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Figure |. Control hierarchy MPC is positioned above a regulatory control level as shown in Figure 1. The manipulated variables for the MPC are typically setpoints of PID controllers, executed in a distributed control system (DCS). The MPC may also directly manipulate valve position signals rather than, e.g., flow.

Figure 1 |. Control hierarchy MPC is positioned above a regulatory control level as shown in Figure 1. The manipulated variables for the MPC are typically setpoints of PID controllers, executed in a distributed control system (DCS). The MPC may also directly manipulate valve position signals rather than, e.g., flow.

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The thinking with respect to cascades with MPC has clearly evolved over the years. In earlier days of MPC, it was often thought preferable to “break” an existing TC cascade and design the MPC to manipulate flow controllers. The motivation was that this would lead to simpler (overdamped) models and allow the interaction to be addressed by the MPC. What was missed with this approach was the rejection capability of the DCS via the higher sampling frequency, and the robustness that results from incorporating a TC into the MPC strategy. Consider the case of the two-by two subsystem associated with the product purities of a binary distillation column, controlled in the — reflux-boilup configuration (so called Z-V configuration). Consider two cases: 1), MPC control of compositions via L and V and 2) MPC control of the compositions via L and a stripping section TC controller that manipulates boilup. We assume that the controlled temperature correlates well with the bottoms product composition. The model relationships for these two cases are Due to its lower triangular structure, L-TC is a more robust formulation compared to a full decoupling strategy with manipulated variable L and V, especially if the process is ill- conditioned, or more accurately, has large RGA elements (Skogestad and Morari, 1987). In most cases a temperature
The thinking with respect to cascades with MPC has clearly evolved over the years. In earlier days of MPC, it was often thought preferable to “break” an existing TC cascade and design the MPC to manipulate flow controllers. The motivation was that this would lead to simpler (overdamped) models and allow the interaction to be addressed by the MPC. What was missed with this approach was the rejection capability of the DCS via the higher sampling frequency, and the robustness that results from incorporating a TC into the MPC strategy. Consider the case of the two-by two subsystem associated with the product purities of a binary distillation column, controlled in the — reflux-boilup configuration (so called Z-V configuration). Consider two cases: 1), MPC control of compositions via L and V and 2) MPC control of the compositions via L and a stripping section TC controller that manipulates boilup. We assume that the controlled temperature correlates well with the bottoms product composition. The model relationships for these two cases are Due to its lower triangular structure, L-TC is a more robust formulation compared to a full decoupling strategy with manipulated variable L and V, especially if the process is ill- conditioned, or more accurately, has large RGA elements (Skogestad and Morari, 1987). In most cases a temperature
Figure 4. Alternate MPC strategies for maintaining valve positions in controllable range — (a) MPC to PID and (b) direct output to valve. An important issue concerns valve positions of PID loops that are directly manipulated by MPC or that are affected by other manipulated variables of the MPC. For example, manipulating an FC controller setpoint will affect the valve position associated with the FC as well as the valve position associated with a downstream pressure controller. When a valve approaches a saturated state (either fully open or closed), not only is PID control lost for its associated controlled variable, but model mismatch (and nonlinearity) is introduced to all MPC-controlled variables that depend on the PID controller response. As a result, the MPC needs to keep PID controller outputs in a controllable range. This can be achieved by bringing the PID controller output into the MPC as a controlled variable. This approach is illustrated in Figure 3a. In this case, MPC manipulates the setpoint of the PID controller setpoint as necessary to keep the controller output in range. How well the PID output can be controlled and how close to saturation the MPC limit can be placed depends on: PID tuning, disturbances characteristics, and the degree of nonlinearity. It may be necessary to retune the PID loop based on the response of the controller output (a smooth response in the valve, without significant proportional “kick” is desirable).
Figure 4. Alternate MPC strategies for maintaining valve positions in controllable range — (a) MPC to PID and (b) direct output to valve. An important issue concerns valve positions of PID loops that are directly manipulated by MPC or that are affected by other manipulated variables of the MPC. For example, manipulating an FC controller setpoint will affect the valve position associated with the FC as well as the valve position associated with a downstream pressure controller. When a valve approaches a saturated state (either fully open or closed), not only is PID control lost for its associated controlled variable, but model mismatch (and nonlinearity) is introduced to all MPC-controlled variables that depend on the PID controller response. As a result, the MPC needs to keep PID controller outputs in a controllable range. This can be achieved by bringing the PID controller output into the MPC as a controlled variable. This approach is illustrated in Figure 3a. In this case, MPC manipulates the setpoint of the PID controller setpoint as necessary to keep the controller output in range. How well the PID output can be controlled and how close to saturation the MPC limit can be placed depends on: PID tuning, disturbances characteristics, and the degree of nonlinearity. It may be necessary to retune the PID loop based on the response of the controller output (a smooth response in the valve, without significant proportional “kick” is desirable).
Figure 3. Step response models for integrating level: open- loop vs. closed-loop with PID disturbance channels and incorporation of additional output measurements (Qin and Badgwell, 2003; Froisy, 2009).
Figure 3. Step response models for integrating level: open- loop vs. closed-loop with PID disturbance channels and incorporation of additional output measurements (Qin and Badgwell, 2003; Froisy, 2009).
Figure 5. Example process to be controlled by MPC PC2.op - column 2 pressure controller output.
Figure 5. Example process to be controlled by MPC PC2.op - column 2 pressure controller output.
Figure 7.Example piece wise linear transformation For the general case, when a_ specific nonlinear transformation is unknown, a piece-wise linear relationship can be empirically derived, assuming testing is over a range wide enough to capture the nonlinearity. An example is shown in Figure 7 for the case of a valve position (controller output) and an associated measurement (e.g., flow). This transformation could be used with either of the valve position scenarios shown in Figure 4.
Figure 7.Example piece wise linear transformation For the general case, when a_ specific nonlinear transformation is unknown, a piece-wise linear relationship can be empirically derived, assuming testing is over a range wide enough to capture the nonlinearity. An example is shown in Figure 7 for the case of a valve position (controller output) and an associated measurement (e.g., flow). This transformation could be used with either of the valve position scenarios shown in Figure 4.
Figure 8. Fluid catalytic cracking unit. An MPC application is typically applied to a unit such as a fluid catalytic cracking unit (FCCU) or ethylene unit. A single MPC or multiple MPC controllers may be applied, depending on the unit objective and constraints. Consider as an example the FCCU shown in Figure 8. If the unit objective is to maximize unit feed and downstream throughput constraints exist, such as DC4 flooding, one would consider a single controller. If there are no throughput constraints in the downstream columns, one would consider two MPC controllers: one for the reactor/regenerator/ main fractionator/wet gas compressor, and one for the all of the downstream distillation columns.
Figure 8. Fluid catalytic cracking unit. An MPC application is typically applied to a unit such as a fluid catalytic cracking unit (FCCU) or ethylene unit. A single MPC or multiple MPC controllers may be applied, depending on the unit objective and constraints. Consider as an example the FCCU shown in Figure 8. If the unit objective is to maximize unit feed and downstream throughput constraints exist, such as DC4 flooding, one would consider a single controller. If there are no throughput constraints in the downstream columns, one would consider two MPC controllers: one for the reactor/regenerator/ main fractionator/wet gas compressor, and one for the all of the downstream distillation columns.
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