Control Of Nonlinear Processes Research Articles

Nonlinear propagation calculation-based irradiation process control for several mJ ultrashort pulse laser processing

In the realm of ultrashort pulse laser processing, surpassing the air ionization threshold, variations in focusing characteristics due to nonlinear optical phenomena pose challenges. Particularly, suitable irradiation conditions and position control methods for high pulse energy processing around 1 mJ remain unestablished. This study explores laser divergence phenomena in several mJ pulse energy range, examining both experimental and computational data. Quantitative demonstrations of laser focusing alterations, including divergence position and fluence, were achieved. Additionally, the dry laser peening effect was enhanced by energy-specific irradiation control. Numerical simulation-based visualization facilitates precise control, advancing the processing techniques.

Control of complex dynamic nonlinear loading process for electromagnetic mill

Control of complex dynamic nonlinear loading process for electromagnetic mill

A reinforcement learning-based transformed inverse model strategy for nonlinear process control

Process control is evolving with a rapid inclusion of artificial intelligence (AI) based methods, which have the potential to significantly boost controller performances. This development is valuable to control engineers, especially for the control of nonlinear processes plagued by higher offsets and larger delays. With this motivation, we develop in this work a new strategy utilizing AI for process control by assimilating reinforcement learning (RL) with a novel approach for inverse model control. This approach involves expressing a dynamic process model in the controlled variable domain to obtain a computationally efficient, transformed inverse model (TIM). In the developed control strategy, the TIM provides baseline control, which is subsequently improved by RL’s deep deterministic policy gradient method in the resultant TIM-RL controller. This controller is examined in three different in-silico case studies of varying nonlinearity and complexity. Relative to nonlinear model predictive control, the TIM-RL controller is observed to have superior performance with more than 30% reduction in integral absolute error, 45% lower settling time, and about an order of magnitude smaller latency.

Robust fuzzy predictive switching control for nonlinear multi-phase batch processes with synchronous vs asynchronous cases

Multi-phase batch processes (MPBP) have the characteristics of nonlinearity and various cases of switching, where the switching between two adjacent phases can be divided into synchronous vs asynchronous cases. The present study introduces a robust fuzzy predictive method for switching control to ensure that an MPBP can still operate stably in the above two cases. First, considering the multi-phase characteristics of MPBP, multiple stable sub-models are established under the synchronous case. On this basis, unstable sub-models are established between adjacent phases under the asynchronous case. Second, in order to deal with the inherent nonlinearity of MPBP, each sub-model is locally linearized and a mixed Takagi-Sugeno (T-S) model is established. Third, using a mapping relationship between controller and local subsystem including direct mapping and fully associative mapping, a global output control law is designed. By combining the Lyapunov stability theory, linear matrix inequality (LMI) theory, mode-dependent average dwell time method, etc., corresponding LMI conditions are derived by the mapping relationship of different cases, making each phase asymptotically stable and each batch exponentially stable. Then, the distribution compensation gains of the corresponding controllers, the shortest operating time of the stable subsystem and the longest operating time of the unstable subsystem can be obtained by solving corresponding LMI conditions in a synchronous or an asynchronous case. Finally, if the MPBP is in an asynchronous case, according to the longest operating time of the unstable subsystem, a time compensation method based on the obtained operating time is proposed to avoid the occurrence of an unstable subsystem. The simulation results demonstrate that the proposed method has greater advantages than the reference methods.

Iterative learning hybrid robust predictive fault-tolerant control for nonlinear batch processes with partial actuator faults

For nonlinear batch processes with uncertainties, disturbances and partial actuator faults, an iterative learning robust predictive fault-tolerant control approach is developed. Based on the conclusion of robustness analysis, the stability conditions combining the robust positive invariant set with the terminal constraint set can guarantee that the system is stable under faults. Furthermore, the real-time optimal gains of control law solved online can significantly reduce the learning cycles of the controller, which in turn can meet the demand for rapid production of batch processes. The injection process is employed as an example to ultimately confirm the viability and efficacy of the developed approach.

Model predictive control of nonlinear processes using neural ordinary differential equation models

Neural Ordinary Differential Equation (NODE) is a recently proposed family of deep learning models that can perform a continuous approximation of a linear/nonlinear dynamic system using time-series data by integrating the neural network model with classical ordinary differential equation solvers. Modeling nonlinear dynamic processes using data has historically been a critical challenge in the field of chemical engineering research. With the development of computer science and neural network technology, recurrent neural networks (RNN) have become a popular black-box approach to accomplish this task and have been utilized to design model predictive control (MPC) systems. However, as a discrete-time approximation model, RNN requires strictly uniform step sequence data to operate, which makes it less robust to an irregular sampling scenario, such as missing data points during operation due to sensor failure or other types of random errors. This paper aims to develop a NODE model and construct an MPC based on this novel continuous-time neural network model. In this context, closed-loop stability is established and robustness to noise is addressed using a variety of data analysis techniques. An example of a chemical process is utilized to evaluate the performance of NODE-based MPC. Furthermore, the performance of the NODE-based MPC under Gaussian and non-Gaussian noise is investigated, and the subsampling method is found to be effective in building models for MPC that are suitable for handling the presence of non-Gaussian noise in the data.

Investigation of nonlinear control of galloping with a linear beam with elastic boundary conditions

The aim of this study is nonlinear passive control of galloping oscillation on overhead transmission lines. The considered system is a linear beam subjected to harmonic and aerodynamic excitations which is coupled to a nonlinear absorber placed on an arbitrary position along the beam. Both extremities of the beam present rotationally and translationally elastic boundary conditions. After projection of spatio-temporal equations of the system on an arbitrary mode of the beam (the mode to be controlled), fast and slow system dynamics are traced which predict periodic or non periodic regimes. All analytical developments are compared with numerical results obtained from direct numerical integration of system equations and also from finite element modeling of the overall structure. Then, nonlinear passive control process of galloping instability by a non smooth nonlinear energy sink (NES) is investigated on a real case of galloping instability on a transmission line cable due to accretion of ice on it.

Real-time adaptive sparse-identification-based predictive control of nonlinear processes

This study introduces a sparse identification-based model predictive control (MPC) framework that incorporates on-line updates of the sparse-identified model to account for nonlinear dynamics and model uncertainty in process systems. The methodology involves obtaining a nonlinear first-order ordinary differential equation model using sparse identification for nonlinear dynamics (SINDy), which is integrated into two control schemes: Lyapunov-based MPC (LMPC) for achieving steady-state operation and Lyapunov-based economic MPC (LEMPC) for achieving both closed-loop stability and optimal economic performance. To improve prediction accuracy, an on-line model update scheme is proposed for the SINDy models. Specifically, an error-trigger mechanism that utilizes prediction errors and then uses the most recent process data to update the parameters of the SINDy model in real-time is designed. By incorporating the error-triggered on-line model updates in the SINDy-based LMPC and LEMPC, the dynamic performance of the process is enhanced, ensuring closed-loop stability, optimality, and smooth control actions. Following theoretical results on the boundedness of the closed-loop states and detailed discussions on the selection criteria for parameters of the error-triggered SINDy update scheme, the effectiveness of the proposed methodology is demonstrated through a chemical process example with time-varying disturbances under the LEMPC framework.

Physics-informed recurrent neural network modeling for predictive control of nonlinear processes

In this work, we present a physics-informed recurrent neural network (PIRNN) modeling approach, and a PIRNN-based predictive control scheme for a general class of nonlinear dynamic systems. Specifically, we first develop a hybrid data-driven and physics-guided modeling framework that integrates measurement data and mechanistic mathematical models to construct high-fidelity RNN models. Then, we derive a generalization error bound of the PIRNN model based on a nominal system model via the Rademacher complexity technique from statistical machine learning theory. Subsequently, the PIRNN model is utilized in Lyapunov-based model predictive controllers and applied to a chemical reactor example with Gaussian measurement noise to demonstrate its improved noise rejection and generalization performance in comparison to the purely data-driven and the purely physics-guided RNN-based predictive control schemes.

A sensitivity-based approach to optimal sensor selection for complex processes

Sensor selection is critical for state estimation, control and monitoring of nonlinear processes. However, it is impractical to evaluate the performance of all the combinations of the potentially available sensors using exhaustive search unless the sensor set is small. In this paper, we present a sensitivity-based approach for determining the minimum number of sensors and their optimal locations for state estimation. The observability is measured using the local sensitivity matrix of the output measurements to initial states. Based on this matrix, we determine the minimum number of sensors required to achieve full column rank. The optimal sensor placement is thought to be the sensor set that provides the maximum degree of observability among all sets that meet the full-rank requirement. The computational complexity of sensor selection is significantly reduced by successive orthogonalization of the columns of the sensitivity matrix. To validate the effectiveness of the proposed method, it is applied to two processes: four continuous stirred-tank reactors and a wastewater treatment plant. In both cases, the proposed approach can obtain the optimal sensor subset.

Modeling and predictive control of nonlinear processes using transfer learning method

AbstractThis work develops a transfer learning (TL) framework for modeling and predictive control of nonlinear systems using recurrent neural networks (RNNs) with the knowledge obtained in modeling one process transferred to another. Specifically, transfer learning uses a pretrained model developed based on a source domain as the starting point, and adapts the model to a target process with similar configurations. The generalization error for TL‐based RNN (TL‐RNN) is first derived to demonstrate the generalization capability on the target process. The theoretical error bound that depends on model capacity and the discrepancy between source and target domains is then utilized to guide the development of pretrained models for improved model transferability. Subsequently, the TL‐RNN model is utilized as the prediction model in model predictive controller (MPC) for the target process. Finally, the simulation study of chemical reactors via Aspen Plus Dynamics is used to demonstrate the benefits of transfer learning.

Non-Hermitian Floquet-free analytically solvable time-dependent systems [Invited

The non-Hermitian models, which are symmetric under parity (P) and time-reversal (T) operators, are the cornerstone for the fabrication of new ultra-sensitive optoelectronic devices. However, providing the gain in such systems usually demands precise control of nonlinear processes, limiting their application. In this paper, to bypass this obstacle, we introduce a class of time-dependent non-Hermitian Hamiltonians (not necessarily Floquet) that can describe a two-level system with temporally modulated on-site potential and couplings. We show that implementing an appropriate non-Unitary gauge transformation converts the original system to an effective one with a balanced gain and loss. This will allow us to derive the evolution of states analytically. Our proposed class of Hamiltonians can be employed in different platforms such as electronic circuits, acoustics, and photonics to design structures with hidden PT-symmetry potentially without imaginary onsite amplification and absorption mechanism to obtain an exceptional point.

Physics-Informed Online Machine Learning and Predictive Control of Nonlinear Processes with Parameter Uncertainty

Physics-Informed Online Machine Learning and Predictive Control of Nonlinear Processes with Parameter Uncertainty

A contraction-constrained economic Model Predictive Control for nonlinear processes using multi-timescale models

Many chemical processes exhibit diverse timescale dynamics with a strong coupling between timescale sensitive variables. Model predictive control with a non-uniformly spaced optimisation horizon is an effective approach to multi-timescale control and offers opportunities for reduced computational complexity. In such an approach, dynamics with different timescales can be included in an optimisation problem by implementing faster timescale models (with shorter time intervals) earlier in the prediction horizon and increasingly slower timescale models (with longer time intervals) towards the end. In this paper, a reference-flexible condition is developed based on contraction theory to provide a stability guarantee for cost minimising control of multiple timescale nonlinear systems using multiple predictive models.

Design of robust fuzzy iterative learning control for nonlinear batch processes.

In this paper, a two-dimensional (2D) composite fuzzy iterative learning control (ILC) scheme for nonlinear batch processes is proposed. By employing the local-sector nonlinearity method, the nonlinear batch process is represented by a 2D uncertain T-S fuzzy model with non-repetitive disturbances. Then, the feedback control is integrated with the ILC scheme to be investigated under the constructed model. Sufficient conditions for robust asymptotic stability and 2D $ H_\infty $ performance requirements of the resulting closed-loop fuzzy system are established based on Lyapunov functions and some matrix transformation techniques. Furthermore, the corresponding controller gains can be derived from a set of linear matrix inequalities (LMIs). Finally, simulations on the three-tank system and the highly nonlinear continuous stirred tank reactor (CSTR) are carried out to prove the feasibility and efficiency of the proposed approach.

Real-Time Level Control of Spherical Tank Process using Gain Scheduled PID Controller

The objective of this paper is to maintain the level inside the process tank in a desired value. The real time implementation of the process is designed and implemented in MATLAB. Gain scheduled PID controller is designed to enhance the performance of the conventional PID controller for nonlinear spherical tank process. It is based on linearization of the nonlinear model around selected operating points. The linear design methods are applied at each region in order to arrive at a set of linear control laws. How to cite this article: Vadivazhagi S, Prabha KS, Vinodhini M et al. Real-Time Level Control of Spherical Tank Process using Gain Scheduled PID Controller. J Adv Res Instru Control Engi 2022; 9(3&4): 1-7. DOI: https://doi.org/10.24321/2456.1398.202201

Расчет оптимальных параметров систем управления нелинейными динамическими процессами импульсных преобразователей напряжения

A technique for choosing the optimal control system parameters for DC voltage converters is proposed, based on the joint application of the theory of linear automatic control systems and the theory of nonlinear dynamic systems. A small-signal structural dynamic model of an open loop of an automatic control system based on a direct step-up voltage converter with a control system for nonlinear dynamic processes based on a delayed feedback method is considered. Applying this model makes it possible to carry out a scientifically substantiated choice of the control system parameters for nonlinear dynamic processes using the methods of linear automatic control system theory. Bode diagrams of an open loop system are calculated without additional control of nonlinear dynamic processes and with additional control. The efficiency of using control systems for nonlinear dynamic processes is shown, which allows eliminating undesirable dynamic modes without additional parametric synthesis of the controller and, consequently, without reducing the system performance as a whole. In addition, applying these methods allows adjusting the controller parameters to increase the system performance without switching the system to undesirable dynamic modes. The results obtained can be applied at the stage of designing wide-class DC voltage pulse converters

On generalization error of neural network models and its application to predictive control of nonlinear processes

In order to approximate nonlinear dynamic systems utilizing time-series data, recurrent neural networks (RNNs) and long short-term memory (LSTM) networks have frequently been used. The training error of neural networks may often be made suitably modest; however, the accuracy can be further improved by incorporating prior knowledge in the construction of machine learning-based models. Specifically, physics-based RNN modeling has yielded more reliable RNN models than traditional RNNs. Yet, a framework for constructing and assessing the generalization ability of such RNN models as well as LSTM models to be utilized in model predictive control (MPC) systems is lacking. In this work, we develop a methodological framework to quantify the generalization error bounds for partially-connected RNNs and LSTM models. The partially-connected RNN model is then utilized to predict the state evolution in a MPC scheme. We illustrate through open-loop and closed-loop simulations of a nonlinear chemical process of two reactors-in-series that the proposed approach provides a flexible framework for leveraging both prior knowledge and data, thereby improving the performance significantly when compared to a fully-connected modeling approach under Lyapunov-based MPC.

Modeling and Control of Nonlinear Processes Using Sparse Identification: Using Dropout to Handle Noisy Data

Sparse identification of nonlinear dynamics (SINDy) is a recent nonlinear modeling technique that has demonstrated superior performance in modeling complex time-series data in the form of first-order ordinary differential equations (ODEs), which are explicit and continuous in time. However, a crucial step in the SINDy algorithm involves estimating the time derivative of the states from the discrete, measured data. Therefore, the presence of noise can greatly deteriorate the performance if it is not carefully considered and accounted for. In this work, SINDy is used with ensemble learning, where multiple models are identified to improve the overall/final nonlinear model’s performance. Specifically, in the SINDy algorithm, a fraction of the library functions considered for the ODE model representation are randomly dropped out in each submodel to favor model sparsity and stability at the possible risk of lowering the model accuracy. This trade-off is controlled by manipulating the fraction of the library functions dropped out and the total number of models generated, both of which are considered as hyperparameters to be tuned in the proposed algorithm. Data from open-loop simulations of a large-scale chemical plant are generated using the well-known high-fidelity process simulator, Aspen Plus Dynamics, and corrupted with substantial sensor noise to be implemented in the newly proposed algorithm, dropout-SINDy. The dropout-SINDy models obtained from training with the noisy data are then tested in open-loop simulations to demonstrate accurate identification of the steady-state and reasonably close transient behavior under a variety of initial conditions and manipulated input values. Finally, the constructed models are used in a Lyapunov-based model predictive controller to control the large-scale Aspen process, meeting desired closed-loop stability and performance specifications.

Feature selection-based machine learning modeling for distributed model predictive control of nonlinear processes

In this work, we develop reduced-order machine learning models using feature selection methods for distributed model predictive control (DMPC) of nonlinear processes. Specifically, filter, wrapper, and embedded methods for feature selection are first utilized to select a subset of input features that significantly impacts the prediction of system output. The feature selection methods are then integrated with the development of reduced-order recurrent neural network (RNN) models that capture the system dynamics using only the selected input features. Subsequently, the reduced-order RNN models are incorporated into sequential and iterative DMPCs to stabilize the nonlinear system at the steady-state. Finally, a reactor–reactor–separator process example is used to demonstrate that the DMPC using reduced-order RNN models achieves the desired closed-loop performance with improved computational efficiency.