Selection of controlled variables (CVs) has recently gained wide attention, because of its paramount importance in real-time optimization (RTO) of plant operation. The so-called self-optimizing control (SOC) strategy aims to select appropriate CVs so that when they are maintained at constant setpoints, the overall plant operation is optimal or near optimal, despite various disturbances and uncertainties. Recent progresses of the SOC methodology have focused on finding linear combinations of measurements as CVs via linearization of the process around its nominal operating point, which results in the plant operation being only locally optimal. In this work, the concept of necessary conditions of optimality (NCO) is incorporated into CV selection to overcome the "local" shortcoming of existing SOC methods. Theoretically, the NCO should be selected as the optimal CV, although it may not be practical because of the measurability of the NCO. To address this issue, in this work, CVs are selected to approximate unmeasured NCO over the entire operation region with zero setpoints to achieve near-optimal operation globally. The NCO approximation CVs can be obtained through any existing regression approaches. Among them, two particular regression methodsnamely, least-squares and neural networksare adopted in this work as an illustration of the proposed methodology. The effectiveness and advantages of the new approach are demonstrated through two case studies. Results are compared with those obtained by using existing SOC methods and an NCO tracking technique.
Self-optimizing control (SOC) constitutes
an important class of
control strategies for real-time optimization (RTO) of chemical plants,
by means of selecting appropriate controlled variables (CVs). Within
the scope of SOC, this paper develops a CV selection methodology for
a global solution which aims to minimize the average economic loss
across the entire operation space. A major characteristic making the
new scheme different from existing ones is that each uncertain scenario
is independently considered in the new solution without relying on
a linearized model, which was necessary in existing local SOC methods.
Although global CV selection has been formulated as a nonlinear programming
(NLP) problem, a tractable numerical algorithm for a rigorous solution
is not available. In this work, a number of measures are introduced
to ease the challenge. First, we suggest representing the economic
loss as a quadratic function against the controlled variables through
Taylor expansion, such that the average loss becomes an explicit function
of the CV combination matrix, and a direct optimizing algorithm is
proposed to approximately minimize the global average loss. Furthermore,
an analytic solution is derived for a suboptimal but much more simplified
problem by treating the Hessian of the cost function over the entire
operating space as a constant. This approach is found to be very similar
to one of the existing local methods, except that a matrix involved
in the new solution is constructed from global operating data instead
of using a local linear model. The proposed methodologies are applied
to two simulated examples, where the effectiveness of the proposed
algorithms is demonstrated.
For control and optimization of chemical processes, the traditional hierarchical control structure (HCS), where an optimizer in the real-time optimization (RTO) layer updates the set-points of controlled variables (CVs) in the lower control layer, has been well-acknowledged and widely adopted in industrial applications. However, a common drawback of such an HCS is that the speed for a plant to converge to an optimal operation is slow because the optimizer has to wait for the process to settle from one steady-state to another to get an accurate disturbance estimation before making any changes to the set-points. In this Article, a novel HCS based on the concepts of controlled variable adaptation (CVA) and nonoptimality detection is proposed. In the CVA strategy, the CVs are determined and adapted on the basis of a so-called just-in-time regression algorithm to approximate the necessary conditions of optimality (NCO), which makes the self-optimizing performance adaptive to operating condition changes. For nonoptimality detection, we apply the theory of statistical process monitoring to monitor the optimality of process operation, where the nonoptimal statuses are treated as a special kind of process faults. The detection results are used as a prerequisite to activate the CVA. With these techniques, the proposed CVA-based HCS exhibits the following distinct features: (1) The regulatory control layer has an ability to approach a near optimal operation automatically through selfoptimizing control, thus accomplishing the majority of the optimization task, and the speed of the process converging to an optimal status is fast. (2) The RTO layer extends the self-optimizing operation range via adapting CVs in the lower control layer, rather than their set-points as in a traditional HCS. (3) The activation of CVA is neither regular nor periodic, but only evoked when it is necessary. Two case studies are provided to demonstrate the basic characteristics and advantages of the proposed CVA-based HCS.
The gold cyanidation leaching process
(GCLP) has been prevalent
in the hydrometallurgical industry. To better control and optimize
the plant operation, mechanistic models have been established which
capture the physical behaviors of the GCLP. However, due to various
disturbances and uncertainties, an optimized operation based on the
nominal model is practically suboptimal. To perform real-time optimization
(RTO) of the GCLP, this paper proposes a two-layer control architecture
integrating the self-optimizing control (SOC) and modifier adaptation
(MA), both of which are useful RTO approaches with distinct advantages.
In the lower layer of the proposed control system, the SOC is implemented
with measurement combinations as the controlled variables that are
tracked at optimally insensitive setpoints to account for parametric
disturbances. In the upper layer, the setpoints of self-optimizing
controlled variables are further optimized in a tailored MA framework,
such that the structural plant–model mismatch is also addressed.
The superior RTO performance for the GCLP is verified through simulation
studies. The results show that the proposed RTO solution achieves
a fast optimizing speed for parametric disturbances, and meanwhile,
has the capacity for finding the true optimum for structurally unknown
Neighborhood preserving embedding (NPE) is a useful tool for learning the manifold of high‐dimensional data. As a linear approximation of nonlinear locally linear embedding, NPE can be applied to dimensionality reduction by neighborhood preserving. However, the original NPE algorithm is an unsupervised method, which extracts features without any reference to the output information. In this paper, a supervised NPE framework is proposed for output‐related feature extraction in soft sensor applications. In the supervised NPE framework, the output information is utilized to guide the procedures for constructing the adjacent graph and calculating the weight matrix, with which the intrinsic structure of the data can be better described. For performance evaluation of the proposed method, experiments on a numerical example and an industrial debutanizer column process are carried out. The results show the effectiveness of the proposed framework.
A soft sensor is
a key component when a real-time measurement is
unavailable for industrial processes. Recently, soft sensor models
based on deep-learning techniques have been successfully applied to
complex industrial processes with nonlinear and dynamic characteristics.
However, the conventional deep-learning-based methods cannot guarantee
that the quality-relevant features are included in the hidden states
when the modeling samples are limited. To address this issue, a supervised
hybrid network based on a dynamic convolutional neural network (CNN)
and a long short-term memory (LSTM) network is designed by constructing
multilayer dynamic CNN-LSTM with improved structures. In each time
instant, data augmentation is implemented by dynamic expansion of
the original samples. Moreover, multiple supervised hidden units are
trained by adding quality variables as part of the layer input to
acquire a better quality-related feature learning performance. The
effectiveness of the proposed soft senor development is validated
through two industrial applications, including a penicillin fermentation
process and a debutanizer column.
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