Model predictive control nonlinearity

Off-line analysis, controller design, and optimization are now performed in the area of dynamics. The largest dynamic simulation has been about 100,000 differential algebraic equations (DAEs) for analysis of control systems. Simulations formulated with process models having over 10,000 DAEs are considered frequently. Also, detailed training simulators have models with over 10,000 DAEs. On-line model predictive control (MPC) and nonlinear MPC using first-principle models are seeing a number of industrial applications, particularly in polymeric reactions and processes. At this point, systems with over 100 DAEs have been implemented for on-line dynamic optimization and control. 

Extended Kalman filtering has been a popular method used in the literature to solve the dynamic data reconciliation problem (Muske and Edgar, 1998). As an alternative, the nonlinear dynamic data reconciliation problem with a weighted least squares objective function can be expressed as a moving horizon problem (Liebman et al., 1992), similar to that used for model predictive control discussed earlier. 

Patwardhan, A. A., Rawlings, J. B., and Edgar, T. F., Model predictive control of nonlinear processes in the presence of constraints, presented at annual AIChE Meeting, Washington, D.C. (1988). 

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. 

P. Kittisupakom, Ph.D. thesis, The use of nonlinear model predictive control techniques for the control of a reactor with exothermic reactions, University of London, 1995. 

One important class of nonlinear programming techniques is called quadratic programming (QP), where the objective function is quadratic and the constraints are linear. While the solution is iterative, it can be obtained quickly as in linear programming. This is the basis for the newest type of constrained multivariable control algorithms called model predictive control, which is heavily used in the refining industry. See the earlier subsection on model predictive control for more details. 

L. Magni, D.M. Raimondo, and F. Allgower, editors, Nonlinear Model Predictive Control. Springer, Berlin, 2009. 

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

A. A. Patwardhan, J.B. Rawlings, and T.F. Edgar. Nonlinear model predictive control. Chemical Engineering Communications, 87 1-23, 1990. 

H. Seki, M. Ogawa, S. Ooyama, K. Akamatsu, M. Ohshima, and W. Yang. Industrial application of a nonlinear model predictive control to polymerization reactors. Control Engineering... 

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

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,... 

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

Liu, J., Munoz de la Pena, D., and Christofides, P. D. (2009). Distributed model predictive control of nonlinear process systems. AIChE J., 55, 1171-1184. 

Ricker, N. L. and Lee, J. H. (1995). Nonlinear model predictive control of the Tennessee Eastman challenge process. Cornput. Chem. Eng., 19, 961. 

Zhu, G. Y., Henson, M.A., and Ogunnaike, B.A. (2000). A hybrid model predictive control strategy for nonlinear plant-wide control. J. Proc. Contr., 10, 449-458. 

LeLann et al. [6] discuss tendency modeling (using approximate stoichiometric and kinetic models for a reaction) and the use of model predictive control (linear and nonlinear) in batch reactor operation. Studies of a hybrid heating-cooling system on a 16-L pilot plant are presented. 

Very few unbiased publications have appeared in the literature comparing control effectiveness using MPC versus a well-designed conventional control system. Most of the MPC applications reported have considered fairly simple processes with a small number of manipulated variables. There are no published reports that discuss the application of MPC to an entire complex chemical plant, with one notable exception. That is the work of Ricker (1996), who compared MPC with conventional PI control for the Eastman process (TE problem). His conclusion was there appears to be little, if any, advantage to the use of nonlinear model predictive control (NMPC) in this application. In particular, the decentralized strategy does a better job of handling constraints—an area in which NMPC is reputed to excel.51... 

Ricker, N. L. Model Predictive Control of a Continuous. Nonlinear, Two-Phase Reactor," /. Proc. Cont., 3, 109-123 (1993),... 

Badgwell, T. A., A robust model predictive control algorithm for stable nonlinear plants. Preprints of ADCHEM 97, Banff, Canada (1997). 

Genceli, H. and Nikolaou, M., Design of robust constrained nonlinear model predictive controllers with Volterra series, AIChE J. 41, 9, 2098-2107 (1995). 

Mayne, D. Q., Nonlinear model predictive control An assessment, in Fifth International Conference on Chemical Process Control (Kantor, J. C., Garcia, C. E., and Carnahan, B., Eds.), AIChE Symposium Series, Vol. 93, pp. 217-231 (1997). 

Morari, M., and de Oliveira, S. L., Contractive model predictive control for constrained nonlinear systems, IEEE Trans. AC, in press (1997). 

Rawlings, J. B., Meadows, E. S., and Muske, K. R., Nonlinear model predictive control A tutorial and survey. Proceedings of ADCHEM 94, 203-214, Kyoto, Japan (1994). 

The challenges in SMB control are not only the complex nonlinear process dynamics, but also the long delays of the effect of disturbances. The required control strategy has to be able to handle multivariable dynamics with time-delays and hard constraints. Model Predictive Control (MPC) has been proven to be the most effective control strategy for this type of problems [1,2]. Only recently, a few scientific publications have addressed the automatic... 

A linear model predictive control law is retained in both cases because of its attracting characteristics such as its multivariable aspects and the possibility of taking into account hard constraints on inputs and inputs variations as well as soft constraints on outputs (constraint violation is authorized during a short period of time). To practise model predictive control, first a linear model of the process must be obtained off-line before applying the optimization strategy to calculate on-line the manipulated inputs. The model of the SMB is described in [8] with its parameters. It is based on the partial differential equation for the mass balance and a mass transfer equation between the liquid and the solid phase, plus an equilibrium law. The PDE equation is discretized as an equivalent system of mixers in series. A typical SMB is divided in four zones, each zone includes two columns and each column is composed of twenty mixers. A nonlinear Langmuir isotherm describes the binary equilibrium for each component between the adsorbent and the liquid phase. 

The model predictive control used includes all features of Quadratic Dynamic Matrix Control [19], furthermore it is able to take into account soft output constraints as a non linear optimization. The programs are written in C++ with Fortran libraries. The manipulated inputs (shown in cm Vs) calculated by predictive control are imposed to the full nonlinear model of the SMB. The control simulations were made to study the tracking of both purities and the influence of disturbances of feed flow rate or feed composition. Only partial results are shown. 

Model Predictive Control, also referred as moving or receding horizon control, has become an attractive control strategy especially for linear but also for nonlinear systems subject to input, state or output constraints [4]. MPC determines the control action based... 

Nonlinear model predictive control of a swelling constrained industrial batch reactor... 

---