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Predictive control of nonlinear systems in the process industry

Project members: H.H.J. Bloemen, T.J.J. van den Boom, J.M.A. Scherpen, M. Verhaegen, V. Verdult, H. Oku, H.B. Verbruggen

Sponsored by: STW

The project aims at the development of methods that enable to transfer the high investment return of currently used Model-based Predictive Controller (MPC) schemes for linear systems to important classes of nonlinear systems in the process industry.

  • The first class contains systems which can, from an input-output point of view, accurately be described by a linear dynamical model when the operating range of the system is limited. Though, the present generation of MPCs are designed for this limited operating range, the tendency to produce more client oriented, will cause the processes to frequently make a transition from one limited operating range to the next. Using existing MPC technology these transient effects are not taken into account, possibly leading to non-smooth transitions and therefore economical losses.

  • The second class contains processes that even for a limited operating range demonstrate a nonlinear behavior. An example is a high purity distillation column which for a particular operating range can accurately be described by a series connection of a linear time-invariant (LTI) dynamic model followed by a static output nonlinearity (NL), a so-called Wiener model (see Figure 6).

Figure 6: Block diagram of a Wiener model.
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The special way in which the nonlinearity enters the Wiener model can be exploited by transforming it into uncertainty. The result will be an uncertain linear model, which enables to use robust linear MPC techniques. A similar approach can be applied for Hammerstein systems, in which case a linear dynamic block is preceded by a static input nonlinearity. This Hammerstein-Wiener MPC algorithm [8] extends the linear MPC algorithm described in [10]. A case study, concerning the distillation column benchmark, has demonstrated the effectiveness of the proposed Wiener MPC algorithm and is presented in [7].

Also discrete-time bilinear models may be useful for black-box identification of nonlinear processes. In bilinear models the nonlinearity enters the dynamic part of the model, i.e. the state equation contains a product term between the current state and the current input. This property can be exploited for solving a ''classical'' finite horizon MPC problem [9]. An application of bilinear MPC to a polymerization reactor is presented in [12]. Extensions to an infinite-horizon bilinear MPC algorithm can be found in [5,11]. Extensions to bilinear MPC algorithms that aim at a low computational demand for the on-line computations are reported in [6,5].

This project is part of STW project DEL 55.3891. This project is done in co-operation with the Control group of the University of Oxford, UK.


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