transfer function of the process (CSTR) for simulation experiments F CITR
0.09265s + 0.085839 (s ) = -:J2;-+-0.-83-9-8-2s-+-0.-17-2-8-98-8
The reactor is assumed as SISO system with one input (Tc) and one output (T).
2 PROCESS DESCRIPTION 3 ARTIFICIAL NEURAL NETWORK CONTROLER DESIGN
We consider a CSTR in which an irreversible k
decomposition A ~ B proceeds. Assume that conversion is manipulated by adjusting the reactor temperature. The reaction temperature is controlled by the coolant temperature. Nonlinear model reactor is described by the following diferential equations of mass and heat balances.
3. J Brief introduction to the theory of neural networks. Neural networks, originaly inspirated by their biologicaly namesakes, are composed many intercomunicating elements (neurons), working a parallel to solve a problem.What makes them interesting is the fact that once a network has been set up, it can learn in a self-organizing way. In this sens, the internal behavior of a network is not designed - it grows as the network learns to operate properly based on a set of training data provided by the user. Once it has mastered the training data it can be turned loose on problems where the answers are not known. Because neural
Transfer function for linearizing model of CSTR is
397
networks can be trained to respond in parallel to the inputs presented to them, they often can be much faster than more conventional methods. Basic functional unit of the artificial neural network is neuron. Neuron can be considered as a processor with n-inputs (synapses) and one output (axon), which performs relatively complicated mathematical operation. Input signals are mUltiplied by the positive or negative value (synaptic weight) in the synapses .. Then they are summed and the sum comes to a non-linearity (or linearity) which determines the intensity of the output signal. If the weighted sum of the inputs exceeds the threshold, neuron sends a signal which is close one. In the opposite case, output signal approaches to zero. Artificial neural networks are created via compiling the neurons into large integrates. Learning is performed on the so called training set, in which the input-otput relation for each element is known. Neural network can be understood as a function y = T(x) adapted by weight and bias parameters for the training set. A neural network can have any number of layers, but networks with more than three are uncommon.
3.2 Control structure based on a model of the inverse dynamics.
u(k) = F(y(k
+ 1); y(k); ..... ;y(k -n);u(k -l); ..... ;u(k -m)]
The model obtained for the inverse dynamics will represent a generalized right inverse of the process.
3.3 Internal model control strategy. The Internal Model Control (lMC) structure will be introduced as an alternative to the classic feedback structure. Because to the controller C it includes the plant model M explicitly, we refer to this feedback configuration as Internal Model Control.
~ _ d
Fig.3. Internal model control The feedback signal is
A model of the inverse dynamics of the same process can be identified directly as shown in following figure.
M)u
+d
= 0) then the model
output y and
the process output y are the same and the feedback signal d is zero. Thus, the control system is openloop when there is no uncertainty - no model uncertainty and no unknown inputs d. If a process and all its inputs are known perfectly, there is no need for feedback control. The feedback signal d expresses the uncertainty about the process. Control objective can be written in the dead-beat form as y(k+l) = w(k). The resulting nonlinear IMC controller can be written Q - CF. Objective at each iteration is y(k+ 1) = w(k). Control system output y( k + 1) can be expressed as y( k + 1) = PCw(k). We have P = M and therefore can written y(k+l) = MCw(k) . Problem y(k+l) = w(k) can be reformulated as choosing C such that (1MC)w(k)=O. Eqn. y(k+l) = PCw(k) is achieved by choosing the controller C to be the right inverse of the model C = M ; 1. The feedback signal represents
Fig.i. Direct identification of the inverse model If the input to the ANN for the identification is now taken to be + 1); y(k); ..... ; y(k -
d =(P -
If the model is exact (P = M) and there are no disturbances (d
1= [y(k
- +
M
n);u(k -I) ; ..... ;u(k -m)f
the error between the system output and the model output
and the output is u(k) then identified mapping F represents the inverse dynamics of the process.
d(k) = y(k) - /( k) / (k+l) = w(k) - d(k) y(kJ y(Ic-1J y(lc-nJ y(k+1J u(k-1J
We obtain the close-loop relation u(kJ
/( k+l) - /(k) = w(k) - y(k)
u(k-mJ --~_---.J
Fig.2. Inverse model
398
3.4 Relationship with "classicfeedback".
IMC controller was used. Structure of inverse and forward models was 4-8-1.
We transform IMC control structure in FigA. on the form in Fig.5. T [K]
C'
700 600
j
i'
500 1\ 400 300
FigA. Equivalent feedback structure
200 100
u=Cv
50
u=C(e+ y )
100
150
200
250
' - - - - - -- - - - - - - T i m e [min]
u=Ce+C y =Ce+CMu u( 1-CM)=Ce C e Fc - = - - u 1- CM
Fig.6. Controlled output of CSTR for cx=O.7 T[K]
Fig.5. Alternative feedback scheme of IMC Equivalent classic feedback (FigA,5) is stable because the internal signal u and y are unaffected by the transformation.
50
100
150
200
250
' - - - - - - - - - - - - - - Time [min]
Fig.7. Control actions of CSTR for cx=0.7
3.5 Filter design.
T [K]
400
Inverse model as feedback controller can produce large control actions which can lead to a unstability. Therefore a robust filter is added as a precompensator to the ANN controller. A common choice for the filter is a exponential filter with following transfer function
300 200 100 50
100
150
200
250
' - - - - - - - - - - - - - - Time [min]
Fig.8. Controlled output of CSTR for cx=O.9
where ex is time constant of the filter. In this time domain the filter can be represented recursively as v(k)=av(k-l)+(l-ex)[w(k)-d(k)}. The pole of the filter ex is used as tuning parameter. ex is chosen such that 0< cx< 1.
T[K]
400 /~ -.
.....
i
/
300
........ -
i '
4 SIMULA nON RESULTS 200 Inverse and forward models of IMC controller was identified by the off-line direct identification. There was obtained 200 inputoutput pairs for each of the models with sampling time equal 5. For training phase of IMC controller was used adaptiv backpropagation algorithm. The linear transfer function of the inverse and forward models of
100
'-------------~
50
100
150
200
250
' - - - - - - - - - - - - - - Time [min]
Fig.9. Control actions of CSTR for cx=0.9
399
5 CONCLUSION
Henson M . A., Seborg D. E. (1991). An internal model control strategy for nonlinear systems. AIChE 1., 37, 1065-1081.
An application of a IMC controller is given . The paper presents the ANN approach to chemical reactor control. The simulation results clearly show the advantages of this approach .
Hunt K. 1., Sbarbaro D., Zbikowski R. (1992). Neural Network for Control Systems-A survey . Automatica, Vol. 28, No. 6, 1083- 1112. Thibault l ., Grandjean B. P. A. (1992). Process Control Using Feedforward Neural Networks . 1. of Systems Engineering, 2, 199-212.
6 REFERENCES Hertz l ., A. Krogh, R. Palmer (1991). Introduction to the theory of neural computation. Addison-Wesley Publishing Company.
400