Dynamic matrix control multivariable

Implementation of MPC For a new MPC application, a cost/benefit analysis is usually performed prior to project approval. Then the steps involved in the implementation of MPC can be summarized as follows (Hokanson and Gerstle, Dynamic Matrix Control Multivariable Controllers, in Practical Distillation Control, Luyben (ed.), Van Nostrand Reinhold, New York, 1992, p. 248 Qin and Badg-well, Control Ene. Practice, 11 773, 2003). 

The current widespread interest in MFC techniques was initiated by pioneering research performed by two industrial groups in the 1970s. Shell Oil (Houston, TX) reported their Dynamic Matrix Control (DMC) approach in 1979, while a similar technique, marketed as IDCOM, was published by a small French company, ADERSA, in 1978. Since then, there have been over one thousand applications of these and related MFC techniques in oil refineries and petrochemical plants around the world. Thus, MFC has had a substantial impact and is currently the method of choice for difficult multivariable control problems in these industries. However, relatively few applications have been reported in other process industries, even though MFC is a veiy general approach that is not limited to a particular industiy. 

Undoubtedly the most popular multivariable controller is the multivariable extension of dynamic matrix control. We developed DMC for a SISO loop in Chap. 8. The procedure was a fairly direct least-squares computational one that solved for the future values of the manipulated variable such that some performance index was rninirnized. 

With the dimension of multivariable MFC systems ever increasing, the probability of dealing with a MIMO process that contains an integrator or an unstable unit also increases. For such units FIR models, as used by certain traditional commercial algorithms such as dynamic matrix control (DMC), is not feasible. Integrators or unstable units raise no problems if state-space or DARMAX model MFC formulations are used. As we will discuss later, theory developed for MFC with state-space or DARMAX models encompasses all linear, time-invariant, lumped-parameter systems and consequently has broader applicability. 

One important class of nonlinear programming techniques is called quadratic programming (QP), where the objective function is quadratic and the constraints are hnear. While the solution is iterative, it can be obtained qmckly as in linear programming. This is the basis for the newest type of constrained multivariable control algorithms called model predic tive control. The dominant method used in the refining industiy utilizes the solution of a QP and is called dynamic matrix con-... 

The states of a dynamic system are simply the variables that appear in the time differential. The time-domain differential equation description of multivariable systems can be used instead of Laplace-domain transfer functions. Naturally, the two are related, and we derive these relationships below. State variables are very popular in electrical and mechanical engineering control problems, which tend to be of lower order (fewer differential equations) than chemical engineering control problems. Transfer function representation is more useful in practical process control problems because the matrices are of lower order than would be required by a state variable representation. For example, a distillation column can be represented by a 2X2 transfer function matrix. The number of state variables of the column might be 200. 

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