Presence Of Process Disturbances Research Articles

Integration of Design and NMPC-Based Control under Uncertainty and Structural Decisions: An MPCC-Based Approach

In this work, we investigate the challenges and limitations of the application of nonlinear model predictive control (NMPC) for the integration of design and control for systems subject to structural decisions and model uncertainty. The problem involving discrete and continuous decisions is referred to as a mixed-integer bilevel programming model (MIBLP), which cannot be directly solved with conventional MINLP solvers. To address this issue, we implement a classical KKT transformation strategy to transform the original MIBLP into a single-level MINLP. The KKT conditions for the NMPC are determined and incorporated as constraints in the problem for process design. A regularization strategy is implemented to reformulate the complementarity constraints. Then, the single-level MINLP is directly solved with a branch and bound strategy. The proposed approach is tested in a reaction system network subject to uncertainty. The performance of a nominal- and a robust-NMPC control approaches are compared in the presence of process disturbances. Results indicate that the strategy with a robust-NMPC returns a more conservative process design with better control performance compared to results with a nominal-NMPC.

Batch-to-Batch Adaptive Iterative Learning Control-Explicit Model Predictive Control Two-Tier Framework for the Control of Batch Transesterification Process.

To harness energy security and reduce carbon emissions, humankind is trying to switch toward renewable energy resources. To this extent, fatty acid methyl esters, also known as biodiesel, are popularly used as a green fuel. Fatty acid methyl esters can be produced by a batch transesterification reaction between vegetable oil and alcohol. Being a batch process, fatty acid methyl esters production is beset with issues such as uncertainties and unsteady state behavior, and therefore, adequate process control measures are necessitated. In this study, we have proposed a novel two-tier framework for the control of the fatty acid methyl esters production process. The proposed approach combines the constrained batch-to-batch iterative learning control technique and explicit model predictive control to obtain the desired concentration of the fatty acid methyl esters. In particular, the batch-to-batch iterative learning control technique is used to generate reactor temperature set-points, which is further utilized to obtain an optimal coolant flow rate by solving a quadratic objective cost function, with the help of explicit model predictive control. Our simulation results indicate that the fatty acid methyl esters concentration trajectory converges to the desired batch trajectory within four batches for uncertainty in activation energy and six batches for uncertainty in both inlet concentration of triglyceride and in activation energy even in the presence of process disturbances. The proposed approach was compared to the heuristic-based approach and constraint iterative learning control approach to showcase its efficacy.

Simultaneous design & control of a reactive distillation system – A parametric optimization & control approach

We present a detailed dynamic model for a reactive distillation system, based on which we develop design-dependent explicit optimal control strategies. A mixed-integer dynamic optimization formulation is then proposed integrating design, control and operational components, the solution of which allows us to derive explicit closed-loop strategies that maintain stable and operable conditions in the presence of process disturbances. The simultaneous approach is illustrated with the design of a methyl tert-butyl ether reactive distillation system example as a part of the developed model library in the RAPID SYNOPSIS project.

State Measurement Error-to-State Stability Results Based on Approximate Discrete-Time Models

Digital controller design for nonlinear systems may be complicated by the fact that an exact discrete-time plant model is not known. One existing approach employs approximate discrete-time models for stability analysis and control design and ensures different types of closed-loop stability properties based on the approximate model and on specific bounds on the mismatch between the exact and approximate models. Although existing conditions for practical stability exist, some of which consider the presence of process disturbances, input-to-state stability (ISS) with respect to state-measurement errors and based on approximate discrete-time models has not been addressed. In this paper, we thus extend existing results in two main directions: 1) we provide ISS-related results, where the input is the state measurement error; and 2) our results allow for some specific varying-sampling-rate scenarios. We provide conditions to ensure semiglobal practical ISS, even under some specific forms of varying sampling rate. These conditions employ Lyapunov-like functions. We illustrate the application of our results on numerical examples, where we show that a bounded state-measurement error can cause a semiglobal practically stable system to diverge.

Neuronal Modeling of a Two Stages Anaerobic Digestion Process for Biofuels Production

The biological processes for biofuels generation are highly nonlinear systems submitted to external disturbances and parameter uncertainties which require estimation, control and optimization strategies to maintain stability and optimal production. In this work, a nonlinear neural network for unknown nonlinear systems in the presence of external disturbances and parameter uncertainties is proposed. The objective is to estimate unmeasurable complex variables in a two continuous stages anaerobic digestion process for hydrogen and methane production. Simulation results are presented, where it is demonstrated that the neural model is efficient to calculate complex dynamics of the process in presence of disturbances. As future work, control and optimization algorithms based on the neural model can be developed to biofuel production optimization.

Sensor‐fault tolerance using robust MPC with set‐based state estimation and active fault isolation

SummaryIn this paper, a sensor fault‐tolerant control scheme using robust model predictive control (MPC) and set‐theoretic fault detection and isolation (FDI) is proposed. The robust MPC controller is used to control the plant in the presence of process disturbances and measurement noises while implementing a mechanism to tolerate faults. In the proposed scheme, fault detection (FD) is passive based on interval observers, while fault isolation (FI) is active by means of MPC and set manipulations. The basic idea is that for a healthy or faulty mode, one can construct the corresponding output set. The size and location of the output set can be manipulated by adjusting the size and center of the set of plant inputs. Furthermore, the inputs can be adjusted on‐line by changing the input‐constraint set of the MPC controller. In this way, one can design an input set able to separate all output sets corresponding to all considered healthy and faulty modes from each other. Consequently, all the considered healthy and faulty modes can be isolated after detecting a mode changing while preserving feasibility of MPC controller. As a case study, an electric circuit is used to illustrate the effectiveness of the proposed scheme. Copyright © 2016 John Wiley & Sons, Ltd.

Sliding Mode Observers for Plasma Signal Identification in Remote Laser Welding

In this paper, a model for the emission of a plasma signal during the zinc coated steel metal fusion phenomenon is proposed. Remote laser welding process and system identification of plasma signal based on the sliding mode observer are presented. The dynamic behaviour of the keyhole is captured using experimental data from the photodiode sensor. A multi-input single-output (MISO) model is designed, the equivalent injection signal using a unit vector sliding mode observer is applied to update the dynamic matrix coefficients. The variation in the model parameters due to process disturbances in the laser fusion phenomenon is captured by recursively updating the matrix parameters, using matrix forgetting factor approach. The simulation result shows an accurate estimation of plasma signal emitted during the laser welding process in the presence of process disturbances.

An Integrated Approach for C-control of Antisolvent Crystallization Processes

Concentration control (C-control) strategy for (semi-)batch antisolvent crystallization processes has been recently developed with the aid of new sensors that measure in situ process variables. This control strategy gives better robustness over traditional flowrate/ temperature control in the presence of process disturbances. However, the setpoint value for the existing C-control is determined through trial-and-error procedure and hence gives sub-optimal product quality in most of the cases. This motivates the current study to develop a two-staged integrated data-based approach to facilitate the determination of setpoint value for the implementation of C-control strategy in anti-solvent crystallization processes. In the first stage of the proposed design, a k-nearest neighborhood LSSVM (k-NN LSSVM) is used to select a subset of the training database that resembles the current batch dynamics as the relevant training database, which is subsequently used in the second stage for determination of the setpoint value of C-control. Simulation results show that the performance of proposed design is near to the best achievable performance of C-control strategy obtained with a known first-principles model for controlling the semi-batch antisolvent crystallization process.

Robust structural control with system constraints

SUMMARY Physical limits of real control systems, such as force saturations and state variable constraints, if attained during the motion, may cause actuator damages, loss of control effectiveness or even a dynamic instability. In order to overcome these drawbacks and improve the overall reliability of the control policy without turning to uneconomic designs, it might be convenient to account for physical limitations directly in the control law. This philosophy is embraced in this paper, where a general approach is presented based on the tool of the state-dependent Riccati equation, in the general framework of nonlinear regulation. The proposed formulation is meant to be feasible to handle limitations on both state variables and control forces. This general control strategy is then specialized to the case of a seismically excited multi-storey frame structure equipped with an active mass damper subjected to actuator saturation and stroke limitation. In-depth numerical simulations are also performed in order to investigate the effectiveness of the proposed approach, for different levels of constraint severities, and its robustness against unknown random variations of structural parameters, also in the case of incomplete number of sensors, measurements affected by noise and the presence of process disturbances. Copyright © 2011 John Wiley & Sons, Ltd.

Threshold computation for fault detection in a class of discrete‐time nonlinear systems

AbstractIn this paper, we address the problem of designing robust thresholds for fault detection in discrete‐time nonlinear uncertain systems in the presence of process disturbances. Both constant and dynamic thresholds are proposed. For the computation of constant thresholds, a generalized framework based on signal norms is developed. Different kinds of constant thresholds are studied in the framework proposed. Using linear matrix inequalities (LMI) techniques, algorithms are derived for the computation of these thresholds. Similarly, the dynamic threshold is designed by deriving an inequality on the upper bound of the modulus of the residual signal. This inequality is based on the solution of discrete‐time nonlinear uncertain systems. The simulation examples illustrate that false alarms are successfully eliminated using the proposed thresholds. Copyright © 2010 John Wiley & Sons, Ltd.

MIQP formulation for Controlled Variable Selection in Self Optimizing Control

In order to facilitate the optimal operation in the presence of process disturbances, the optimal selection of controlled variables plays a vital role. In this paper, we present a Mixed Integer Quadratic Programming methodology to select controlled variables c=Hy as the optimal combinations of fewer/all measurements of the process. The proposed method is evaluated on a toy test problem and on a binary distillation column case study with 41 trays.

Modifier-Adaptation Methodology for Real-Time Optimization

The process industries are characterized by a large number of continuously operating plants, for which optimal operation is of economic importance. However, optimal operation is particularly difficult to achieve when the process model used in the optimization is inaccurate or in the presence of process disturbances. In highly automated plants, optimal operation is typically addressed by a decision hierarchy involving several levels that include plant scheduling, real-time optimization (RTO), and process control. At the RTO level, medium-term decisions are made by considering economic objectives explicitly. This step typically relies on an optimizer that determines the optimal steady-state operating point under slowly changing conditions such as catalyst decay or changes in raw material quality. This optimal operating point is characterized by setpoints that are passed to lower-level controllers. Model-based RTO typically involves nonlinear first-principles models that describe the steady-state behavior of the plant. Since accurate models are rarely available in industrial applications, RTO typically proceeds using an iterative two-step approach, namely a parameter estimation step followed by an optimization step. The idea is to repeatedly estimate selected uncertain model parameters and use the updated model to generate new inputs via optimization. This way, the model is expected to yield a better description of the plant at its current operating point. The classical two-step approach works well provided that (i) there is little structural plant-model mismatch, and (ii) the changing operating conditions provide sufficient excitation for estimating the uncertain model parameters. Unfortunately, such conditions are rarely met in practice and, in the presence of plant-model mismatch, the algorithm might not converge to the plant optimum, or worse, to a feasible operating point. As far as feasibility is concerned, the updated model should be able to match the plant constraints. Alternatively, feasibility can be enforced without requiring the solution of a parameter estimation problem by adding plant-model bias terms to the model outputs. These biases are obtained by subtracting the model outputs from the measured plant outputs. A bias-update scheme, where the bias terms are used to modify the constraints in the steady-state optimization problem, has been used in industry. However, the analysis of this scheme has received little attention in the research community. In the context of this thesis, such an RTO scheme is referred to as constraint adaptation. The constraint-adaptation scheme is studied, and its local convergence properties are analyzed. Constraint adaptation guarantees reaching a feasible operating point upon convergence. However, the constraints might be violated during the iterations of the algorithm, even when starting the adaptation from within the feasible region. Constraint violations can be avoided by controlling the constraints in the optimization problem, which is done at the process control level by means of model predictive control (MPC). The approach for integrating constraint adaptation with MPC described in this thesis places high emphasis on how constraints are handled. An alternative constraint-adaptation scheme is proposed, which permits one to move the constraint setpoints gradually in the constraint controller. The constraint-adaptation scheme, with and without the constraint controller, is illustrated in simulation through the real-time optimization of a fuel-cell system. It is desirable for a RTO scheme to achieve both feasibility and optimality. Optimality can be achieved if the underlying process model is able to predict not only the constraint values of the plant, but also the gradients of the cost and constraint functions. In the presence of structural plant-model mismatch, this typically requires the use of experimental plant gradient information. Methods integrating parameter estimation with a modified optimization problem that uses plant gradient information have been studied in the literature. The approach studied in this thesis, denoted modifier adaptation, does not require parameter estimation. In addition to the modifiers used in constraint adaptation, gradient-modifier terms based on the difference between the estimated and predicted gradient values are added to the cost and constraint functions in the optimization problem. With this, a point that satisfies the first-order necessary conditions of optimality for the plant is obtained upon convergence. The modifier-adaptation scheme is analyzed in terms of model adequacy and local convergence conditions. Different filtering strategies are discussed. The constraint-adaptation and modifier-adaptation RTO approaches are illustrated experimentally on a three-tank system. Finite-difference techniques can be used to estimate experimental gradients. The dual modifier-adaptation approach studied in this thesis drives the process towards optimality, while paying attention to the accuracy of the estimated gradients. The gradients are estimated from the successive operating points generated by the optimization algorithm. A novel upper bound on the gradient estimation error is developed, which is used as a constraint for locating the next operating point.

A dynamically-constructed fuzzy neural controller for direct model reference adaptive control of multi-input-multi-output nonlinear processes

Conventional industrial control systems are in majority based on the single-input-single-output design principle with linearized models of the processes. However, most industrial processes are nonlinear and multivariable with strong mutual interactions between process variables that often results in large robustness margins, and in some cases, extremely poor performance of the controller. To improve control accuracy and robustness to disturbances and noise, new design strategies are necessary to overcome problems caused by nonlinearity and mutual interactions. We propose to use a dynamically-constructed, feedback fuzzy neural controller (DCF-FNC) from the input–output data of the process and a reference model, for direct model reference adaptive control (MRAC) to deal with such problems. The effectiveness of our approach is demonstrated by simulation results on a real-world example of cold mill thickness control and is compared with the performances of the conventional PID controller and the cascade correlation neural network (CCN). Exploiting the advantage of intelligent adaptive control, both the CCN and our DCF-FNC significantly increases the control precision and robustness, compared to the linear PID controller, with our DCF-FNC giving the best results in terms of both accuracy and compactness of the controller, as well as being less computationally intensive than the CCN. We argue that our DCF-FNC feedback controller with both structure and parameter learning can provide a computationally efficient solution to control of many real-world multivariable nonlinear processes in presence of disturbances and noise.

Adaptive Control of Chaotic Systems Based on Poincaré Map and Controlled Closing Lemma

The new method of output feedback adaptive control of oscillatory processes in presence of disturbances is proposed based on the goal inequalities and input-output form of linearized controlled Poincaré map. Conditions of achieving the goal (tracking) with given accuracy are established. The method is applied to modifying behavior of the ROssler system. Also the“controlled” version of the well known closing lemma is established.

Optimal control of a fed-batch fermentation process

Optimisation of fed-batch fermentation processes usually employs the calculus of variations to determine optimal feed-rate profiles that will maximise a given objective function. This results in a two-point boundary-value problem and because of the nonlinear nature of the pro cesses, the optimal solution usually falls out as an open-loop control algorithm. One advantage of this approach is that it does not need measurements of state variables which are often difficult to obtain on-line. Instead it assumes that the state variables are proceeding along known paths a-priori determined by models. However, the disadvantage of such an approach is that the performance will severely deteriorate in the presence of process disturbances or plant-model mismatch. Recently, on-line estimation of state variables has been successfully developed and used in the industry and therefore a method which operates the fed-batch fermentation in a closed-loop control scheme using state feedback is proposed. This is achieved by a two-step method. First, the optimal substrate concentration profile which governs the biochemical reactions in the fermentation process is determined. Then a controller is designed in closed-loop form to track this desired profile. Simulation studies for both primary and secondary metabolite production processes show that better performance is obtained by this closed-loop aptifaaal control method than by the open- loop optimal feed rate profile method. This is due to the self-correcting property of the proposed method, which proves to be advantageous when there are disturbances or plant-model mismatch.

Yield optimization using a GaAs process simulator coupled to a physical device model

A physics-based large-signal GaAs MESFET model and circuit simulator has been developed to predict and optimize the yield of GaAs MESFET designs before fabrication. Device acceptance criteria include both small- and large-signal RF operating characteristics such as small-signal gain, maximum power added efficiency, and output power at 1-dB gain compression. Channel doping details are described on the basis of processing specifications for parameters such as material deposition, ion implantation, and implant annealing. Monte Carlo techniques are used to estimate yield when disturbances in the physical parameters are modeled as multivariate Gaussian distributions. The yield estimator is integrated with an optimizer so that a design can be centered for maximum yield in the presence of process disturbances.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

CONTROL OF MOLECULAR WEIGHT IN A BATCH POLYMERIZATION REACTOR USING LONG-RANGE PREDICTIVE CONTROL METHODS

Abstract Recently two powerful control algorithms, namely, dynamic matrix control (DMC) and extended self-tuning regulator (ESTR), have been advocated for the design of robust industrial controllers. The present paper demonstrates the application of DMC and ESTR algorithms to a bulk methyl methacrylate batch polymerization reactor operating under strong diffusional limitations of termination and propagation reactions. A realistic mathematical model is employed to simulate the strong nonlinear, time-varying dynamics of the polymerization process. The general control objective is to maintain the monomer conversion and number-average molecular weight along some desired state trajectories despite the presence of process disturbances in the total initiator concentration. It is shown that both controllers can satisfactorily control the monomer conversion and number-average molecular weight by manipulating the polymerization temperature. The similarities and the main operating features of the two controllers are...