Process control nonlinear models

Simulation of Dynamic Models Linear dynamic models are particularly useful for analyzing control-system behavior. The insight gained through linear analysis is invaluable. However, accurate dynamic process models can involve large sets of nonlinear equations. Analytical solution of these models is not possible. Thus, in these cases, one must turn to simulation approaches to study process dynamics and the effect of process control. Equation (8-3) will be used to illustrate the simulation of nonhnear processes. If dcjdi on the left-hand side of Eq. (8-3) is replaced with its finite difference approximation, one gets ... 

Sinnar, R., Impact of model uncertainties and nonlinearities on modem controller design In Chemical Process Control, CPC-III. (Morari, M. and McAvoy, T. J., eds.), p. 53 CACHE-Elsevier, 1986. 

In principle, any type of process model can be used to predict future values of the controlled outputs. For example, one can use a physical model based on first principles (e.g., mass and energy balances), a linear model (e.g., transfer function, step response model, or state space-model), or a nonlinear model (e.g., neural nets). Because most industrial applications of MPC have relied on linear dynamic models, later on we derive the MPC equations for a single-input/single-output (SISO) model. The SISO model, however, can be easily generalized to the MIMO models that are used in industrial applications (Lee et al., 1994). One model that can be used in MPC is called the step response model, which relates a single controlled variable y with a single manipulated variable u (based on previous changes in u) as follows ... 

NN applications, perhaps more important, is process control. Processes that are poorly understood or ill defined can hardly be simulated by empirical methods. The problem of particular importance for this review is the use of NN in chemical engineering to model nonlinear steady-state solvent extraction processes in extraction columns [112] or in batteries of counter-current mixer-settlers [113]. It has been shown on the example of zirconium/ hafnium separation that the knowledge acquired by the network in the learning process may be used for accurate prediction of the response of dependent process variables to a change of the independent variables in the extraction plant. If implemented in the real process, the NN would alert the operator to deviations from the nominal values and would predict the expected value if no corrective action was taken. As a processing time of a trained NN is short, less than a second, the NN can be used as a real-time sensor [113]. 

Batch processes, such as autoclave curing, are inherently nonlinear and dynamic. For on-line quality control, the model must predict the outcome of the batch (i.e., product quality) in terms of the input and processing variables. The variables associated with the process are ... 

For continuous process systems, empirical models are used most often for control system development and implementation. Model predictive control strategies often make use of linear input-output models, developed through empirical identification steps conducted on the actual plant. Linear input-output models are obtained from a fit to input-output data from this plant. For batch processes such as autoclave curing, however, the time-dependent nature of these processes—and the extreme state variations that occur during them—prevent use of these models. Hence, one must use a nonlinear process model, obtained through a nonlinear regression technique for fitting data from many batch runs. 

Ansari, R.M. arid M.O. Tade Nonlinear Model-Bated Process Control Applications in Petroleum Refining, Springer-Vedag, Inc-, New York. NY, 2000. 

Adaptive controllers can be usefully applied because most processes are nonlinear (Section 7.16) and common controller design criteria (Section 7.12) are based on linear models. Due to process non-linearities, the controller parameters required to give the desired response of the controlled variable change as the process steady state alters. Furthermore, the characteristics of many processes vary with time, e.g. due to catalyst decay, fouling of heat exchangers, etc. This leads to a deterioration in the performance of controllers designed upon a linear basis. 

W. Marquardt. Nonlinear model reduction for optimization based control of transient chemical processes. AIChE Symposium Series 326, 98 12-42, 2001. 

Early applications of MPC took place in the 1970s, mainly in industrial contexts, but only later MPC became a research topic. One of the first solid theoretic formulations of MPC is due to Richalet et al. [53], who proposed the so-called Model Predictive Heuristic Control (MPHC). MPHC uses a linear model, based on the impulse response and, in the presence of constraints, computes the process input via a heuristic iterative algorithm. In [23], the Dynamic Matrix Control (DMC) was introduced, which had a wide success in chemical process control both impulse and step models are used in DMC, while the process is described via a matrix of constant coefficients. In later formulations of DMC, constraints have been included in the optimization problem. Starting from the late 1980s, MPC algorithms using state-space models have been developed [38, 43], In parallel, Clarke et al. used transfer functions to formulate the so-called Generalized Predictive Control (GPC) [19-21] that turned out to be very popular in chemical process control. In the last two decades, a number of nonlinear MPC techniques has been developed [34,46, 57],... 

Several process control design methods, such as the Generic Model Control (GMC) [41], the Globally Linearizing Control (GLC) [37], the Internal Decoupling Control (IDC) [7], the reference system synthesis [8], and the Nonlinear Internal Model Control (NIMC) [29], are based on input-output linearization. 

J.B. Balchen, B. Lie, and I. Solberg. Internal decoupling in nonlinear process control. Modeling Identification and Control, 9 137-148, 1988. 

Z.K. Nagy and R.D. Braatz. Robust nonlinear model predictive control of batch processes. AIChE Journal, 49 1776-1786, 2003. 

Rigorous nonlinear models must be used in analyzing batch reactors because of the changing process parameters. Continuous reactors operate around some steady-state level, so linear models are sometime adequate for establishing controller tuning constants. 

R. K. A1 Seyab and Y. Cao, Nonlinear model predictive control of the ALSTOM gasifier, J. Process Control, 16, 795-808 (2006). 

Finally, nonlinear wave can also be used for nonlinear model reduction for applications in advanced, nonlinear model-based control. Successful applications were reported for nonreactive distillation processes with moderately nonideal mixtures [21]. For this class of mixtures the column dynamics is entirely governed by constant pattern waves, as explained above. The approach is based on a wave function which can be used for the approximation of the concentration profiles inside the column. The wave function can be derived from analytical solutions of the corresponding wave equations for some simple limiting cases. It is given by... 

Wave models were successfully used for the design of a supervisory control system for automatic start-up of the coupled column system shown in Fig. 5.15 [19] and for model-based measurement and online optimization of distillation columns using nonlinear model predictive control [15], The approach was also extended to reactive distillation processes by using transformed concentration variables [22], However, in reactive - as in nonreactive - distillation, the approach applies only to processes with constant pattern waves, which must be checked first. 

S. Griiner, S. Schwarzkopf, I. Uslu, et ah, Nonlinear model predictive control of multicomponent distillation columns using wave models. Proceedings, jth International Symposium on Advanced Control of Chemical Processes. Vol. 1,... 

Finally, we analyzed the control implications of the presence of impurities in a process, concluding that the control of impurity levels must be addressed over an extended time horizon using the flow rate of the purge stream as a manipulated input. To close the impurity-levels loop, one should resort either to an appropriately tuned linear controller (e.g., a PI controller with long reset time) or to a (nonlinear) model-based controller that uses (an inverse of) the reduced-order model of the slow dynamics - as developed in this chapter - to compute the necessary control action. 

Baldea, M., Daoutidis, P., and Nagy, Z.K. (2010). Nonlinear Model Predictive Control of integrated process systems. In Proceedings Nonlinear Control Systems (NOLCOS 2010). 

Kanadibhotla, R. S. and Riggs, J. B. (1995). Nonlinear model based control of a recycle reactor process. Comput. Chem. Eng., 19, 933-948. 

Kravaris, C., Niemiec, M., Berber, R., and Brosilow, C.B. (1998). Nonlinear model-based control of nonminimum-phase processes. In R. Berber and C. Kravaris, eds., Nonlinear Model Based Process Control, pp. 115-143. Dordrecht Kluwer Academic Publishers. 

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