Modifier Adaptation Research Articles

Use of Transient Measurements for Static Real-Time Optimization

Modifier adaptation (MA) is an iterative real-time optimization (RTO) method characterized by its ability to enforce plant optimality upon convergence despite the presence of model uncertainty The approach is based on correcting the available model using gradient estimates computed at each iteration. MA uses steady-state measurements and solves a static optimization problem at each iteration. Hence, after every input change, one typically waits for the plant to reach steady state before measurements are taken. With many iterations, this can make convergence to the plant optimum rather slow. Recently, an approach that uses transient measurements for steady-state MA has been proposed. This way, plant optimality can be reached in a single transient operation. This paper proposes to improve this approach by using a dynamic model to process transient measurements for gradient computations. The approach is illustrated through the simulated example of a CSTR. Furthermore, the proposed method is less dependent on the choice of the RTO period. The time needed to reach plant optimality is of the order of the plant settling time, whereas several transitions to steady state would be necessary with the standard static MA scheme.

Accelerated and Adaptive Modifier-Adaptation Schemes for Unconstrained Uncertain Systems

The steady-state performance of a parametrically or structurally uncertain system can be optimized using iterative real-time optimization methods such as modifier adaptation (MA). Here, we extend a recently proposed MA scheme in two important and novel directions. First, we accelerate its convergence, i.e., we reduce the number of potentially time-consuming and suboptimal transitions to intermediate steady states by appropriate filtering. Second, we propose an adaptation strategy to reduce conservatism related to the unknown curvature of the system’s steady-state performance curve. Moreover, we combine these two innovations and demonstrate their benefits on two numerical examples.

Real-Time Optimization of Gold Cyanidation Leaching Process in a Two-Layer Control Architecture Integrating Self-Optimizing Control and Modifier Adaptation

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...

Extension of modifier adaptation for controlled plants using static open-loop models

Model-based optimization methods suffer from the limited accuracy of the available process models. Because of plant-model mismatch, model-based optimal inputs may be suboptimal or, worse, unfeasible for the plant. Modifier adaptation (MA) overcomes this obstacle by incorporating measurements in the optimization framework. However, the standard MA formulation requires that (1) the model satisfies adequacy conditions and (2) the model and the plant share the same degrees of freedom. In this article, three extensions of MA to problems where (2) does not hold are proposed. In particular, we consider the case of controlled plants for which the only a model of the open-loop plant is available. These extensions are shown to preserve the ability of MA to converge to the plant optimum despite disturbances and plant-model mismatch. The proposed methods are illustrated in simulation for the optimization of a CSTR.

Real-time optimization for a laboratory-scale flotation column

In this paper, a supervisory layer with real-time optimization (RTO) has been implemented in an experimental laboratory-scale flotation column for copper concentration. A two-stage and modifier adaptation (MA) methodology for RTO has been compared under structural, experimental and dynamic uncertainty. In addition, a gradient-free alternative for MA, called nested modifier optimization, has been proposed and tested. The results show that the KKT updates of the MA approach allow the process optimum to be determined under uncertain scenarios, unlike the two-stage approach. From the perspective of gradient modifiers, the performance of the nested methodology is comparable to the dual approach because previous past values are used to update the modifiers without requiring the gradient estimation step. In addition, the interaction of RTO with the regulatory layer must be considered to propose an optimal implementation.