Dynamic Neural Model for DMC Applications

In this work the development of a Dynamic Matrix Control (DMC) strategy based on the use of a dynamic neural network model is discussed for a three components distillation unit, used as prototype of an industrial C3/C4 splitter tower. A novel dynamic neural network model is set-up and its advantages for DMC applications are addressed. The neural network is used to describe the temporal evolution of the outlet concentrations of C3 and of C4 in the residue and distillate streams, respectively. In particular, the structure of the dynamic net is such that the nonlinear dependence of the outlet concentrations on the process inputs is described in an effective way through a pseudo-linear ODE model. This makes the implementation of the DMC strategy very effective since the dynamic matrix becomes time invariant and this leads to a reduction of the matrix algebra involved. Introduction Real applications of advanced control schemes such as model predictive controllers, MPC, (DMC, gain process controller, GPC, etc.) are increasing in the chemical process industries because of their ability to deal with multivariable, possibly, constrained systems by making use of simple, generally linear, process models. Unfortunately, the strong nonlinearities of many chemical processes restrict the application of MPC strategies only to the neighbourhood of the nominal operating conditions about which the models are tuned. This limitation can be overcome by developing simple nonlinear process models or by using on-line multivariable gain structures integrated with time constant scheduling techniques for updating the process model (Ogunnaike and Ray, 1994). In this work a simple novel dynamic neural network topology (with only one internal layer) is proposed to describe the dynamic behavior of a distillation column. The dynamics is accounted for by making recurrent the output layer of a multi feed-forward neural network model and using a linear combination of the neuron outputs of the internal layer as forcing functions. This leads to the formulation of a simple linear dynamic model, with constant coefficients, in which the process nonlinearities are described through the forcing functions. Indeed, these depend on the process inputs in a non-linear fashion, because the conventional S -shape activation function is adopted for the neurons of the internal layer. The advantage of using the outlined modeling approach to develop DMC control structures is twofold. Firstly, the nonlinearities of the process are accounted for in an effective fashion through a linear model structure. Secondly, the inversion of the transfer matrix must be carried out only once because its entries are time invariant. As a result, the computational efforts are strongly reduced allowing the implementation of DMC control strategies directly on DCS systems. In this communication, the performance of a DMC control structure based on the outlined dynamic neural model is discussed for a three components distillation column used as prototype of a C3/C4 splitter tower. The transient data required for the net training and for the assessment of the DMC strategy were generated through a simplified dynamic simulator previously described (Baratti et al., 1996). As it is in real practice, the control objectives were set so as to keep as low as possible the concentration of C4 in the distillate and of C3 in the residue. Dynamic Neural Model As stated in the Introduction a simple dynamic neural network model of a multicomponent distillation column has been developed by making recurrent the output layer of a multi feed-forward neural net as depicted in Figure 1. Care must be paid in selecting the net topology because the application of a DMC strategy requires the inversion of the net that becomes possible only when the hidden and output layers have the same number of neurons (Baratti et al., 1996). The outputs of the dynamic neural model, namely the mole fractions of C4 (y1) in the distillate and of C3 (y2) in the residue, are computed as follows: τ1 d y1 d t + y1 = w 1,1 z2 1 ( ) + w 2,1 z2 2 ( ) ; y1 t = to ( ) = y1