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illustrates the square output estimation error plotted in logarithmic scale. This error prove the efficiency of the neural emulation approach. The evolution of neural emulator parameters η e and τ e is given by Fig. 11. This figure illustrates a satisfactory adaptation of the parameters τ e , η e. The obtained results prove the good performance of the neural emulator method adapted for the real time emulation of chemical reactor.
Source publication
In this paper, we develop an indirect adaptive control struc-
ture based on recurrent neural networks. An adaptive emulator inspired
from the Real Time recurrent Learning algorithm is presented. Neural
network does not learn the plant dynamics but emulates the input-output
mapping with a small time window. Thereafter, a controller with a struc-
tur...
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Citations
... In the following, the used NE is a fully connected recurrent neural networks ( Fig. 1) [22]. ...
... Researchers had considered different strategies. Among them, we can cite the proposition of Neural emulators based on Real-Time Recurrecnt Learnning algorithm, Uncoupled multimodel emulators, emulators based on fuzzy logic... [12,14,22]. However, these strategies present some disadvantages which are mentioned previously. ...
... In order to show the efficiency of the proposed PSONE strategy, a comparison with the method based on fuzzy adaptive rate is considered (Fig. 16). Noting that the last strategy has been compared previously with the classical selection of NE adaptive rate [22] and it has given good results. So, it is clearly that the proposed emulator using the PSONE algorithm to update the NE adaptive rate, provides a satisfactory estimation of the reactor output with regards to the fuzzy supervision of the NE adapting rate (Fig. 16). ...
Searching an optimal value of the neural emulator adaptive rate presents a great problem. Indeed, a new scheme of neural emulators based on the Particle Swarm Optimization (PSO) algorithm for nonlinear systems is adopted in this paper. The main goal of this approach consists in adjusting effectively the neural emulator adaptive rate in order to accelerate the convergence speed and to improve the precision degree. The obtained results are compared with those reached with an intelligent tuning strategy. An experimental validation of the new emulator adaptation is carried on chemical reactor. Efficiency of the proposed method is proved according to the obtained performances.
... To examine the performance of the control design, we consider a conventional NC based on the starting term as proposed in (Atig et al., 2010a). The evolution of the real system and the desired outputs are presented in Figure 8. ...
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... In recent works, the neural emulator parameter is self tuned beginning with zero initial conditions. In addition, the performances achieved depend on an emulator starting term which is chosen arbitrarily [3]. Indeed, a random and faulty selection of the emulator startup term affects the performance in terms of speed and accuracy of the output prediction. ...
... is the system inputs. w i j (t) and 1/ |τ e (t)| represent respectively the weight from j th neuron to i th neuron and the NE time parameter [17]. ...
... In the present study, a numerical example is defined to highlight the good performances of the NC using the neural emulator fuzzy adapting parameter for Multi-Input Multi-Output (MIMO) nonlinear processes. We consider a MIMO nonlinear process given by (24) [3]: To prove the efficiency of the developed approach, results are compared with those based on neural emulator using the starting term [17], given by figure 5, and results with those based on neural emulator using constant adapting parameter [18], illustrated by figure 6. The simulation results demonstrate the satisfactory closed-loop performances of the developed approach. ...
... 29 The good performance of the proposed adaptive scheme including the augmented NC structure and the relaxed adaptive rates and time parameters have been illustrated for the control of single-input-singleoutput (SISO) and multiple-input-multiple-output (MIMO) square systems. 29,30 The main drawback of the approaches proposed in Leclercq et al., 27 Zerkaoui et al., 28 and Atig et al. 29 is the necessity to fulfill some conditions so that the methods can be applied with numerous processes and the slowness convergence of the gradient algorithm. However, an emulator and controller terms, used for the starting and the autonomous evolution of the algorithm starting from zero initial conditions, are chosen arbitrarily. ...
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... According to the asymptotic stability theory, the adaptive control scheme is Lyapunov asymptotically stable if Tl c(t ) satisfy this condition: (13) where ac(t ) and bc(t ) are two functions defined by (14) and ...
... Let us define the test function fe(t ) that check if Tle(t ) satisfies the sufficient stability conditions when the emulation error is used as a Lyapunov function. Then, we can conclude the stability of the controlled plant according to the inter section of the sufficient conditions on TIe (20) and TIc (13). So, fc-e(t ) is a test function obtained from the intersection between the test functions fe(t ) and fc(t ) . ...
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... Weights are online updated. The major advantage of this algorithm is its use for real time applications [17]- [19]. ...
... The discretization of the dynamic equations (1) and (5) is given respectively with (18) and (19) [11]: ...
... and D(k) are considered constant during each ∆T [11], [19]. ...
This paper deals with a new indirect adaptive control scheme with decoupled adaptive rates, developed for complex square systems with unknown dynamics. This scheme, based on fully connected neural networks, is inspired from the real time recurrent learning (RTRL) algorithm. Both neural emulator and neural controller networks do not learn the plant dynamics but only adapt their parameters using an online adaptation algorithm in order to track the process variations. The contributions of this paper are to propose a new structure of neural control with a full structure of neural controller and to demonstrate the efficiency of the relaxation of networks parameters relative to the new proposed structure. Advantages of Neural controller with full structure and relaxation of its parameters from neural emulator ones are suggested according to simulation of nonlinear system. Effectiveness of the new proposed control structure is established by its application to the well-known Tennessee Eastman Challenge Process.
