SISO Constraint Control

The first indication that the process is operating at the maximum feed rate is the fuel valve fully opening. A single-input single-output (SISO) controller, with this valve opening as its PV, manipulates the SP of the feed flow controller until the fuel valve reaches the desired maximum opening. On most processes, valve position transmitters are only installed in special circumstances. What is actually used here is the output of the fuel flow controller. We assume that the valve positioner is properly calibrated and working well. 

On our case study heater, the process operator will typically enter a SP of around 90 %. This effectively converts a hard constraint to a soft constraint. In order to maintain control of the outlet temperature during minor process disturbances some leeway is required. This means that the process capacity is not fuUy utilised. Conditioning the constraint, as described in Chapter 5, offers an alternative method of converting it to a soft constraint and would permit this leeway to be reduced. 

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The minimization of the quadratic performance index in Equation (16.2), subject to the constraints in Equations (16.5-16.7) and the step response model such as Equation (16.1), forms a standard quadratic programming (QP) problem, described in Chapter 8. If the quadratic terms in Equation (16.2) are replaced by linear terms, a linear programming program (LP) problem results that can also be solved using standard methods. The MPC formulation for SISO control problems described earlier can easily be extended to MIMO problems and to other types of models and objective functions (Lee et al., 1994). Tuning the controller is carried out by adjusting the following parameters ... 

The dynamic simulation model has been adapted to meet the constraints of a large scale problem and of the equation solving mode of Aspen Dynamics. The final model contained more than 6000 equations. Since the change in material balance (inventory) takes place at long time scales, some substantial simplifications of the local control of units can be considered. Finally, the plantwide control problem is reduced to analyse a 3x7 system, where three outputs (concentration of impurities li, I2, and I3) should be controlled with three among five inputs (D2, SS2, Q2, D4, and Q4), in the presence of two disturbances (Fdce, X ). Because of decentralised control, at most three SISO controllers should be physically implemented. 

PI control Simple proportional-integral SISO loops provide effective control of the vast majority of all chemical plants. These systems require process understanding to set up, rational tuning methods, the use of overrides to handle constraints and split-ranged valves to handle the case where several manipulated variables can be used to control a single controlled variable. 

Besides model uncertainty, actuator limitations are the main source of bandwidth limitations for linear control. In a SISO control loop with symmetric input constraints U < M, the attainable maximal output move after time T can be computed as... 

Multi-input single-output (MISO) controllers are required when there is more than one constraint that is approached by adjusting just one MV. Such controllers require some form of logic to select the most limiting constraint. Once selected the controller behaves just like a SISO controller. 

For the simple distillation column in Figure 8.1 there are five degrees of freedom, which translates into five independent valves from a control point of view. In this 5x5 system, there are 120 possible SISO control combinations of controlled and manipulated variables. Fortunately, most of these combinations are not useable due to various constraints, such as economics. From a steady-state degree of freedom analysis there are only two degrees of freedom, since a total condenser is assumed. If the column had a partial condenser then there would, of course, be three degrees of freedom instead of two. Inventories that must be controlled are the reflux drum level Hr, level in column base or reboiler Hr, and the column pressure (vapour holdup). The remaining two variables are used to control the feed split and the fractionation. 

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