Dynamic Predictive Multivariable Control

As noted in the introduction to this chapter and in Section 16.1, several factors may compromise the effectiveness and stability of conventional control techniques for multiple variable processes, and specifically for multistage separations. A successful, comprehensive control strategy for such processes must take into account these factors, most of which are interrelated. 

Effective decoupling of interacting control loops may be hampered by different response times for each of the interacting loops. Decouplers are intended to cancel out interactions by implementing certain adjustments in each control loop. Predictors are also used with decouplers to forecast the dynamic responses. These techniques require considerable periodic tuning due to changes in feed flow rates, feed compositions, and other external conditions, and their success is limited. 

Process dynamics is another important factor that must be considered. In a distillation column, for instance, the time elapsed between changing the reflux rate and observing a change in a product composition could be measured in hours. With this response time, and in the absence of dynamic prediction capability, the controller will start taking action hours after a disturbance occurs, and it would take even longer for the correction to take effect. Linear predictions are commonly used to forecast trends of process variables but many processes, particularly multistage separations, are often highly nonlinear. Substantial improvement can be achieved with a nonlinear model. 

Another contributor to the lag between a disturbance and controller action is associated with product analyzers response time. Inferential property models that correlate product properties to readily measurable column variables can cut that response time (Smith, 2002). 

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Multivariable controls (MVCs) are particularly well suited for controlling highly interactive fractionators where several control loops need to be simultaneously decoupled. MVCs can simultaneously consider all the process lags, and apply safety constraints and economic optimization factors in determining the required manipulations to the process. The technique of multivariable control requires the development of dynamic models based on fractionator testing and data collection. Multivariable control applies the dynamic models and historical information to predict future fractionator characteristics. For towers that are subject to many constraints, towers that have severe interactions, and towers with complex configurations, multivariable control can be a valuable tool. 

One important class of nonlinear programming techniques is called quadratic programming (QP), where me 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. The dominant method used in the refining industry utilizes the solution of a QP and is called dynamic matrix con-... 

This paper describes the development of a novel dynamic predictive and optimal control method for the wet end of a papermaking systems. This part of the system plays an important function in the process in terms of its controllability and potential for optimisation. The wet end process is complicated and the control systems are always multivariable and dynamic in nature. Due to the severe interactions between each variable, general physical and chemistry based modelling techniques cannot be established. As such, feed-forward neural networks are selected as a modelling tool so as to build up a number of non-linear models that link all the variables to the concerned quality outputs and process efficiency. 

This paper has presented the development of a dynamic, predictive and optimal control method for the wet end of a papermaking system. The control of this part of the papermaking process is difficult because of its complex, multivariable and non-linear nature with long time delays. The main objective of this work has been to develop a closed loop control strategy suitable for control of the wet end processes of a paper machine. This includes industrial implementation directed towards achieving optimal control of the wet end of a paper making system. 

In multiple control loops each manipulated variable is associated with one controlled variable. A multivariable control strategy may involve a dynamic predictive feature as well as a process optimization step that would maximize an objective function by manipulating additional variables. 

For the industrial application of multivariable model predictive process control, the dynamic relationships between the manipulated inputs and con-... 

In control applications, for which conventional multiloop control systems are not satisfactory, an alternative approach, multivariable control, can be advantageous. In multivariable control, each manipulated variable is adjusted based on the measurements of all the controlled variables rather than only a single controlled variable, as in multiloop control. The adjustments are based on a dynamic model of the process that indicates how the manipulated variables affect the controlled variables. Consequently, the performance of multivariable control, or any model-based control technique, will depend heavily on the accuracy of the process model. A specific type of multivariable control, model predictive control, has had a major impact on industrial practice, as discussed in Chapter 20. 

In this chapter we consider model predictive control (MPC), an important advanced control technique for difficult multivariable control problems. The basic MPC concept can be summarized as follows. Suppose that we wish to control a multiple-input, multiple-output process while satisfying inequality constraints on the input and output variables. If a reasonably accurate dynamic model of the process is available, model and current measurements can be used to predict future values of the outputs. Then the appropriate changes in the input variables can be calculated based on both predictions and measurements. In essence, the changes in the individual input variables are coordinated after considering the input-output relationships represented by the process model. In MPC applications, the output variables are also referred to as controlled variables or CVs, while the input variables are also called manipulated variables or MVs. Measured disturbance variables are... 

The MPC control problem illustrated in Eqs. (8-66) to (8-71) contains a variety of design parameters model horizon N, prediction horizon p, control horizon m, weighting factors Wj, move suppression factor 6, the constraint limits Bj, Q, and Dj, and the sampling period At. Some of these parameters can be used to tune the MPC strategy, notably the move suppression faclor 6, but details remain largely proprietary. One commercial controller, Honeywell s RMPCT (Robust Multivariable Predictive Control Technology), provides default tuning parameters based on the dynamic process model and the model uncertainty. 

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... 

Al-Haj Ali et al. [5,6] developed different types of linear time invariant models by system identification, which adequately represent the fluidized-bed drying dynamics. MBC techniques such as IMC and model predictive control (MPC) were used for the designing of the control system. Simulations with multivariable MPC strategy... 

II Single-loop PID control with compensation for difficult dynamics (e.g., Smith predictors for time-delays), again with appropriate loop pairing for multivariable processes. Alternatively, the use of explicitly model-based control strategies like direct synthesis control. Internal Model Control (IMC), or Model Predictive Control (MPC) may be appropriate ... 

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