Control Of Nonlinear Processes Research Articles

Symposium Title: The Very Young Brain and the Auditory World

This paper proposes a novel proportional-integral observer (PIO) based high-order data-driven iterative learning control (HODDILC) for nonlinear batch processes with non-repetitive disturbances subject to input constraints. First, an equivalent dynamic linearization data model (DLDM) with an uncertainty term arising from the nonrepetitive disturbances is constructed in the batch direction. Based on the established DLDM along with a gradient estimation algorithm, a data-driven PIO is then designed to estimate the uncertainty term along the batch direction, followed by designing a HODDILC law in terms of the tracking errors over more than one previous batches and control inputs in the previous time instants of the current batch. Using the contraction mapping principle and matrix theory, rigorous convergence analysis is conducted in the iteration domain. A notable advantage of the proposed design is that only input and output measurement data are used rather than a process model. Finally, an illustrative example from the literature is given to demonstrate the effectiveness and merit of the proposed method.

Statistical Machine Learning in Model Predictive Control of Nonlinear Processes

Recurrent neural networks (RNNs) have been widely used to model nonlinear dynamic systems using time-series data. While the training error of neural networks can be rendered sufficiently small in many cases, there is a lack of a general framework to guide construction and determine the generalization accuracy of RNN models to be used in model predictive control systems. In this work, we employ statistical machine learning theory to develop a methodological framework of generalization error bounds for RNNs. The RNN models are then utilized to predict state evolution in model predictive controllers (MPC), under which closed-loop stability is established in a probabilistic manner. A nonlinear chemical process example is used to investigate the impact of training sample size, RNN depth, width, and input time length on the generalization error, along with the analyses of probabilistic closed-loop stability through the closed-loop simulations under Lyapunov-based MPC.

Constrained nonlinear model predictive control of pH value in wet flue gas desulfurization process

AbstractIn wet flue gas desulfurization (WFGD) process, the pH value of the absorption tower slurry is a crucial factor to the efficiency of desulfurization system. Aiming at the nonlinearity and large lag of the pH change in WFGD process, a predictive control strategy based on Hammerstein–Wiener inverse model compensation is proposed. During the calculation of optimal control, an anti‐model of Wiener nonlinearity unit is adopted to transform the output setting values and sampling values. Similarly in the control process, the controller output is applied to the actual controlled object after inverse transformation of the static nonlinear Hammerstein model. Through the above two inverse transformations, the controller output is identical with the input of linear link in the closed‐loop system. In this article, the inverse model compensation method is utilized to transform nonlinear process control into linear system control, avoiding the large computation of nonlinear model optimization. Finally, the feasibility and effectiveness of the proposed scheme are verified by simulation.

Giant All-Optical Modulation of Second-Harmonic Generation Mediated by Dark Excitons

All-optical control of nonlinear photonic processes in nanomaterials is of significant interest from a fundamental viewpoint and with regard to applications ranging from ultrafast data processing to spectroscopy and quantum technology. However, these applications rely on a high degree of control over the nonlinear response, which still remains elusive. Here, we demonstrate giant and broadband all-optical ultrafast modulation of second-harmonic generation (SHG) in monolayer transition-metal dichalcogenides mediated by the modified excitonic oscillation strength produced upon optical pumping. We reveal a dominant role of dark excitons to enhance SHG by up to a factor of ∼386 at room temperature, 2 orders of magnitude larger than the current state-of-the-art all-optical modulation results. The amplitude and sign of the observed SHG modulation can be adjusted over a broad spectral range spanning a few electronvolts with ultrafast response down to the sub-picosecond scale via different carrier dynamics. Our results not only introduce an efficient method to study intriguing exciton dynamics, but also reveal a new mechanism involving dark excitons to regulate all-optical nonlinear photonics.

Design and Implementation of GSO Based PI Controller for Non Linear Spherical Tank System

From literature point of view process parameter control for non linear process found to be issue in process control industries. The main dilemma lies on managing liquid level in globular tank which is non linear in nature owing to its area disparity in cross section consequent to the change in shape. System identification is made with black box model which is nonlinear and approximated to first order plus dead time model using the worst case model parameter criterion. Group Search Optimization based Proportional Integral controller is implemented to control the non linear system. The real time work is implemented in MATLAB using VMAT-01 module. The servo and regulatory responses of GSO based proportional integral controller intended for different operating region is noted and results are compared with the algorithms such as Big Bang - Big Crunch optimization, Particle swarm optimization and Bacterial Foraging optimization . The most admirable controlling method is determined based on indices such as reduced overshoot, better set point tracking, disturbance rejection , lower performance indices, faster settling time and rise time.

Control of negative gain nonlinear processes using sliding mode controllers with modified Nelder-Mead tuning equations

Abstract This paper proposes a sliding mode controller (SMC) with modified Nelder-Mead tuning, for the control of nonlinear chemical processes, which are represented as first order plus dead time process with negative gain (FOPDT-NG). In the controller design, the SMC controller parameter in continuous part is obtained based on the time constant and dead time of the process, and controller parameters in the discontinuous part is obtained using Nelder-Mead tuning equations. Even though the controller parameters of conventional SMC are tuned using Nelder-Mead tuning, zero dynamics are noticed in the closed loop response of few FOPDT-NG processes and, with few other FOPDT-NG processes tracking of set-point is unachievable. This work proposes modification in the Nelder-Mead tuning equations using Nelder-Mead optimization to overcome the above disadvantages. Four different types of FOPDT-NG processes are considered in this work, and for every type the Nelder-Mead tuning equations are modified, for the design of proposed controllers. The performances of proposed controllers are evaluated for FOPDT-NG processes and also for three different chemical processes taken from literature. A simulation results demonstrate that, the proposed controller prevailed the performance of the conventional SMC in tracking the set-point and the elimination of zero dynamic behavior of FOPDT-NG processes. Hence, the proposed controllers provide improved closed loop performances as compared to the conventional SMC.

Application of metaheuristic algorithms in interval type-2 fractional order fuzzy TID controller for nonlinear level control process under actuator and system component faults*

PurposeThe two-tank level control system is one of the real-world's second-order system (SOS) widely used as the process control in industries. It is normally operated under the Proportional integral and derivative (PID) feedback control loop. The conventional PID controller performance degrades significantly in the existence of modeling uncertainty, faults and process disturbances. To overcome these limitations, the paper suggests an interval type-2 fuzzy logic based Tilt-Integral-Derivative Controller (IT2TID) which is modified structure of PID controller.Design/methodology/approachIn this paper, an optimization IT2TID controller design for the conical, noninteracting level control system is presented. Regarding to modern optimization context, the flower pollination algorithm (FPA), among the most coherent population-based metaheuristic optimization techniques is applied to search for the appropriate IT2FTID's and IT2FPID's parameters. The proposed FPA-based IT2FTID/IT2FPID design framework is considered as the constrained optimization problem. System responses obtained by the IT2FTID controller designed by the FPA will be differentiated with those acquired by the IT2FPID controller also designed by the FPA.FindingsAs the results, it was found that the IT2FTID can provide the very satisfactory tracking and regulating responses of the conical two-tank noninteracting level control system superior as compared to IT2FPID significantly under the actuator and system component faults. Additionally, statistical Z-test carried out for both the controllers and an effectiveness of the proposed IT2FTID controller is proven as compared to IT2FPID and existing passive fault tolerant controller in recent literature.Originality/valueApplication of new metaheuristic algorithm to optimize interval type-2 fractional order TID controller for nonlinear level control system with two type of faults. Also, proposed method will compare with other method and statistical analysis will be presented.

Machine learning modeling and predictive control of nonlinear processes using noisy data

AbstractThis work focuses on machine learning modeling and predictive control of nonlinear processes using noisy data. We use long short‐term memory (LSTM) networks with training data from sensor measurements corrupted by two types of noise: Gaussian and non‐Gaussian noise, to train the process model that will be used in a model predictive controller (MPC). We first discuss the LSTM training with noisy data following a Gaussian distribution, and demonstrate that the standard LSTM network is capable of capturing the underlying process dynamic behavior by reducing the impact of noise. Subsequently, given that the standard LSTM performs poorly on a noisy data set from industrial operation (i.e., non‐Gaussian noisy data), we propose an LSTM network using Monte Carlo dropout method to reduce the overfitting to noisy data. Furthermore, an LSTM network using co‐teaching training method is proposed to further improve its approximation performance when noise‐free data from a process model capturing the nominal process state evolution is available. A chemical process example is used throughout the manuscript to illustrate the application of the proposed modeling approaches and demonstrate their open‐ and closed‐loop performance under a Lyapunov‐based model predictive controller with state measurements corrupted by industrial noise.

Machine-learning-based state estimation and predictive control of nonlinear processes

Machine learning techniques have demonstrated their capability in capturing dynamic behavior of complex, nonlinear chemical processes from operational data. As full state measurements may be unavailable in chemical plants, this work proposes two machine-learning-based state estimation approaches. The first approach integrates recurrent neural networks (RNN) within the extended Luenberger observer framework to develop data-based state estimators. The second approach utilizes a hybrid model that integrates feed-forward neural networks with first-principles models to capture process dynamics in the state estimator. Then, an output feedback model predictive controller is designed based on the state estimates provided by the machine-learning-based estimators to stabilize the closed-loop system at the steady-state. A chemical process example is utilized to illustrate the effectiveness of the proposed machine-learning-based state estimation and control approaches.

Optimized Fuzzy-Based Wavelet Neural Network Controller for a Non-Linear Process Control System

One of the common non-linear process control problems is the continuous stirred tank reactor problem and the reactor is applied widely in chemical process industries. It is of high importance to develop a suitable controller scheme for the concentration and temperature control of the considered non-linear continuous stirred tank reactor (CSTR) model. In this paper, a novel wavelet neural network (WNN) controller model is developed to carry out the control action and to meet the performance requirements of the system model. The developed wavelet neural network model is tuned for its weights employing the proposed deterministic grey wolf optimizer algorithm and its input is fed from the Mamdani fuzzy model. The optimal number of rules to be formulated for the fuzzy rule base model is computed using the deterministic grey wolf optimizer (DGWO) which is the variant of the classic grey wolf optimizer (GWO). WNN controller devise, based on the inputs from the fuzzy model and weights from DGWO, is designed to perform control action on the non-linear CSTR model. The concentration and temperature control is carried out by the proposed controller and the responses are obtained. Also, the respective time response specifications are evaluated for the developed WNN controller. Simulation experiments prove the effectiveness of the proposed controller for the considered non-linear CSTR model in comparison with that of the existing controllers from the literature.

PIO Based Data-Driven Iterative Learning Control for Nonlinear Batch Processes with Nonrepetitive Disturbances Subject to Input Constraints

Abstract This paper proposes a novel proportional-integral observer (PIO) based high-order data-driven iterative learning control (HODDILC) for nonlinear batch processes with non-repetitive disturbances subject to input constraints. First, an equivalent dynamic linearization data model (DLDM) with an uncertainty term arising from the nonrepetitive disturbances is constructed in the batch direction. Based on the established DLDM along with a gradient estimation algorithm, a data-driven PIO is then designed to estimate the uncertainty term along the batch direction, followed by designing a HODDILC law in terms of the tracking errors over more than one previous batches and control inputs in the previous time instants of the current batch. Using the contraction mapping principle and matrix theory, rigorous convergence analysis is conducted in the iteration domain. A notable advantage of the proposed design is that only input and output measurement data are used rather than a process model. Finally, an illustrative example from the literature is given to demonstrate the effectiveness and merit of the proposed method.

Optimization based internal model control design

Control of nonlinear and/or constrained processes is a challenging and important task, especially chemical processes that need special attention to maximize the product thereby the profit. In this work, an optimization-based internal model control design is presented for both linear and nonlinear systems. For controlling nonlinear systems, the process dynamics are linearized around the operating point. The use of an optimizer as an internal model controller will enable the control engineer to deal with the constraints posed by the various process parameters and the effect of various process parameter variations in the closed-loop response is reported. Simulation case studies are presented viz., a first-order LTI system, and Continuous Stirred Tank Reactor(CSTR) to prove the efficacy of the optimization based internal model controller in controlling linear and nonlinear constrained processes.

Fractional-order multi-model predictive control for nonlinear processes

Fractional-order multi-model predictive control for nonlinear processes

Co-Teaching Approach to Machine Learning-based Predictive Control of Nonlinear Processes

Abstract Machine learning modeling of chemical processes using noisy data is practically a challenging task due to the occurrence of overfitting during learning. In this work, we propose a co-teaching learning algorithm that develops Long short-term memory (LSTM) networks to capture the ground truth (i.e., underlying process dynamics) from noisy data. We consider an industrial chemical reactor example and use Aspen Plus Dynamics to generate process operational data that is corrupted by sensor noise generated by industrial noisy measurements. An LSTM model is developed using the co-teaching method with additional noise-free data generated from simulations of the reactor first-principles model. Through open-loop and closed-loop simulations, we demonstrate that compared to the LSTM model developed from the standard training process, the co-teaching LSTM model is more accurate in predicting process dynamics, and therefore, achieves better closed-loop performance under model predictive control.

Fractional-order multi-model predictive control for nonlinear processes

This paper proposes a novel fractional-order multi-model predictive control (FO-MMPC) design to deal with a class of nonlinear fractional order systems. Based on the assumption that the plant is governed by a fractional order nonlinear dynamical model, we are able for each operating region, to determine the linear portion of the nonlinear process as a single fractional order pole transfer function. The predictive model is then approximated by rational transfer functions using the singularity function approach in the frequency domain. The main contribution in this control approach is the use of a switching algorithm between fractional order prediction models that are approximating the nonlinear system dynamics for different operating points and input range intervals. By using the FO-MMPC for controlling the level of a conical tank system with nonlinear dynamics using a multiple fractional-order predictive models, it is shown by means of numerical simulations the effectiveness of the proposed control strategy.

An Efficient Iterative Learning Predictive Functional Control for Nonlinear Batch Processes.

Iterative learning model-predictive control (ILMPC) is very popular in controlling the batch process since it possesses not only the learning ability along batches but also the strong time-domain tracking properties. However, for a fast batch process with strong nonlinear dynamics, the application of the ILMPC is challenging due to the difficulty in balancing the computational efficiency and tracking accuracy. In this article, an efficient iterative learning predictive functional control (ILPFC) is proposed. The original nonlinear system is linearized along the reference trajectory to derive a 2-D tracking-error predictive model. The linearization error is compensated by utilizing the Lipschitz condition so that the objective function can be formulated with the upper bound of the actual tracking error. For enhancing control efficiency, predictive functional control (PFC) is applied in the time domain, which reduces the dimension of the decision variable in order to effectively cut down the computational burden. The stability and convergence of this ILPFC with terminal constraint are analyzed theoretically. Simulations on an unmanned ground vehicle and a typical fast batch reactor verify the effectiveness of the proposed control algorithm.

Control of constrained high dimensional nonlinear liquid level processes using a novel neural network based Rapidly exploring Random Tree algorithm

The control of constrained nonlinear liquid level systems is a problem of fundamental importance in pharmaceutical, chemical, food-processing, oil refining and natural liquid gas separation industries. This paper proposes a novel control strategy for the control of such constrained high-dimensional interacting liquid level systems. The nonlinear liquid level regulation problem is formulated as a path planning problem in high-dimensional state space where constraint satisfaction is viewed as obstacle avoidance. An approximate control policy to steer the system to the goal state while satisfying numerous level and flow-rate constraints is computed using the famous RRT path planning algorithm which can efficiently explore non-convex spaces. To further improve performance a neural network was trained to generalize the approximate control policy computed by the RRT to unexplored states and provide smooth control. The generalized control policy learnt by the neural network is then used to achieve large changes in state and bring the system close to the goal state after which computationally cheap linear control is used to keep the system close to the goal state. The effectiveness of the proposed ANN-RRT control approach is demonstrated by applying it to the control of constrained high dimensional 5, 10, 20, 30 and 50 interacting tank systems. Experimental results for a highly interacting quadruple tank system indicate that the ANN-RRT algorithm significantly outperforms alternate approaches like PID, Fuzzy control, MPC, IMC and SMC from recent literature.

Machine learning‐based distributed model predictive control of nonlinear processes

AbstractThis work explores the design of distributed model predictive control (DMPC) systems for nonlinear processes using machine learning models to predict nonlinear dynamic behavior. Specifically, sequential and iterative DMPC systems are designed and analyzed with respect to closed‐loop stability and performance properties. Extensive open‐loop data within a desired operating region are used to develop long short‐term memory (LSTM) recurrent neural network models with a sufficiently small modeling error from the actual nonlinear process model. Subsequently, these LSTM models are utilized in Lyapunov‐based DMPC to achieve efficient real‐time computation time while ensuring closed‐loop state boundedness and convergence to the origin. Using a nonlinear chemical process network example, the simulation results demonstrate the improved computational efficiency when the process is operated under sequential and iterative DMPCs while the closed‐loop performance is very close to the one of a centralized MPC system.

Recent advances in artificial intelligence and machine learning for nonlinear relationship analysis and process control in drinking water treatment: A review

Because of its robust autonomous learning and ability to address complex problems, artificial intelligence (AI) has increasingly demonstrated its potential to solve the challenges faced in drinking water treatment (DWT). AI technology provides technical support for the management and operation of DWT processes, which is more efficient than relying solely on human operations. AI-based data analysis and evolutionary learning mechanisms are capable of realizing water quality diagnosis, autonomous decision making and operation process optimization and have the potential to establish a universal process analysis and predictive model platform. This review briefly introduces AI technologies that are widely used in DWT. Moreover, this paper reviews in detail the mature applications and latest discoveries of AI and machine learning technologies in the fields of source water quality, coagulation/flocculation, disinfection and membrane filtration, including source water contaminant monitoring and identification, accurate and efficient prediction of coagulation dosage, analysis of the formation of disinfection by-products and advanced control of membrane fouling. Finally, the challenges facing AI technologies and the issues that need further study are discussed; these challenges can be briefly summarized as a) obtaining more effective characterization data to screen and identify targeted contaminants in the complex background with the assistance of AI technologies and b) establishing a macro intelligence model and decision scheme for entire drinking water treatment plants (DWTPs) to support the management of the water supply system.

Decentralized machine-learning-based predictive control of nonlinear processes

This work focuses on the design of decentralized model predictive control (MPC) systems for nonlinear processes, where the nonlinear process is broken down into multiple, yet coupled subsystems and the dynamic behavior of each subsystem is described by a machine learning model. One decentralized MPC is designed and used to control each subsystem while accounting for the interactions between subsystems through feedback of the entire process state. The closed-loop stability of the overall nonlinear process network and the performance properties of the decentralized model predictive control system using machine-learning prediction models are analyzed. More specifically, multiple recurrent neural network models suited for each different subsystem need to be trained with a sufficiently small modeling error from their respective actual nonlinear process models to ensure closed-loop stability. These recurrent neural network models are subsequently used as the prediction model in decentralized Lyapunov-based MPCs to achieve efficient real-time computation time while ensuring closed-loop state boundedness and convergence to the origin. The simulation results of a nonlinear chemical process network example demonstrate the effective closed-loop control performance when the process is operated under the decentralized MPCs using the independently-trained recurrent neural network models, as well as the improved computational efficiency compared to the closed-loop simulation of a centralized MPC system.