- Email: [email protected]
Nonlinear process control with neural nets
Neurocomputing 2 (1990) 51-59 Elsevier
51
Nonlinear process control with neural nets Yoh-Han Pao and Dejan J. Sobajic Case Western Reserve University; and A I W A R E Inc. Cleveland, OH 44106, USA
Abstract. There exists a need to develop better mathematical models for physicalprocesses, but it is also essential to understand that it is impossible to describe real-world industrial processes by exact mathematical models. Pattern recognition based methodology implemented in the architecture of artificial neural networks can be used to model knowledge intensive feedback control systems. The procedure for development and practical design of neural-net based control systems is described and demonstrated by the example of a nonlinear hydraulic system. The results obtained in computer simulations and experimentsare presented to illustrate the new approach.
1. Introduction Real-world industrial processes have always been of considerable interest for control theorists and practitioners. These processes are typically characterized with partially understood nonlinear system dynamics, lack of knowledge of true system parameters, noisy measurement subsystems and a great amount o f uncertainty in the interactions between the process and its environment. Over the decades, the theorists of classical and modern control have been offering new and sophisticated techniques to cope effectively with some of these difficult problems. However a rigorous mathematical treatment is constrained usually by a set of various assumptions. To ensure applicability of certain theories, it turns out that continuous verification of underlying assumptions has to be enforced, which f r o m the practical viewpoint is often impossible. This is one among the reasons that most of the process industry in the last 40 years has based their automatic control decisions on the actions of a rather simplistic structure o f proportional integral derivation (PID) controllers. A P I D controller has three tunable parameters (gain, reset and rate), that can be used to modify system's behaviour over the wide frequency range. 0925-2312/90/$03.50
© 1990--Elsevier Science Publishers B.V.
Development of techniques for tuning of the P I D constants has a long history. Ziegler and Nichols [20] estimated tuning constants from the gain required for sustained system oscillations. Cohen and Coon [5] and Yuwana and Seborg [18] suggested the use of the open loop step response to calculate the tuning values. More recently, Astrom and Hagglund [1] in their "relay m e t h o d " proposed gain and phase-margin techniques to find the gain, reset and rate parameters. The techniques mentioned above belong to the group of off-line tuning methods. On-line tuning, or self-tuning is based on automatic system identification and self-adjustment of adaptive feedback law. The adaptive controllers, like most other controllers, are designed on models that are simpler than the real processes. Self-tuning and model reference adaptive control methods from [2, 4, 15, 6, 19] mostly deal with linear systems and specialized algorithms exist for nonlinear systems such as those where unknown parameters enter linearly in the nonlinear model. Reliable results are obtained on n o n m i n i m u m phase systems and on systems with unknown variable delays.
2. Pattern recognition based process control In this paper, we discuss and demonstrate the use
52
Y.-H Pao, D.J. Sobajic / Nonlinear process control
of the pattern recognition approach in nonlinear process control. In spite of the need for development of better mathematical models for physical systems it is essential to have in mind that the behaviour of the real-world processes is extremely hard, if not impossible, to describe with exact mathematical models. In such cases, the feedback may be a very effective approach to control design (see Fig. 1). Until recently, the pattern recognition (PR) paradigm has been viewed as useful for recognizing and categorizing objects that belong to different and distinct classes. Namely, PR has been employed as the classification mechanism. In 1987, Pao suggested the use of pattern recognition in the context of the estimation task. The task was carried out on the distributed parallel computational architectures of artificial neural networks (ANN). The ANN implementations of PR exhibit several important characteristics [9]. First, the behaviour of an ANN is conditioned through the training phase. The network is incrementally adjusting its performance in response to the presented samples (patterns). There is no task-specific coding involved. Consequently, changes or modification in the network behaviour are obtained through the continuation of training process and presentation of new data. Secondly, the trained neural-net system is capable of generalization over the set of previously learned instances and is able to perform in new "unseen" circumstances. The neural-net system behaves as if it has discovered the rules that are im-
plicitly contained in the presented data set [11]. Moreover, starting with a finite number of data points with information measure zero, the supervised learning neural-net creates the data-based model with finite information measure. Consequently, in some instances it is possible to exploit transparency of the synthesized mapping and learn different sensitivities between corresponding input and output pattern features. The feedback control law can be viewed as the mapping from the space of actual system measurements and their corresponding desired values, to the space of synthesized control actions. As shown in Fig. 2, this mapping is represented in the direct form using the structure of the ANN. Training process may be designed in several ways, depending on the intent of the control designer. This is the case where the control task is knowledge intensive and there is a need to integrate various decision making modules into one effectively functioning mechanism. The training process reflects that complexity superimposing different pieces of knowledge onto the distributed memory of the ANN [17, 3, 16, 14]. In the indirect mode (Fig. 3), both the conventional control module and the knowledge-based module can coexist [12, 7, 10]. The hybrid system functions in two modes. Co-operative: Both modules are continually in operation. The KB module modifies the behaviour of a conventional controller in real-time by
~ Disturbance
~ Disturbance
Control ~
[
CONTROLLER
Control
Measurements
SYSTEM
v
[
I-
Fig. 1. A feedbackcontrolsystem.
v
SYSTEM
I Measurements
I
NEURAL-NET,, [ Fig. 2. A directmodeneural-netcontroller.
Y.-H Pao, D.J. Sobajic / Nonlinear process control
53
~ Disturbance Control
_l-I
Measurements
SYSTEM
h v
Controlled Input F l o w
NEURAL NET CONTROL SYSTEM
~
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Uncontrolled Output Flow
I
I '
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.
N
!
Fig. 4. A schematic of the water tank.
~.~
Fig. 3. An indirect mode neural-net controller.
(a) tuning the controller parameters, (b) modifying the controller structure, (c) providing an additional signal that will compensate the actions of conventional control mechanism. Competitive: Both models are employed through the temporal decoupling logic. This mechanism is trained to monitor the system's performance in order to utilize the control resources in an optimum manner.
3.1. Neural-net controller The development of the neural-net control system strategy proceeds in two steps. In the first step, we deal with a simulated environment. For that purpose, the tank model is established on a separate computer as a stand-alone and free running system. In this way, the neural-net control algorithm can be developed independently without any a priory knowledge of the tank model. In the second step, the simulated tank model is replaced by the real tank.
3. Neural-net control of a nonlinear hydraulic system
In this section, we describe the design and functionality of a neural-net based control system for the liquid level control (Fig. 4). The control system design is carried out in two phases: (a) the design of a neural-net controller for feedback control; (b) the design o f a neural-net predictor for detection and identification of bad sensor data.
a) straight tank
t
b) parabolic tank
?i
c) hourglass
tank
d) "step" tank
Fig. 5. Four different profiles of the water tank.
Y.-H Pao, D.J. Sobajic / Nonlinear process control
54
Four different tank shapes examined in the simulations are shown in Fig. 5. The actual tank used in experiments is shaped in the form of the capital letter " I " as presented in Fig. 4. A nonlinear input valve is employed to regulate the flow rate at the tank input and two sensors, L1 and L2, are installed for detecting the level of the liquid. The output valve is under the operator's control and is utilized to generate various unforeseen disturbances. In the simulations, we can empty the tank by the gravity force, as well as with a constant pressure pump. The input valve is modeled as a linear, exponential or dynamic valve with delays. Both the input and output tank measurements are corrupted by Gaussian noise. The two-level sensor readings are also simulated with or without Gaussian noise and the stuck meter option is provided at the operator's request. In both the simulation and the actual experimentation, we assume that readings from the tank output (outflow) are not available to the control algorithm. 3.2. Training o f neural-net controller
The neural-net feedback control system is shown
in Fig. 6. The control objective is to maintain the liquid level at the desired target x T through the stabilizing actions of the nonlinear input value. In the course of developing the neural network controller, we assume both sensor readings, x[1] and x[2], are within 0.5% error tolerance of the actual level. On the display, the operator can see the target and the current level of the liquid. He is given the control of the input valve through keyboard command, and he can either increase or decrease the opening of the input valve, Uin. Several scenarios with different input flow rate, output flow rate, liquid level and target level are presented to the operator and training data are collected while keeping the output valve, Uout, at the same position throughout each scenario. The operator will control the liquid level until the system is stable and the target level is reached. The error, c, between the actual and the target level of the liquid for several consecutive instances at the beginning of the scenario is used as input pattern for the neural network. During the scenario, the operator control actions are integrated (Fig. 7). The resulting total control action is used as target pattern for supervised training of neural network.
" B e s t " Level
i Uout UIn
Process
up~e I
Decision Unit
! , Con~ollei'::::. ~: - Level Error Buffer
~ r
i
÷
Xr
Fig. 6. Neural-net based system for bad sensor detection and feedback control.
Buffer
55
Y.-H Pao, D.J. Sobajic / Nonlinear process control
i Training Session I '
Opera~
, User
Interface
H
See.,rio
Generator
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~
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Fig.7.Trainingenvironment. Training patterns are expressed as (input, target) pairs for each scenario. After a set of training examples is collected (17 of them in our case), the supervised learning network is trained [13]. The neural net is configured as a flat, no hidden layer architecture with the functional link comprising 5 inputs and 1 output. We used the third-order joint activation model to enhance the pattern representation [8]. As we mentioned already, network inputs are 5 consecutive readings of the liquid level while network output provides the graded opening of the tank input valve. The (+1, - 1 ) range of the sigmoidal curve is mapped into the maximal allowed changes in valve positions from one time instant to
another. The control throughput is approximately 0.25 seconds.
3.3. Neural-net predictor The role of the neural-net predictor is to learn the mapping of the closedqoop system dynamics under different operating conditions. Once this mapping is obtained, the decision unit will be able to choose the level sensor, x[1] or x[2], that gives a closer reading, Z, compared to the predicted level, £. The training samples for predictor network are collected from the closed-loop system operation. Several scenarios are set up with different flow in rate, flow out rate,
56
Y.-H Pao, D.J. Sobajic / Nonlinear process control
liquid level and target level. The neural-net controller is employed to generate control actions for each scenario. History sequences of liquid levels at separate time intervals are collected providing the training set for the predictor. The predictor serves as the real time pointer to the "better" sensor reading. The decision unit is supposed to pass this informa-
tion to the neural-net controller which generates the control signal. 4. N u m e r i c a l r e s u l t s
Figures 8 and 9 describe the nature of the system behaviour in the simulated environment. In both
normoliJed
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0.75
i
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,
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0. -
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I
I
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5
10
15
20
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Fig. 8. System response to output demand decrease. Stable control response generated by tracking less noisy sensor. (l: first level measurement, 2: second leve! measurement, 3: target level, 4: predicted level, 5: input flow rate, 6: output demand). normalized
l.O
i
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Fig. 9. System response to target level increase with sensor 2 stuck. Stable control response generated by tracking less noisy sensor; system ignores momentarily correct reading at time t I of stuck sensor.
Y.-H Pao, D.J. Sobajic / Nonlinear process control
cases we are dealing with t h e " step t a n k " shape (Fig. 5(d)) and it is assumed that the tank is emptied by a constant pressure pump. Sensor 1 is modelled as the more accurate one with standard deviation of 0.5°7o while standard deviation for sensor 2 is 5 070. In Fig. 8, we see the typical stabilizing control action that occurs after the step decrease in the demand (curve 6). In Fig. 9, we are observing the process of filling the tank. Of a particular interest, is the fact that the less accurate sensor 2 suddenly jumps to the value that will at some later time (tl) become
57
correct. It is noticeable that the predictor (curve 4) " f o l l o w s " the correct, more accurate, sensor, namely x[1]. As a matter o f fact we have observed the tendency that the predictor will always follow the less noisy signal. In Fig. 10, we demonstrate similar ability of the predictor under different circumstances. This experiment has been performed using the real tank. One of the two sensor readings (curve 2) suddenly has dropped to approximately 1/3 of the correct reading (by inserting an external capacitance 1 0 / ~
normalited rabies
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4
0.75
0.5
~
0.25
¢.2
O.
lime Isec|
,a.-
0
10
5
IS
20
25
Fig. 10. System response to target level decrease immediately followed by malfunctioning of sensor 2.
~t)
Ws
x(t-l)
x(t-2)
x(t-n)
second order joint activation terms
third order joint activation
{x(t-i)*x(t-j)} for i
{x(t-i)*x(t-j)*x(t-k)} for i
terms
Fig. 11. A schematic diagram of the functional link net state predictor.
58
Y.-H Pap, D.J. Sobajic / Nonlinear process control
across the sensor outputs). The decision logic compares the predicted state (curve 4) to the actual ones (curves 1 and 2) and passes the correct information to the neural-net controller, which continues to maintain the new desired target level (curve 3). The experiments have shown that the neural-net control system is capable of maintaining the tank liquid level at any desired level, stabilizing the system in the presence of large disturbances, detecting and identifying defective level sensors, and estimating parameters in nonlinear processes. In the training of the neural-net controller, training examples represent the control actions under different scenarios. The system will learn to respond to the real-time situations so as to maintain the desired level readings. The approach taken in the predictor design is to teach the network to learn the associative mapping between the system dynamics and the expected error in level readings. The predictor network is configured as the flat functional link net, as shown in Fig. 11, with 8 inputs and one output. The inputs constitute 8 consecutive "best" level readings and the output is the estimate of the level reading in the next scanning interval. The common feature of the neural-net controller and the predictor is the use of functional link net architectures. This higher order network architecture speeds up the training process exhibiting favorable characteristics for the use in on-line process control.
Conclusion Most of the real-world industrial processes cannot be described by exact mathematical models. Emphasizing the significance of feedback control in reducing the effects of uncertainties we have proposed a new design of the flexible and robust stabilizing controller. The control system design is based on the pattern recognition principle and the implementation on the parallel distributed computational architectures of artificial neural systems. The neural-net control system has been trained to provide stabilizing controls and to detect and identify malfunctioning sensors. Developed meth-
odology is demonstrated on the nonlinear liquid level control problem. The results presented in this paper include both simulations and experiments on the real system.
References [1] K.J. Astrom and T. Hagglund, Automatic tuning of simple regulators for phase and amplitude margins specification, IFAC Workshop on Adaptive Systems in Control and Signal Processing, San Francisco, CA (1983). [2] K.J. Astrom and B. Wittenmark, On self-tuning regulators, Automatica 9 (1973) 185 - 199. [3] A. Barto, R. Sutton and C. Anderson, Neuronlike elements that can solve difficult learning control problems, IEEE Trans. Systems Man Cybernet.13 (1983) 835- 846. [4] D.W. Clarke and P.J. Gawthrop, Self-tuning controller, Proc. IEEE 122 (1975) 929-934. [5] G.H. Cohen and G.A. Coon, Theoretical investigation of retarded control, Trans. A S M E 75 (1953) 827. [6] T.R. Fortescue, L.S. Kershenbaum and B.E. Ydstie, Implementation of self-tuning regulators with variable forgetting factors, Automatica 17 (6) (1981) 831 -835. [7] A. Guez, J.L. Eilbert and M. Kam, Neural network architecture for control, IEEE Control System Magazine 8 (2) (1988) 22 - 25. [8] M.S. Klassen, Y.-H. Pap and V. Chen, Characteristics of the functional link net: a higher order delta rule net, IEEE International Conference on Neural Networks 1, San Diego, CA (1988) 507-513. [9] Y.-H. Pao, Adaptive Pattern Recognition and Neural Networks (Addison-Wesley, Reading, MA, 1989). [I0] Y.-H. Pap, V.C. Chen and D.J. Sobajic, A perspective on research aimed at understanding the systems nature of neural controllers, in: Proceedings o f the International Joint Conference on Neural Networks, Washington, DC (1989). [11] Y.-H. Pap and D.J. Sobajic, A perspective on the role of parallel distributed processing of the neural-net type in implementing automation, in: Proceedings o f the IEEE Workshop on Languages f o r A utomation, Vienna (1987). [12] D. Psaltis, A. Sideris and A. Yamamura, A multilayered Neural Network Controller, IEEE Control System Magazine 8 (2) (1988) 1 7 - 21. [13] D.J. Sobajic, D.T. Lee, and Y.-H. Pap, Increased effectiveness of learning by local neural feedback, INNS First Annual Meeting, Boston, MA (1988) 222. [14] D.J. Sobajic, Y.-H. Pap and J.J. Lu, Neural-net control for robotics: design criteria and learning structures, SPIE Conference, Cambridge, MA (1988). [15] P.E. Wellstead, D. Prager and P. Zanker, Pole assignment
Y.-H Pao, D.J. Sobajic / Nonlinear process control
self-tuning regulator, Proc. lEE 126 (8) (1979) 781 -786. [16] B. Widrow, The original adaptive neural-net broombalancer, IEEE International Symposium on Circuits and Systems (1987) 351 - 357. [17] B. Widrow, J.M. McCool, M.G. Larimore and C.R. Johnson Jr, Stationary and nonstationary learning characteristics of the LMS adaptive filter, Proc. IEEE 64 (8) (1976) 1151 - 1162. [18] M. Yuwana and D. Seborg, A new method for on-line controller tuning, AIChE J. 28 (1982) 434-440. [19] C. Zervos, P.R. Belanger and G.A. Dumont, On PID controller tuning using orthonormal series identification, Automatica 24 (2) (1988) 165- 175. [20] J.G. Ziegler and N.B. Nichols, Optimum setting for PID controllers, Trans. A S M E 64 (1942) 759 - 768.
Yoh-Han Pan, has been a Professor of Electrical Engineering and Computer Science at Case Western Reserve University (CWRU) since 1976. He has served as chairman of the University's Electrical Engineering Department (1969-77), as Director of the Electrical, Computer and System Engineering Division at NSF (1978 - 80), and as founding director of the Center of Automation and In~ inn telligent Systems Research at CWRU. He is the George S. Direly Distinguished Professor of Engineering at CWRU, is a Fellow of IEEE and of the American Optical Society. He has been a NATO Senior Science Fellow; has visited MIT, Edinburgh University, and the Turing Institute as lecturer/research, and has been a member of the technical staff at AT&T Bell Laboratories in Murray Hill, NJ. He is co-founder and president of AI Ware Inc., Cleveland, OH.
59
D.J. Sobajic, (M'80-SM'89) was born in Yugoslavia in 1949. He received the BSEE and the MSEE degrees from the University of Belgrade, Belgrade, Yugoslavia in 1972 and 1976, respectively and the Ph.D. degree from Case Western Reserve University, Cleveland, OH in 1988. At present, he is with the Department of Electrical Engineering and Applied Physics, Case Western Reserve University, Cleveland, OH. He is also Engineering Manager of AI WARE, Inc. His current research interests include power system operation and control, neural net systems and adaptive control. Dr. Sobajic is a member of the IEEE Task Force on Neural Network Applications in Power Systems and of the IEEE Intelligent Control Committee. He is the Chairman of the International Neural Networks Society Special Interest Group on Power Engineering.
51
Nonlinear process control with neural nets Yoh-Han Pao and Dejan J. Sobajic Case Western Reserve University; and A I W A R E Inc. Cleveland, OH 44106, USA
Abstract. There exists a need to develop better mathematical models for physicalprocesses, but it is also essential to understand that it is impossible to describe real-world industrial processes by exact mathematical models. Pattern recognition based methodology implemented in the architecture of artificial neural networks can be used to model knowledge intensive feedback control systems. The procedure for development and practical design of neural-net based control systems is described and demonstrated by the example of a nonlinear hydraulic system. The results obtained in computer simulations and experimentsare presented to illustrate the new approach.
1. Introduction Real-world industrial processes have always been of considerable interest for control theorists and practitioners. These processes are typically characterized with partially understood nonlinear system dynamics, lack of knowledge of true system parameters, noisy measurement subsystems and a great amount o f uncertainty in the interactions between the process and its environment. Over the decades, the theorists of classical and modern control have been offering new and sophisticated techniques to cope effectively with some of these difficult problems. However a rigorous mathematical treatment is constrained usually by a set of various assumptions. To ensure applicability of certain theories, it turns out that continuous verification of underlying assumptions has to be enforced, which f r o m the practical viewpoint is often impossible. This is one among the reasons that most of the process industry in the last 40 years has based their automatic control decisions on the actions of a rather simplistic structure o f proportional integral derivation (PID) controllers. A P I D controller has three tunable parameters (gain, reset and rate), that can be used to modify system's behaviour over the wide frequency range. 0925-2312/90/$03.50
© 1990--Elsevier Science Publishers B.V.
Development of techniques for tuning of the P I D constants has a long history. Ziegler and Nichols [20] estimated tuning constants from the gain required for sustained system oscillations. Cohen and Coon [5] and Yuwana and Seborg [18] suggested the use of the open loop step response to calculate the tuning values. More recently, Astrom and Hagglund [1] in their "relay m e t h o d " proposed gain and phase-margin techniques to find the gain, reset and rate parameters. The techniques mentioned above belong to the group of off-line tuning methods. On-line tuning, or self-tuning is based on automatic system identification and self-adjustment of adaptive feedback law. The adaptive controllers, like most other controllers, are designed on models that are simpler than the real processes. Self-tuning and model reference adaptive control methods from [2, 4, 15, 6, 19] mostly deal with linear systems and specialized algorithms exist for nonlinear systems such as those where unknown parameters enter linearly in the nonlinear model. Reliable results are obtained on n o n m i n i m u m phase systems and on systems with unknown variable delays.
2. Pattern recognition based process control In this paper, we discuss and demonstrate the use
52
Y.-H Pao, D.J. Sobajic / Nonlinear process control
of the pattern recognition approach in nonlinear process control. In spite of the need for development of better mathematical models for physical systems it is essential to have in mind that the behaviour of the real-world processes is extremely hard, if not impossible, to describe with exact mathematical models. In such cases, the feedback may be a very effective approach to control design (see Fig. 1). Until recently, the pattern recognition (PR) paradigm has been viewed as useful for recognizing and categorizing objects that belong to different and distinct classes. Namely, PR has been employed as the classification mechanism. In 1987, Pao suggested the use of pattern recognition in the context of the estimation task. The task was carried out on the distributed parallel computational architectures of artificial neural networks (ANN). The ANN implementations of PR exhibit several important characteristics [9]. First, the behaviour of an ANN is conditioned through the training phase. The network is incrementally adjusting its performance in response to the presented samples (patterns). There is no task-specific coding involved. Consequently, changes or modification in the network behaviour are obtained through the continuation of training process and presentation of new data. Secondly, the trained neural-net system is capable of generalization over the set of previously learned instances and is able to perform in new "unseen" circumstances. The neural-net system behaves as if it has discovered the rules that are im-
plicitly contained in the presented data set [11]. Moreover, starting with a finite number of data points with information measure zero, the supervised learning neural-net creates the data-based model with finite information measure. Consequently, in some instances it is possible to exploit transparency of the synthesized mapping and learn different sensitivities between corresponding input and output pattern features. The feedback control law can be viewed as the mapping from the space of actual system measurements and their corresponding desired values, to the space of synthesized control actions. As shown in Fig. 2, this mapping is represented in the direct form using the structure of the ANN. Training process may be designed in several ways, depending on the intent of the control designer. This is the case where the control task is knowledge intensive and there is a need to integrate various decision making modules into one effectively functioning mechanism. The training process reflects that complexity superimposing different pieces of knowledge onto the distributed memory of the ANN [17, 3, 16, 14]. In the indirect mode (Fig. 3), both the conventional control module and the knowledge-based module can coexist [12, 7, 10]. The hybrid system functions in two modes. Co-operative: Both modules are continually in operation. The KB module modifies the behaviour of a conventional controller in real-time by
~ Disturbance
~ Disturbance
Control ~
[
CONTROLLER
Control
Measurements
SYSTEM
v
[
I-
Fig. 1. A feedbackcontrolsystem.
v
SYSTEM
I Measurements
I
NEURAL-NET,, [ Fig. 2. A directmodeneural-netcontroller.
Y.-H Pao, D.J. Sobajic / Nonlinear process control
53
~ Disturbance Control
_l-I
Measurements
SYSTEM
h v
Controlled Input F l o w
NEURAL NET CONTROL SYSTEM
~
CONTROLLER
Uncontrolled Output Flow
I
I '
NEURAL.NET d~
H
.
N
!
Fig. 4. A schematic of the water tank.
~.~
Fig. 3. An indirect mode neural-net controller.
(a) tuning the controller parameters, (b) modifying the controller structure, (c) providing an additional signal that will compensate the actions of conventional control mechanism. Competitive: Both models are employed through the temporal decoupling logic. This mechanism is trained to monitor the system's performance in order to utilize the control resources in an optimum manner.
3.1. Neural-net controller The development of the neural-net control system strategy proceeds in two steps. In the first step, we deal with a simulated environment. For that purpose, the tank model is established on a separate computer as a stand-alone and free running system. In this way, the neural-net control algorithm can be developed independently without any a priory knowledge of the tank model. In the second step, the simulated tank model is replaced by the real tank.
3. Neural-net control of a nonlinear hydraulic system
In this section, we describe the design and functionality of a neural-net based control system for the liquid level control (Fig. 4). The control system design is carried out in two phases: (a) the design of a neural-net controller for feedback control; (b) the design o f a neural-net predictor for detection and identification of bad sensor data.
a) straight tank
t
b) parabolic tank
?i
c) hourglass
tank
d) "step" tank
Fig. 5. Four different profiles of the water tank.
Y.-H Pao, D.J. Sobajic / Nonlinear process control
54
Four different tank shapes examined in the simulations are shown in Fig. 5. The actual tank used in experiments is shaped in the form of the capital letter " I " as presented in Fig. 4. A nonlinear input valve is employed to regulate the flow rate at the tank input and two sensors, L1 and L2, are installed for detecting the level of the liquid. The output valve is under the operator's control and is utilized to generate various unforeseen disturbances. In the simulations, we can empty the tank by the gravity force, as well as with a constant pressure pump. The input valve is modeled as a linear, exponential or dynamic valve with delays. Both the input and output tank measurements are corrupted by Gaussian noise. The two-level sensor readings are also simulated with or without Gaussian noise and the stuck meter option is provided at the operator's request. In both the simulation and the actual experimentation, we assume that readings from the tank output (outflow) are not available to the control algorithm. 3.2. Training o f neural-net controller
The neural-net feedback control system is shown
in Fig. 6. The control objective is to maintain the liquid level at the desired target x T through the stabilizing actions of the nonlinear input value. In the course of developing the neural network controller, we assume both sensor readings, x[1] and x[2], are within 0.5% error tolerance of the actual level. On the display, the operator can see the target and the current level of the liquid. He is given the control of the input valve through keyboard command, and he can either increase or decrease the opening of the input valve, Uin. Several scenarios with different input flow rate, output flow rate, liquid level and target level are presented to the operator and training data are collected while keeping the output valve, Uout, at the same position throughout each scenario. The operator will control the liquid level until the system is stable and the target level is reached. The error, c, between the actual and the target level of the liquid for several consecutive instances at the beginning of the scenario is used as input pattern for the neural network. During the scenario, the operator control actions are integrated (Fig. 7). The resulting total control action is used as target pattern for supervised training of neural network.
" B e s t " Level
i Uout UIn
Process
up~e I
Decision Unit
! , Con~ollei'::::. ~: - Level Error Buffer
~ r
i
÷
Xr
Fig. 6. Neural-net based system for bad sensor detection and feedback control.
Buffer
55
Y.-H Pao, D.J. Sobajic / Nonlinear process control
i Training Session I '
Opera~
, User
Interface
H
See.,rio
Generator
[~
l
~
I Monitoring
Run ~ ~
Proces~
1
"
I PatternData ,'-I
Neural-Net Lesrning Algorithm
t
I
Fig.7.Trainingenvironment. Training patterns are expressed as (input, target) pairs for each scenario. After a set of training examples is collected (17 of them in our case), the supervised learning network is trained [13]. The neural net is configured as a flat, no hidden layer architecture with the functional link comprising 5 inputs and 1 output. We used the third-order joint activation model to enhance the pattern representation [8]. As we mentioned already, network inputs are 5 consecutive readings of the liquid level while network output provides the graded opening of the tank input valve. The (+1, - 1 ) range of the sigmoidal curve is mapped into the maximal allowed changes in valve positions from one time instant to
another. The control throughput is approximately 0.25 seconds.
3.3. Neural-net predictor The role of the neural-net predictor is to learn the mapping of the closedqoop system dynamics under different operating conditions. Once this mapping is obtained, the decision unit will be able to choose the level sensor, x[1] or x[2], that gives a closer reading, Z, compared to the predicted level, £. The training samples for predictor network are collected from the closed-loop system operation. Several scenarios are set up with different flow in rate, flow out rate,
56
Y.-H Pao, D.J. Sobajic / Nonlinear process control
liquid level and target level. The neural-net controller is employed to generate control actions for each scenario. History sequences of liquid levels at separate time intervals are collected providing the training set for the predictor. The predictor serves as the real time pointer to the "better" sensor reading. The decision unit is supposed to pass this informa-
tion to the neural-net controller which generates the control signal. 4. N u m e r i c a l r e s u l t s
Figures 8 and 9 describe the nature of the system behaviour in the simulated environment. In both
normoliJed
values
!0
2
v
0.75
i
~
4
,,-~ AA rl L ~A
,t,
,
0.25 -
0. -
lime Isec)
0
I
I
I
I
I ~
5
10
15
20
25
Fig. 8. System response to output demand decrease. Stable control response generated by tracking less noisy sensor. (l: first level measurement, 2: second leve! measurement, 3: target level, 4: predicted level, 5: input flow rate, 6: output demand). normalized
l.O
i
vnlue~
6t
_-
,--'-'--'x
0.75
3J 0.5-
0.25 -
Ihue I SL'C) 0.-
0
II
I
I
I
I
In"
S
10
15
2o
25
Fig. 9. System response to target level increase with sensor 2 stuck. Stable control response generated by tracking less noisy sensor; system ignores momentarily correct reading at time t I of stuck sensor.
Y.-H Pao, D.J. Sobajic / Nonlinear process control
cases we are dealing with t h e " step t a n k " shape (Fig. 5(d)) and it is assumed that the tank is emptied by a constant pressure pump. Sensor 1 is modelled as the more accurate one with standard deviation of 0.5°7o while standard deviation for sensor 2 is 5 070. In Fig. 8, we see the typical stabilizing control action that occurs after the step decrease in the demand (curve 6). In Fig. 9, we are observing the process of filling the tank. Of a particular interest, is the fact that the less accurate sensor 2 suddenly jumps to the value that will at some later time (tl) become
57
correct. It is noticeable that the predictor (curve 4) " f o l l o w s " the correct, more accurate, sensor, namely x[1]. As a matter o f fact we have observed the tendency that the predictor will always follow the less noisy signal. In Fig. 10, we demonstrate similar ability of the predictor under different circumstances. This experiment has been performed using the real tank. One of the two sensor readings (curve 2) suddenly has dropped to approximately 1/3 of the correct reading (by inserting an external capacitance 1 0 / ~
normalited rabies
1.0
4
0.75
0.5
~
0.25
¢.2
O.
lime Isec|
,a.-
0
10
5
IS
20
25
Fig. 10. System response to target level decrease immediately followed by malfunctioning of sensor 2.
~t)
Ws
x(t-l)
x(t-2)
x(t-n)
second order joint activation terms
third order joint activation
{x(t-i)*x(t-j)} for i
{x(t-i)*x(t-j)*x(t-k)} for i
terms
Fig. 11. A schematic diagram of the functional link net state predictor.
58
Y.-H Pap, D.J. Sobajic / Nonlinear process control
across the sensor outputs). The decision logic compares the predicted state (curve 4) to the actual ones (curves 1 and 2) and passes the correct information to the neural-net controller, which continues to maintain the new desired target level (curve 3). The experiments have shown that the neural-net control system is capable of maintaining the tank liquid level at any desired level, stabilizing the system in the presence of large disturbances, detecting and identifying defective level sensors, and estimating parameters in nonlinear processes. In the training of the neural-net controller, training examples represent the control actions under different scenarios. The system will learn to respond to the real-time situations so as to maintain the desired level readings. The approach taken in the predictor design is to teach the network to learn the associative mapping between the system dynamics and the expected error in level readings. The predictor network is configured as the flat functional link net, as shown in Fig. 11, with 8 inputs and one output. The inputs constitute 8 consecutive "best" level readings and the output is the estimate of the level reading in the next scanning interval. The common feature of the neural-net controller and the predictor is the use of functional link net architectures. This higher order network architecture speeds up the training process exhibiting favorable characteristics for the use in on-line process control.
Conclusion Most of the real-world industrial processes cannot be described by exact mathematical models. Emphasizing the significance of feedback control in reducing the effects of uncertainties we have proposed a new design of the flexible and robust stabilizing controller. The control system design is based on the pattern recognition principle and the implementation on the parallel distributed computational architectures of artificial neural systems. The neural-net control system has been trained to provide stabilizing controls and to detect and identify malfunctioning sensors. Developed meth-
odology is demonstrated on the nonlinear liquid level control problem. The results presented in this paper include both simulations and experiments on the real system.
References [1] K.J. Astrom and T. Hagglund, Automatic tuning of simple regulators for phase and amplitude margins specification, IFAC Workshop on Adaptive Systems in Control and Signal Processing, San Francisco, CA (1983). [2] K.J. Astrom and B. Wittenmark, On self-tuning regulators, Automatica 9 (1973) 185 - 199. [3] A. Barto, R. Sutton and C. Anderson, Neuronlike elements that can solve difficult learning control problems, IEEE Trans. Systems Man Cybernet.13 (1983) 835- 846. [4] D.W. Clarke and P.J. Gawthrop, Self-tuning controller, Proc. IEEE 122 (1975) 929-934. [5] G.H. Cohen and G.A. Coon, Theoretical investigation of retarded control, Trans. A S M E 75 (1953) 827. [6] T.R. Fortescue, L.S. Kershenbaum and B.E. Ydstie, Implementation of self-tuning regulators with variable forgetting factors, Automatica 17 (6) (1981) 831 -835. [7] A. Guez, J.L. Eilbert and M. Kam, Neural network architecture for control, IEEE Control System Magazine 8 (2) (1988) 22 - 25. [8] M.S. Klassen, Y.-H. Pap and V. Chen, Characteristics of the functional link net: a higher order delta rule net, IEEE International Conference on Neural Networks 1, San Diego, CA (1988) 507-513. [9] Y.-H. Pao, Adaptive Pattern Recognition and Neural Networks (Addison-Wesley, Reading, MA, 1989). [I0] Y.-H. Pap, V.C. Chen and D.J. Sobajic, A perspective on research aimed at understanding the systems nature of neural controllers, in: Proceedings o f the International Joint Conference on Neural Networks, Washington, DC (1989). [11] Y.-H. Pap and D.J. Sobajic, A perspective on the role of parallel distributed processing of the neural-net type in implementing automation, in: Proceedings o f the IEEE Workshop on Languages f o r A utomation, Vienna (1987). [12] D. Psaltis, A. Sideris and A. Yamamura, A multilayered Neural Network Controller, IEEE Control System Magazine 8 (2) (1988) 1 7 - 21. [13] D.J. Sobajic, D.T. Lee, and Y.-H. Pap, Increased effectiveness of learning by local neural feedback, INNS First Annual Meeting, Boston, MA (1988) 222. [14] D.J. Sobajic, Y.-H. Pap and J.J. Lu, Neural-net control for robotics: design criteria and learning structures, SPIE Conference, Cambridge, MA (1988). [15] P.E. Wellstead, D. Prager and P. Zanker, Pole assignment
Y.-H Pao, D.J. Sobajic / Nonlinear process control
self-tuning regulator, Proc. lEE 126 (8) (1979) 781 -786. [16] B. Widrow, The original adaptive neural-net broombalancer, IEEE International Symposium on Circuits and Systems (1987) 351 - 357. [17] B. Widrow, J.M. McCool, M.G. Larimore and C.R. Johnson Jr, Stationary and nonstationary learning characteristics of the LMS adaptive filter, Proc. IEEE 64 (8) (1976) 1151 - 1162. [18] M. Yuwana and D. Seborg, A new method for on-line controller tuning, AIChE J. 28 (1982) 434-440. [19] C. Zervos, P.R. Belanger and G.A. Dumont, On PID controller tuning using orthonormal series identification, Automatica 24 (2) (1988) 165- 175. [20] J.G. Ziegler and N.B. Nichols, Optimum setting for PID controllers, Trans. A S M E 64 (1942) 759 - 768.
Yoh-Han Pan, has been a Professor of Electrical Engineering and Computer Science at Case Western Reserve University (CWRU) since 1976. He has served as chairman of the University's Electrical Engineering Department (1969-77), as Director of the Electrical, Computer and System Engineering Division at NSF (1978 - 80), and as founding director of the Center of Automation and In~ inn telligent Systems Research at CWRU. He is the George S. Direly Distinguished Professor of Engineering at CWRU, is a Fellow of IEEE and of the American Optical Society. He has been a NATO Senior Science Fellow; has visited MIT, Edinburgh University, and the Turing Institute as lecturer/research, and has been a member of the technical staff at AT&T Bell Laboratories in Murray Hill, NJ. He is co-founder and president of AI Ware Inc., Cleveland, OH.
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D.J. Sobajic, (M'80-SM'89) was born in Yugoslavia in 1949. He received the BSEE and the MSEE degrees from the University of Belgrade, Belgrade, Yugoslavia in 1972 and 1976, respectively and the Ph.D. degree from Case Western Reserve University, Cleveland, OH in 1988. At present, he is with the Department of Electrical Engineering and Applied Physics, Case Western Reserve University, Cleveland, OH. He is also Engineering Manager of AI WARE, Inc. His current research interests include power system operation and control, neural net systems and adaptive control. Dr. Sobajic is a member of the IEEE Task Force on Neural Network Applications in Power Systems and of the IEEE Intelligent Control Committee. He is the Chairman of the International Neural Networks Society Special Interest Group on Power Engineering.