Dynamic matrix control

The last decade has seen the development a several control concepts that are based on using a model of the process as part of the controller. Most of these methods use Laplace or z-transform representations of the process, which we are not yet ready to handle. After our Russian lessons have been completed, we will discuss some of these. 

There is one method that is based on a time-domain model. It was developed at Shell Oil Company (C, R. Cutler and B. L. Kamaker, Dynamic Matrix Control A Computer Control Algorithm, paper presented at the 86th National AlChE Meeting, 1979) and is called dynamic matrix control (DMC). Several other methods have also been proposed ihat are quite similar. The basic idea is to use a time-domain step-response model of the process to calculate the future changes in the manipulated variable that will minimize some performance index. Much of the explanation of DMC given in this section follows the development presented by C. C. Yu in his Ph.D. thesis (Lehigh University, 1987). 

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C. R. Cutier and B. L. Ramaker, "Dynamic Matrix Control A Computer Control Algorithm," Proceedings of Joint Auto. Control Conference, Paper... 

A. M. Morshedi, C. R. Cutier, and T. A. Skrovanek, "Optimal Solution of Dynamic Matrix Control with Linear Programming Techniques,"... 

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. 

Finally, a brief discussion is given of a new type of control algorithm called dynamic matrix control. This is a time-domain method that uses a model of the process to calculate future changes in the manipulated variable such that an objective function is minimized. It is basically a least-squares solution. 

Dynamic matrix control uses time-domain step-response models (called convolution models). As sketched in Fig. 8.18, the response (x) of a process to a unit step change in the input (Ami = ) made at time equal zero can be described by the values of x at discrete points in time (the fc, s shown on the figure). At r nTJ, the value of X is h r,. If Affii is not equal to one, the value of x at f = n7 is b j Aibi, The complete response can be described using a finite number (NP) values of b coefficients. NP is typically chosen such that the response has reached 90 to 95 percent of its final value. 

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. 

Morshedi, A. M., Universal dynamic matrix control, Chemical Process Control Conf. Ill (Morari and McAvoy, eds.). CACHE Corp., 1986, p. 547. 

When thermodynamics or physics relates secondary measurements to product quality, it is easy to use secondary measurements to infer the effects of process disturbances upon product quality. When such a relation does not exist, however, one needs a solid knowledge of process operation to infer product quality from secondary measurements. This knowledge can be codified as a process model relating secondary to primary measurements. These strategies are within the domain of model-based control Dynamic Matrix Control (DMC), Model Algorithmic Control (MAC), Internal Model Control (IMC), and Model Predictive Control (MPC—perhaps the broadest of model-based control strategies). 

DMC has its origins in industry. Cutler and Ramaker [35] outlined the DMC strategy Prett and Gillette [36] showed its application to a fluid catalytic cracking unit. The most popular version of DMC is now Quadratic Dynamic Matrix Control (QDMC) [37,38] which... 

Quadratic Dynamic Matrix Control Qualitative Process Automation fractional weighting factor in EWMA regression correlation coefficient reference rate of resin curing... 

Garcia, C.E. Quadratic/Dynamic Matrix Control of Nonlinear Processes An Application to a Batch Reaction Process, (1984) AIChE 1984 National Meeting, San Francisco... 

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). 

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],... 

J.R. Cutler and B.L. Ramaker. Dynamic matrix control—a computer control algorithm. In Proceedings of the Joint Automatic Control Conference, 1980. 

Dynamic matrix control (DMC) is also an MVC technique, but it uses a set of linear differential equations to describe the process. The DMC method obtains its data from process step responses and calculates the required manipulations utilizing an inverse model. Coefficients for the process dynamics are determined by process testing. During these tests, manipulated and load variables are perturbed, and the dynamic responses of all... 

Other recent developments in the field of adaptive control of interest to the processing industries include the use of pattern recognition in lieu of explicit models (Bristol (66)), parameter estimation with closed-loop operating data (67), model algorithmic control (68), and dynamic matrix control (69). It is clear that discrete-time adaptive control (vs. continuous time systems) offers many exciting possibilities for new theoretical and practical contributions to system identification and control. 

Model predictive control (MPC) has become widely known as dynamic matrix control (DMC) and model algorithmic control (MAC). A review of the origins of this class of techniques and their theoretical foundations is provided by Garcia et al. [10]. Many complex applications were reported at the recent IFAC Workshop [11]. 

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. 

Garda, C. E., and Morshedi, A. M., Quadratic programming solution of dynamic matrix control (QDMC), Chem. Eng. Comm. 46, 73-87 (1986). 

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. 

Cutler, C. R. and Ramaker, B. L., Dynamic Matrix Control - A Computer Control Algorithm, Paper i 5 h,AIChE 86 Meeting (April, 1979)... 

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