Control Of Nonlinear Processes Research Articles

Two-dimensional iterative learning hybrid robust fuzzy predictive control for nonlinear multi-phase batch processes with asynchronous switching

For nonlinear multi-phase batch processes with uncertainties, time-varying delays, and unknown bounded disturbances, an iterative learning hybrid robust fuzzy predictive control approach is developed within the context of two-dimensional systems. First, a two-dimensional T-S fuzzy Fornasini-Marchesini comprehensive feedback error model is constructed, which includes a state increment and an output error. Based on the established model and considering an asynchronous switching situation between a controller and a system state, a feedback error switching model, including match and mismatch cases, is developed. Then, a two-dimensional iterative learning hybrid robust fuzzy predictive controller is built, based on the established switching model. Second, building on related theories and methodologies, the stability conditions are derived by a linear matrix inequality form, while the system's asymptotic and exponential stability are analyzed. Next, the stability conditions are calculated to get the control law gains, minimum and maximum dwelling times. The acquired gains of control law greatly minimize the controller's learning cycle, while the advanced switching signal based on the obtained dwelling times is dynamically adjusted to ensure a smooth transition and the system's stability during switching. Ultimately, a simulation case is utilized to validate the proposed method's effectiveness and feasibility.

Two-dimensional iterative learning hybrid robust fuzzy predictive control for nonlinear multi-phase batch processes with asynchronous switching

Two-dimensional iterative learning hybrid robust fuzzy predictive control for nonlinear multi-phase batch processes with asynchronous switching

Performance evaluation of PID and Fuzzy Logic controllers for residential ORC-based cogeneration systems

Cogeneration systems have been identified as a way to reduce primary energy consumption, especially the ones using fossil fuels. Although this technology has already reached maturity on a medium-to-large scale, it is not very well explored on a micro-scale, especially at a residential level where the market is currently filled with carbon-fueled boilers and combi-boilers. For implementation at a residential level, the organic Rankine cycle has been mentioned as a suitable technology because of its simplicity and thermal/ electrical efficiencies. Despite its performance, one of the most important aspects of these applications is the response time, which is mainly connected to the system’s control. Due to its influence, this study aims to provide insights for developing flexible control strategies and analyze two different control methodologies, a standard PID and a Fuzzy Logic controller, considering the operating conditions of an experimental ORC-based micro-cogeneration test rig.Before being implemented in the test rig, both control methodologies were optimized and tested in a virtual environment in order to avoid the exposure of the test rig to unsafe operating conditions. While both controllers show a reasonable response in operating conditions similar to the ones used in the virtual environment, the Fuzzy Logic approach proved to be more adaptable to changes in the system’s dynamics, which are caused by intrinsic (e.g., unpredicted evaporative phenomena) or external disturbances (e.g., a pressure ratio variation), obtaining an overall better performance. Additionally, the limitations of static PID controllers for complex nonlinear processes, like the ORC, were highlighted by their incapacity to stabilize the system when the organic fluid is diverted from the bypass line to the expansion valve. Conversely, it was concluded that the ability to incorporate expert knowledge and heuristics makes the Fuzzy Logic controller well-suited for ORC systems with uncertain, unstable, and fluctuating behavior.

Explicit machine learning-based model predictive control of nonlinear processes via multi-parametric programming

Machine learning-based model predictive control (ML-MPC) has been developed to control nonlinear processes with unknown first-principles models. While ML models can capture nonlinear dynamics of complex systems, the complexity of ML models leads to increased computation time for real-time implementation of ML-MPC. To address this issue, in this work, we propose an explicit ML-MPC framework for nonlinear processes using multi-parametric programming. Specifically, a self-adaptive approximation algorithm is first developed to obtain a piecewise linear affine function that approximates the behaviors of ML models. Then, multi-parametric quadratic programming (mpQP) problems are formulated to generate the solution map for states in discretized state–space. Furthermore, to accelerate the implementation of explicit ML-MPC, a neighbor-first search algorithm is developed. Finally, an example of a chemical reactor is used to demonstrate the effectiveness of the explicit ML-MPC.

Pseudo-model-based iterative learning control for nonlinear multi-phase batch processes

In this article, a pseudo-model-based iterative learning control (ILC) is exploited for multi-phase batch processes which can be described as a nonlinear switched system with unknown functions and identical states in different phases. The nonlinear switched system is converted into a linear model whose system parameter matrix is approximated by minimizing the discrepancy from the real system output increment to the approximated system output increment. A data-driven ILC is constructed in an interactive form with system parameter matrix approximate algorithm. Meanwhile, the signs of the diagonal elements of system lower triangular parameter matrix are introduced into the construction of control input law. Theoretical analysis shows that the pseudo-model-based ILC (PM-ILC) concept can be extended to multi-phase batch processes with non-identical states in different phases. Furthermore, the approximation error of the system parameters matrix is bounded and the proposed PM-ILC is robust if the parameter is appropriately chosen. Simulation results illustrate the effectiveness and practicability of the proposed PM-ILC.

Model predictive control of nonlinear processes using transfer learning-based recurrent neural networks

Artificial neural networks (ANNs), one of the deep learning techniques that has sparked a lot of attention recently for its exceptional modeling capabilities of nonlinear systems, are an essential candidate for model-based control systems. In particular, recurrent neural networks (RNN) have shown remarkable capacity to forecast the dynamic behavior of nonlinear processes using time-series data. In order to regulate the rate at which chemical species are produced in intricate processes, RNNs have successfully served as the predictive model in model-based controllers. However, the necessity for massive amounts of data to capture complex processes is a drawback of typical RNN models. With the goal of efficient utilization of the available data, a different, transfer learning-based training approach for RNNs is presented in this work. The transfer learning strategy is taken into consideration to overcome the challenges stemming from lack of data for the construction of RNN models. In particular, weight-sharing RNNs are developed using a priori physical knowledge. Next, a comprehensive analysis of a complex chemical process on a large scale is conducted to showcase the benefits of the suggested approach across various data sizes and its effectiveness when combined with MPC in contrast to conventional RNNs.

Predictive fault-tolerant control for nonlinear batch processes with small time delays via iterative learning control: A Lyapunov–Razumikhin approach

For batch processes with small time delays and actuator partial fault, the existing methods based on iterative learning control still have some limitations, including the conservative and computationally burdensome of stability conditions and the limited fault-tolerant control capabilities. For this background, an iterative learning robust predictive fault-tolerant control method is developed, which integrates the Lyapunov–Razumikhin function method and derives stability conditions based on robust positive definite invariant set and terminal constraint set. With small time delays, the stability conditions of the system deduced using the Lyapunov–Razumikhin function are solved at a lower computational cost, which is due to the fact that the dimensionality of the stabilization condition is directly related to the size of the time delay, and thus the small time delay implies a lower dimensionality. Especially, the computational effort for solving the stability conditions online is reduced, allowing real-time control law gains to be obtained and combined with historical batches of control inputs, reducing the learning cycles of the system, and realizing stable tracking of the setpoints within shorter operating batches. Moreover, the robust positive invariant set and the set of terminal constraints are able to constrain the state of the system within a safe range for all possible uncertainties, bounded disturbances, and faults. This makes the proposed methods based on them more robust and fault tolerant. Finally, a nonlinear batch reactor is used as an example to demonstrate the effectiveness and feasibility of the developed method.

Robust reduced-order machine learning modeling of high-dimensional nonlinear processes using noisy data

Autoencoder-based reduced-order machine learning models have been developed for modeling and predictive control of nonlinear chemical processes with high dimensionality such as discretization of reaction–diffusion processes. However, in the presence of data noise, autoencoders may over-fit the training data and subsequently learn an inaccurate low-dimensional representation of the process variables. This leads to an inaccurate prediction model when the models are integrated with model predictive control (MPC). To address this issue, this work develops a novel machine-learning-based reduced-order modeling method by integrating SpectralDense layers into autoencoders and incorporating them with recurrent neural networks. We demonstrate that the new architecture of autoencoders using SpectralDense layers is more robust against over-fitting than conventional autoencoders in the presence of data noise, which improves the prediction accuracy in MPC. A diffusion–reaction process simulation example is used to demonstrate that the robust autoencoders outperform those using conventional layers for reduced-order modeling in predictive control.

Two-dimensional optimization design of constrained minmax model predictive tolerant-fault control for nonlinear batch processes

The presence of actuator faults and disturbances, coupled with the nonlinear characteristics inherent in batch processes, poses challenges to the design of high-precision control algorithms, especially for variables that vary over a large range. To solve this issue, we propose a two-step 2D constrained model predictive fault-tolerant control method that integrates the theory of min-max optimization. First, the original nonlinear batch process is approximated at different operating points and transformed into multiple polytopic systems (MPSs), which includes the “worst case” scenario, i.e., a case with all internal effects. Next, according to its characteristics and by introducing an output tracking error and batch state differences, an equivalent model of a MPS is created and an iterative learning control law was used. Based on this model, a quadratic performance index function, including anti-external disturbances, is designed, which is divided into two parts covering the entire infinite horizon. The linear state feedback control law plus the initial free control moves comprise the control law. In this way, the optimal control inputs are generated, and the system can be controlled with a greater margin, improving feasibility. Moreover, for closed-loop stability, a parameter-dependent Lyapunov function is constructed. An allowable range of actuator faults that the designed controller can resist is also considered and constructed. The advantage of the proposed control algorithm is that it fully considers the repetitive characteristics of batch processes, and for the first time, a 2D two-step control strategy related to time and batch directional information is designed, which greatly improves the system output tracking performance. Using a nonlinear batch reactor as an example, the method proposed in this study demonstrates its superiority tracking performance and ability to resist external disturbances than that of the traditional method.

Constrained model predictive fault-tolerant control for nonlinear batch processes with time delay by integrating a LRF method and a switching strategy

To guarantee the control performance of batch processes under time delays and actuator failures, a novel iterative learning model-based predictive fault-tolerant control approach is developed. First, a two-dimensional switched model was developed by linearizing the system at multiple operating points so as to describe the actual process with and without actuator faults. Second, a switching controller with greater robustness and diminished conservativeness was developed based on this switched model. Compared to conventional fault-tolerant control methods, the switching controller has stronger fault-tolerant ability, less conservativeness, and higher energy efficiency. Third, by integrating the Lyapunov-Razumikhin function (LRF) method, sufficient conditions for system stability could be provided based on the robust positive invariant and terminal constraint sets. Solving the stability conditions could then allow us to obtain the control law gains under faulty or normal cases. Compared to the existing Lyapunov-Krasovskii function method (LKF) method, the developed stability conditions were simpler, less complex, and less conservative. Finally, the effectiveness of the proposed method is tested on a continuous stirred reactor (CSTR).

Data-driven two-dimensional integrated control for nonlinear batch processes

Two-dimensional control has been considered as an effective strategy to accomplish high-accuracy tracking for batch processes because of its excellent learning ability and time-domain stability. However, being a model-based control method, the performance of the two-dimensional control system will inevitably decrease due to unknown uncertainties or unmodeled dynamics. In addition, the high computational cost and complex design process of the control system severely limit its application in batch processes. For this reason, this paper proposes a new data-driven two-dimensional integrated control (DDTDIC) method for nonlinear batch processes. In the presented control scheme, the P-type iterative learning control (ILC) is adopted along the batch-axis to ensure the convergence of the system, and the proportional-integral-differential (PID) control is used in the time-axis to reject the influence of real-time disturbance. The parameters of the PID controller are obtained by utilizing the virtual reference feedback tuning (VRFT) method. The entire design process of the control system only requires the input and output (I/O) data of the batch processes and does not depend on any explicit model information. The simulation results show that compared with the ILC and the two-dimensional control, the presented control method not only has faster convergence speed and smaller tracking error, but also the computational efficiency is improved by more than 40% and 50% respectively.

Fuzzy MIMO model for efficient control of complex processes with uncertainties and nonlinearities

This paper shows the impact of the MIMO model on control system solutions for efficient control of complex nonlinear processes (multiple input, multiple output model) in terms of efficiency, product quality and energy efficiency. In modern automatic control systems, there is a need for increased capacity in long-distance data transmission, high-speed local area networks, etc. Capacity can be increased by extending the frequency range. However, the application of these techniques is limited by biosafety requirements, limited power supply (in mobile devices), and electromagnetic compatibility. Therefore, if these approaches to communication systems do not ensure the speed of transmission of information about technological processes, a weak correlation will appear. The values of indicators for the construction and use of fuzzy MIMO models of control decisions are expressed in the form of linguistic variables. The fuzzy MIMO model makes qualitative decisions in the control of complex processes. This includes uncertainty and nonlinearity problems, which are used to optimize complex systems.

Modeling and Control of Non-Linear CSTH Process using Hybrid Optimized Technique

Modeling and Control of Non-Linear CSTH Process using Hybrid Optimized Technique

An Experimental Validation of Model Based Control Techniques for Interacting Nonlinear Systems

Model based controllers are those controllers that has gained significant attention in the arena of nonlinear process control. Conical tank is a nonlinear process whose nonlinearity increases when it interacts with another conical tank. Maintaining the level of an interacting nonlinear process operating with constraints is the control objective of this paper. Model Predictive Control (MPC) has the capability of handling constraints and exerts a control action with optimization. MPC is employed for this process and the experimental results obtained are subjected to time domain analysis and the performances are compared with the performance of Proportional’, ’Integral’, ’Derivative (PID) and Internal Model controller based PID (IMC’, ’PID) controller.

Distributed Control of an Ill-Conditioned Non-Linear Process Using Control Relevant Excitation Signals

Efficient control schemes for ill-conditioned systems, such as the high-purity distillation column, can be challenging and costly to design and implement. In this paper, we propose a distributed control scheme that utilizes well-designed excitation signals to identify the system. Unlike traditional systems, we found that a summation of correlated and uncorrelated signals can yield better excitation of the plant. Our proposed distributed model predictive control (MPC) scheme uses a shifted input sequence to address loop interactions and reduce the computational load. This approach deviates from traditional schemes that use iteration, which can increase complexity and computational load. We initially tested the proposed method on the linear model of a highly coupled 2 × 2 process and compared its performance with decentralized proportional-integral-derivative (PID) controllers and centralized MPC. Our results show improved performance over PID controllers and similar results to centralized MPC. Furthermore, we compared the performance of the proposed approach with a centralized MPC on a nonlinear model of a distillation column. The results for the second study also demonstrated comparable performance between the two controllers with the decentralised control slightly outperforming the centralised MPC in some cases. These findings are promising and may be of interest to practitioners that are more comfortable with tuning decentralised loops.

A practically implementable reinforcement learning control approach by leveraging offset-free model predictive control

This work addresses the problem of designing an offset-free implementable reinforcement learning (RL) controller for nonlinear processes. RL-based controllers can update the control policy using observed data obtained online based on the controller-process interactions. This allows to alleviate the regular model maintenance step that is essential in advanced control techniques such as model predictive control (MPC). However, random explorations are required for an RL agent to find optimal state–action regions so as to finally reach the optimal policy. This is not implementable in practical situations due to safety concerns and economic objectives. To address this issue, a pre-training strategy is proposed to provide a secure platform for online implementations of the RL controllers. To this end, an offset-free MPC (representative industrial MPC) optimization problem is leveraged to train the RL agent offline. Having obtained similar performance to the offset-free MPC, the RL agent is utilized for online control to interact with the actual process. The efficacy of the proposed approach to handle nonlinearity and changes in plant operating conditions (due to unmeasured disturbances) are demonstrated through simulations on a chemical reactor example for a pH neutralization process. The results show that the proposed RL controller can significantly improve the oscillatory closed-loop responses, obtained by running the offset-free MPC due to the plant-model mismatch and unmeasured disturbances.

Encrypted decentralized model predictive control of nonlinear processes with delays

This work focuses on enhancing the operational safety, cybersecurity, computational efficiency, and closed-loop performance of large-scale nonlinear time-delay systems. This is achieved by employing a decentralized model predictive controller (MPC) with encrypted networked communication. Within this decentralized setup, the nonlinear process is partitioned into multiple subsystems, each controlled by a distinct Lyapunov-based MPC. These controllers take into account the interactions between subsystems by utilizing full state feedback, while computing the control inputs only corresponding to their respective subsystem. To address the performance degradation associated with input delays, we integrate a predictor with each LMPC to compute the states after the input delay period. The LMPC model is initialized with these predicted states. To cope with state delays, the LMPC model is formulated using differential difference equations (DDEs) that describe the state-delays in the system. Further, to enhance cybersecurity, all signals transmitted to and received from each subsystem are encrypted. A stability analysis is carried out for the encrypted decentralized MPC when it is utilized in a time-delay system. Bounds are set up for the errors arising from encryption, state-delays, and sample-and-hold implementation of the controller. Guidelines are established to implement this proposed control structure in any nonlinear time-delay system. The simulation results, conducted on a nonlinear chemical process network, illustrate the effective closed-loop performance of the decentralized MPCs alongside the predictor with encrypted communication when dealing with input and state delays in a large-scale process.

Optimal tracking control of nonlinear batch processes with unknown dynamics using two-dimensional off-policy interleaved Q-learning algorithm

A novel two-dimensional (2D) off-policy interleaved Q-learning algorithm is proposed to handle the optimal tracking control problem without prior knowledge of nonlinear batch processes and an initial control policy, which overcomes the drawback that the system dynamic parameters change intermittently and the difficulty of obtaining the initial parameters, greatly reducing the computational difficulty of the optimal policy. Consequently, three-layer neural networks, including the model network, the critic network and the action network are designed as the approximate parameter structure to search for a control policy via the 2D off-policy interleaved Q-learning algorithm. The weights in each layer of the neural network are continuously learned and renewed by historical data in both time and batch directions in order to obtain the optimal control policy. After that, the convergence and optimality are scrupulously verified. Ultimately, the simulation results of the injection stage confirmed the validity and feasibility of the proposed algorithm.

Reduced-order Koopman modeling and predictive control of nonlinear processes

In this paper, we propose an efficient data-driven predictive control approach for general nonlinear processes based on a reduced-order Koopman operator. A Kalman-based sparse identification of nonlinear dynamics method is employed to select lifting functions for Koopman identification. The selected lifting functions are used to project the original nonlinear state–space into a higher-dimensional linear function space, in which Koopman-based linear models can be constructed for the underlying nonlinear process. To curb the significant increase in the dimensionality of the resulting full-order Koopman models caused by the use of lifting functions, we propose a reduced-order Koopman modeling approach based on proper orthogonal decomposition. A computationally efficient linear robust predictive control scheme is established based on the reduced-order Koopman model. A case study on a benchmark chemical process is conducted to illustrate the effectiveness of the proposed method. Comprehensive comparisons are conducted to demonstrate the advantage of the proposed method.

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.