Nonlinear model predictive control strategy based on soft computing approaches and real time implementation on a coupled-tank system

In order to effectively implement a good model based control strategy, the combination of different linear models working at various operating regions are mostly utilised since a single model that can operate in that fashion is always a difficult task to develop. This work presents the use of soft computing approaches such as evolutional algorithm called simulated annealing (SA), a genetic algorithm (GA) and an artificial neural network (ANN) to design both a robust single nonlinear dynamic ANN model derived from an experimental data driven system identification approach and a nonlinear model predictive control (NMPC) strategy. SA is employed to give an initial weight for the training of the ANN model structure while a gradient descent based Levenberg–Marquardt Algorithm (LMA) approach is used to optimise the ANN weights. The designed NMPC strategy is optimised using a stochastic GA optimisation method and is tested first in simulation and then implemented in real time practical experiment on a highly nonlinear single input single output (SISO) coupled tank system (CTS). An excellent control performance is reported over the conventional proportional-integral-derivative (PID) controller and results show the effectiveness of the approach under disturbances. The nonlinear neural network model proved very reliable in different operating regions. The SISO system can be upgraded to multi-input multi-output (MIMO) system while the whole NMPC approach can easily be adapted to other industrial processes

Variational approach for learning Markov processes from time series data

Inference, prediction and control of complex dynamical systems from time series is important in many areas, including financial markets, power grid management, climate and weather modeling, or molecular dynamics. The analysis of such highly nonlinear dynamical systems is facilitated by the fact that we can often find a (generally nonlinear) transformation of the system coordinates to features in which the dynamics can be excellently approximated by a linear Markovian model. Moreover, the large number of system variables often change collectively on large time- and length-scales, facilitating a low-dimensional analysis in feature space. In this paper, we introduce a variational approach for Markov processes (VAMP) that allows us to find optimal feature mappings and optimal Markovian models of the dynamics from given time series data. The key insight is that the best linear model can be obtained from the top singular components of the Koopman operator. This leads to the definition of a family of score functions called VAMP-r which can be calculated from data, and can be employed to optimize a Markovian model. In addition, based on the relationship between the variational scores and approximation errors of Koopman operators, we propose a new VAMP-E score, which can be applied to cross-validation for hyper-parameter optimization and model selection in VAMP. VAMP is valid for both reversible and nonreversible processes and for stationary and non-stationary processes or realizations

Advanced control of nonlinear beams with Pancharatnam-Berry metasurfaces

The application of the Pancharatnam-Berry (PB) phase approach to the design of nonlinear metasurfaces has recently enabled subdiffractive phase control over the generated nonlinear fields, embedding phased array features in ultrathin structures. Here, we rigorously model, analyze, and design highly efficient nonlinear metasurfaces with advanced functionalities, including the generation of pencil beams steered in arbitrary directions in space, as well as vortex beams with polarization-dependent angular momentum, and we extend the PB approach to various nonlinear processes. To this purpose, we develop an accurate and efficient theoretical framework-inspired by the linear phase array theory-based on the effective nonlinear susceptibility method, thus avoiding the use of time-consuming numerical simulations. Our findings allowexploiting the flat nonlinear optics paradigm, enabling exciting applications based on subwavelength field control over flat and large-scale structures with giant nonlinear responsesclos

Nonlinear analysis of Type 1 Diabetes Models by Differential Geometric Approach

The control of physiological systems is a highly demanding task. The requirements are strict and there is a little margin of error, since failure can directly endanger the patient's life. In the same time the performance of the available sensors and actuators are limited in most cases, leaving even higher burden on the control algorithm. Finally the models themselves, which can describe the biophysical and biochemical processes that are most significantly linked to the system we wish to regulate, are rather complex and nonlinear in nature. In general, linear model-based approaches are used, but linearization gives a first source of errors in the further development. The aim of this paper is to investigate two frequently used models describing the metabolism of the human body in case of Type 1 Diabetes Mellitus (T1DM) from nonlinear control perspective: the model presented by Magni et al. (2009) and Hovorka et al. (2004). These models will be investigated using differential geometric approach for the first time

Transonic Flutter Suppression Control Law Design, Analysis and Wind Tunnel Results

The benchmark active controls technology and wind tunnel test program at NASA Langley Research Center was started with the objective to investigate the nonlinear, unsteady aerodynamics and active flutter suppression of wings in transonic flow. The paper will present the flutter suppression control law design process, numerical nonlinear simulation and wind tunnel test results for the NACA 0012 benchmark active control wing model. The flutter suppression control law design processes using (1) classical, (2) linear quadratic Gaussian (LQG), and (3) minimax techniques are described. A unified general formulation and solution for the LQG and minimax approaches, based on the steady state differential game theory is presented. Design considerations for improving the control law robustness and digital implementation are outlined. It was shown that simple control laws when properly designed based on physical principles, can suppress flutter with limited control power even in the presence of transonic shocks and flow separation. In wind tunnel tests in air and heavy gas medium, the closed-loop flutter dynamic pressure was increased to the tunnel upper limit of 200 psf The control law robustness and performance predictions were verified in highly nonlinear flow conditions, gain and phase perturbations, and spoiler deployment. A non-design plunge instability condition was also successfully suppressed

NEURAL NETWORKS ARCHITECTURES FOR MODELING AND SIMULATION OF THE ECONOMY SYSTEM DYNAMICS

This research work investigates the possibility to apply several neural network architectures for simulation and prediction of the dynamic behavior of the complex economic processes. Therefore we will explore different neural networks architectures to build several neural models of the complex dynamic economy system. In future work we will use these architectures to be trained by well-known training algorithms, such as Levenberg-Marquardt back-propagation error and Radial Basic Function (RBF), to compare their results and to decide at the end, which one is the best among the different applications from the economy field. The results presented in this work are based on the experience accumulated by the authors in the field of identification, modeling and control of the industrial and economic processes, namely chemical, HVAC, automotive industry and satellites constellation. The neural networks are strongly recommended for the highly nonlinear processes for which an analytic description is almost impossible. It is well known that the single-index economic models and selection of leading indicator variables are normally based on linear regression methods. Moreover, in statisti- cal modeling of the business cycle, it has been well established that cycles are asymmetric; therefore it is doubtful that linear models can adequately describe them. With recent development in nonlinear time series analysis, several authors have begun to examine the forecasting properties of nonlinear models in economics. Probably the largest share of economic appli- cations of nonlinear models can be found in the field of prediction of time series capital markets. Furthermore recently, the neural network architectures use financial variables to forecast industrial production by estimating a nonlinear, non- parametric nearest-neighbor regression model, and are very useful for fault detection, diagnosis and isolation ( FDDI) of the models fault in the control systems.The simulation results reveal a high capability of the neural networks to capture more accurate the nonlinear dynamics behavior of the process and to yield high performance, comparable to the Kalman filters techniques and all other control strategies developed in literature. The nonlinear mapping and self-learning abilities of neural networks have been motivating factors for development of intelligent contol strategies. The neural networks approach is very interesting because don`t need the linear model of the process that means time consuming and increasing the risk to reduce the accuracy in capturing the appropriate dynamics of the process.Dynamic Systems, Kalman Filers, Neural Networks Architectures, ARMA Models, Estimation, Neural-Models, Neural-Control Strategy, Inverse Neural-Control Strategy, MIMO Control Strategies. Market-Oriented Economy

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

Advancing block-oriented modeling in process control

The increasing pressure in industry to maintain tight control over processes has led to the development of many advanced control algorithms. Many of these algorithms are model-based control schemes, which require an accurate predictive model of the process to achieve good controller performance. Because of this, research in the fields of nonlinear process modeling and predictive control has advanced over the past several decades.;In this dissertation, a new method for identifying complicated block-oriented nonlinear models of processes will be proposed. This method is applied for LNL and LLN sandwich block-oriented models and will be shown to accurately predict process response behavior for a simulated continuous-stirred tank reactor (CSTR) and a pilot-scale distillation column. In addition, it will be shown to effectively model the pilot-scale distillation column using closed-loop, highly correlated input data.;Using the block-oriented models identified, a new feedforward control framework has been developed. This feedforward control framework represents the first that compensates for multiple input disturbances occurring simultaneously. Only a single process model is needed to account for all measured disturbances. In addition, it allows a plant engineer to develop the predictive model of the process from plant historical data instead of introducing a series of disturbances to the process to try to identify the model. This has the potential to considerably reduce the cost of implementing an advanced control scheme in terms of time, effort and money. The proposed feedforward control framework is tested on a simulated CSTR process in Chapter 4, and on a pilot-scale distillation column in Chapter 5

Necessary conditions of first-order for an optimal boundary control problem for viscous damage processes in 2D

Controlling the growth of material damage is an important engineering task with plenty of real world applications. In this paper we approach this topic from the mathematical point of view by investigating an optimal boundary control problem for a damage phase-field model for viscoelastic media. We consider non-homogeneous Neumann data for the displacement field which describe external boundary forces and act as control variable. The underlying hyberbolic-parabolic PDE system for the state variables exhibit highly nonlinear terms which emerge in context with damage processes. The cost functional is of tracking type, and constraints for the control variable are prescribed. Based on recent results from [M. H. Farshbaf-Shaker, C. Heinemann: A phase field approach for optimal boundary control of damage processes in two-dimensional viscoelastic media. Math. Models Methods Appl. Sci. 25 (2015), 2749--2793], where global-in-time well-posedness of strong solutions to the lower level problem and existence of optimal controls of the upper level problem have been established, we show in this contribution differentiability of the control-to-state mapping, well-posedness of the linearization and existence of solutions of the adjoint state system. Due to the highly nonlinear nature of the state system which has by our knowledge not been considered for optimal control problems in the literature, we present a very weak formulation and estimation techniques of the associated adjoint system. For mathematical reasons the analysis is restricted here to the two-dimensional case. We conclude our results with first-order necessary optimality conditions in terms of a variational inequality together with PDEs for the state and adjoint state system