T he Aspen DMC3 Difference An Industry White Paper
Robert Golightly, Product Marketing Manager, Aspen Technology, Inc.
Introduction
There is a classic dichotomy in APC: the technology delivers maximum benefits
when the underlying algorithms leverage accurate models for the aggressive
pursuit of profits. However, we also want the controller to gracefully handle the
prence of errors or poor model conditioning. The controller algorithms have traditionally been slanted in one direction or the other; to be very aggressive in the pursuit of benefits, or be less aggressive in order to compensate for the potential for reduced accuracy in the models.诺丁汉特伦特大学
There was, of cour, a price to be paid for either choice. When errors are prent in aggressive controllers, the optimizer can jump from solution to solution as it
chas the potential profit it identified as a result of the model inaccuracies. When
the choice of a less aggressive controller is made, the price equals lower benefits as
the controller is esntially tuned to ignore improvements below a certain
有个性的微信头像threshold.
指日可下Part of the problem is that this is also a temporal issue and not just about the initial
model accuracy. We know that the changes that occur in the plant between
香蕉片是怎么做出来的revamps of the controller cau slowly evolving differences between the actual
plant behavior and the model predictions—hence the eroding benefits of the
controller. In fact, there are veral points within the APC lifecycle where the issues surface. Figure 1 depicts the facets of APC that offer opportunities to tune the behavior of the APC solution to address issues affecting benefits, operating stability, and product quality in the prence of model inaccuracies.
For the last 10 years, AspenT ech has been working on a comprehensive solution for top-of-mind issues for APC
practitioners. Beginning with offline collinearity repair nearly a decade ago, and now with Adaptive Process Control, LP Tuning, and Constrained Model Identification, AspenT ech is again tting the standard for multivariable model predictive control and optimization with Aspen DMC3.
Model Conditioning
怎么养玫瑰花
There are many reasons why a substantially inaccurate model can lead to performance issues, and
this applies to all MPC formulations. In model conditioning, we are addressing aspects of the model实木衣柜图片大全
that create ambiguity with respect to decisions made in the cour of optimization. The most
illustrative example is near collinearity in the models. When this condition exists, there are very small
differences in the gains that an aggressively tuned optimizer will e as opportunities for profit. This type of “numerical fuzziness” can create cycling. Certain tools that have been in existence help expert practitioners fix the Relative Gain Arrays (RGAs) of the models to prevent this situation. The most recent innovations in this area surface the tools as an integrated part of the workflow and simplify the u of the tools via automation, thereby enabling non-expert practitioners to correct issues with collinearity during the offline modeling pha.
Figure 1: Facets of APC
Controller Tuning
Dynamic model accuracy (curve shape) is also important as it affects the dynamic control move
calculation, which can also lead to cycles if the main model curves are very inaccurate. This is usually
not the dominant reason for cycling, unless MV tuning (move suppression) is very aggressive. A
good control solution would need the ability to handle instability resulting from inaccuracy in the dynamic models, as well as inappropriate tuning.
Model Adaptation
AspenT ech has been working steadily for the last decade to solve the model maintenance side of this
灵芝孢子粉副作用issue. This technology includes the ability to alter the “personality” of the controller in terms of the
aggressiveness of plant testing. The adaptive technology alters the optimization behavior of the
controller to direct it to be less aggressive during testing, and in the prence of the errors, inherent in
initial ed models. The Adaptive Process Control technology provides the engineer with an analog parameter to adjust the tradeoff between testing aggressiveness and the capture of benefits. Previous to this technology, the choice was binary—focus on testing OR optimization, not a ur-specified balance of objectives.
The adaptive technology allows the ur to tune the personality of the controller to particular circumstances encountered during the testing and model construction phas. Rather than a one-size-fits-all t of binary choices, we now have the ability to fine-tune the tradeoff to unique needs.
LP Tuning
T o complement the Adaptive capability, we also need a way to shape the behavior of the controller
when in optimizing control mode. As changes occur in the plant over time, or via transient events, we
need to be able to easily modify the behavior of the controller until the issues can be addresd, or
simply modify as a technical hedge tactic.
It is a well-known fact that a Linear Program (LP) algorithm has the ability to lect the most optimal t of simultaneous constraints where a process unit will make the most money. Most APC applicatio
ns contain two to three times more controlled variables than manipulated variables. Therefore, the controller model is referred to as “non-square,” and potentially millions of constraint combinations are possible. The objective is to find the constraint t that maximizes the benefits. For most control applications, the interior point LP algorithm can lect the most optimal solution within a
孔子的核心思想是什么
matter of milliconds. This is possible due to the ability of the LP to “square up” the control problem by preferentially finding the constraint t where all controlled variables (CVs) are inside their safety and operability limits, while maximizing profitability of the process unit. If there is no feasible solution— becau limits are t too conrvatively or inconsistency exists in model relationship—then a ranked approach is ud to decide which CVs are allowed to violate constraints.
Linear Programming has many advantages in optimization, but there are a few disadvantages too. If the model is not accurate with respect to the process variable costs, the LP might pick an unfavorable solution. It is often the ca that when this occurs, operators get frustrated, complaining that the controller “is not doing the right thing.”
In what follows, we’ll illustrate the behavior of the Aspen DMC3 controller, using its ability to adjust the LP aggressiveness to address the more common types of model inaccuracies.
Steady-State Gain Errors
The current biad prediction is ud as the starting point to initialize the LP at every execution cycle. If the gain matrix is very inaccurate, then the LP might make bigger-than-required MV moves to steer the unit back toward the chon LP targets. This leads to excessive MV movement and potential cycling between solutions. This behavior is uptting to operators, and leads to being unprofitable.
Another form of model inaccuracy, where a clod material balance does not add up to zero, is when the LP might think it can optimize in ways that violate the laws of by creating mass. The gain matrix does not need to be perfectly accurate, but as gain errors increa there comes a point where the LP will switch to the wrong solution.
The LP might also pick a new solution bad on feedback information, allowing the controller to move in that direction.But due to the model errors, the controller will obrve a process respon quite different from what it predicted. A few steps later, the LP might conclude that the original constraint was better after all. This can result in a cycle where the LP flips between two or more active constraint ts.
A good robust control solution would prevent LP flipping by avoiding the u of weak process handles to deal with new CV limit excursions. The robust solution would also need to prevent giving up too much in terms of dynamic performance. It must not become so sluggish that it cannot adequately reject disturbances. In terms of optimization performance, it should not move too far away from the theoretically optimal solution.
The next few figures display some simulations of Aspen DMC3. Figure 2 shows where the controller model has a gain that is 5x too low (worst ca direction).
Figure 2: Increasing the robustness factor prevents LP flipping in the prence of model mismatch
All MVs and CVs except for FC2001 and AI2020 have been turned off, making this is a simple 1x1 controller, similar to a PID single loop controller. We would typically not build applications this small, but it rves to illustrate the ability of the new algorithm to stabilize the dynamic move plan when the LP is not active since the controller is already squared up.We intentionally started with a very large model mismatch (500% in the worst ca direction), and inappropriate MV tuning (move suppression of 0.1, which is very aggressive). As can be expected, the 1x1 controller cycled poorly using the standard move plan algorithm. The new global tuning parameter called “Robustness Factor” (R) was
ud, a normalized number between 0 and 1. As the Robustness Factor incread, the loop became better damped (less cyclical) until Time (min)Time (min)
C V –%C 5 T o p M V –R e f l u x
acceptable performance was achieved at R=0.2. Clearly, the robust control algorithm managed to stabilize this controller in the prence of vere model mismatch. This example highlights how the robust algorithm adjusts the dynamic move plan optimization to provide improved performance.
Figure 3 below shows where we created random gain errors in the controller model varying from 0.1 (10x or 1000% too low) to 2x (200% too high).
Figure 3: Cycling is cured with Robust operation
The controller was started with the Robustness Factor (R) t to zero, i.e. the ur is saying “no additional controller robustness is needed; I trust my model completely.” Clearly, the excessive (unreasonable) model mismatch was sufficiently large in this example to cau the controller to cycle or “flip” between alternate solutions.
Errors in the gain and shape of the model curves can also contribute to controller instability, as the m
ove plan engine will respond to bias feedback. As the R was incread to a small non-zero value (0.005), the cycle persisted and got smaller.By increasing R to 0.05 (still small, 5% of range) it cured the cycle completely. C V - % C 5 T o p M V -R e f l u x C V - % C 7 M i d -p r o d u c t Time (min)
Time (min)R=0.0R=0.005R=0.05
R=0.0R=0.005R=0.05R=0.0R=0.005R=0.05
