Nonlinear model predictive control for the ALSTOM gasifier benchmark problem

Model predictive control has become a first choice control strategy in industry because it is intuitive and can explicitly handle MIMO linear and nonlinear systems with the presence of variable constraints and interactions. In this work a nonlinear state-space model has been developed and used as the internal model in predictive control for the ALSTOM gasifier. A linear model of the plant at 0% load is adopted as a base model for prediction. Secondly, a static nonlinear neural network model has been created for a particular output channel, fuel gas pressure, to compensate its strong nonlinear behaviour observed in open-loop simulation. By linearizing the neural network model at each sampling time, the static nonlinear model provides certain adaptation to the linear base model. Noticeable performance improvement is observed when compared with pure linear model based predictive control

Nonlinear model predictive control using automatic differentiation

Although nonlinear model predictive control (NMPC) might be the best choice for a nonlinear plant, it is still not widely used. This is mainly due to the computational burden associated with solving online a set of nonlinear differential equations and a nonlinear dynamic optimization problem in real time. This thesis is concerned with strategies aimed at reducing the computational burden involved in different stages of the NMPC such as optimization problem, state estimation, and nonlinear model identification. A major part of the computational burden comes from function and derivative evaluations required in different parts of the NMPC algorithm. In this work, the problem is tackled using a recently introduced efficient tool, the automatic differentiation (AD). Using the AD tool, a function is evaluated together with all its partial derivative from the code defining the function with machine accuracy. A new NMPC algorithm based on nonlinear least square optimization is proposed. In a first–order method, the sensitivity equations are integrated using a linear formula while the AD tool is applied to get their values accurately. For higher order approximations, more terms of the Taylor expansion are used in the integration for which the AD is effectively used. As a result, the gradient of the cost function against control moves is accurately obtained so that the online nonlinear optimization can be efficiently solved. In many real control cases, the states are not measured and have to be estimated for each instance when a solution of the model equations is needed. A nonlinear extended version of the Kalman filter (EKF) is added to the NMPC algorithm for this purpose. The AD tool is used to calculate the required derivatives in the local linearization step of the filter automatically and accurately. Offset is another problem faced in NMPC. A new nonlinear integration is devised for this case to eliminate the offset from the output response. In this method, an integrated disturbance model is added to the process model input or output to correct the plant/model mismatch. The time response of the controller is also improved as a by–product. The proposed NMPC algorithm has been applied to an evaporation process and a two continuous stirred tank reactor (two–CSTR) process with satisfactory results to cope with large setpoint changes, unmeasured severe disturbances, and process/model mismatches. When the process equations are not known (black–box) or when these are too complicated to be used in the controller, modelling is needed to create an internal model for the controller. In this thesis, a continuous time recurrent neural network (CTRNN) in a state–space form is developed to be used in NMPC context. An efficient training algorithm for the proposed network is developed using AD tool. By automatically generating Taylor coefficients, the algorithm not only solves the differentiation equations of the network but also produces the sensitivity for the training problem. The same approach is also used to solve online the optimization problem of the NMPC. The proposed CTRNN and the predictive controller were tested on an evaporator and two–CSTR case studies. A comparison with other approaches shows that the new algorithm can considerably reduce network training time and improve solution accuracy. For a third case study, the ALSTOM gasifier, a NMPC via linearization algorithm is implemented to control the system. In this work a nonlinear state–space class Wiener model is used to identify the black–box model of the gasifier. A linear model of the plant at zero–load is adopted as a base model for prediction. Then, a feedforward neural network is created as the static gain for a particular output channel, fuel gas pressure, to compensate its strong nonlinear behavior observed in open–loop simulations. By linearizing the neural network at each sampling time, the static nonlinear gain provides certain adaptation to the linear base model. The AD tool is used here to linearize the neural network efficiently. Noticeable performance improvement is observed when compared with pure linear MPC. The controller was able to pass all tests specified in the benchmark problem at all load conditions.EThOS - Electronic Theses Online ServiceGBUnited Kingdo

Dynamics of Evanescently-Coupled Laser Pairs With Unequal Pumping: Analysis Using a Three-Variable Reduction of the Coupled Rate Equations

The five coupled rate equations used to describe laterally-coupled pairs of lasers with weak coupling and unequal pumping are reduced to a new system of three equations. This enables approximate closed-form steady-state solutions and explicit expressions for the boundaries between regions of stable and unstable dynamics to be found. The results of applying these approximations to specific cases of coupled laser pairs are shown to be in good agreement with results obtained from numerical solutions of the original set of five equations as well as earlier results from the literature. In addition the approximations based on the reduced set of equations allow a systematic investigation of the effects of material, device and operating conditions on trends and novel features in the dynamics of laterally-coupled laser pairs. The algebraic results give insight into trends with parameters without the need for extensive numerical computation and should therefore be of use in modelling two-element VCSEL arrays for numerous potential applications

Optically-pumped dilute nitride spin-VCSEL

We report the first room temperature optical spin-injection of a dilute nitride 1300 nm vertical-cavity surface-emitting laser (VCSEL) under continuous-wave optical pumping. We also present a novel experimental protocol for the investigation of optical spin-injection with a fiber setup. The experimental results indicate that the VCSEL polarization can be controlled by the pump polarization, and the measured behavior is in excellent agreement with theoretical predictions using the spin flip model. The ability to control the polarization of a long-wavelength VCSEL at room temperature emitting at the wavelength of 1.3 μm opens up a new exciting research avenue for novel uses in disparate fields of technology ranging from spintronics to optical telecommunication networks. © 2012 Optical Society of America

Spiking Behaviour in Laterally-Coupled Pairs of VCSELs With Applications in Neuromorphic Photonics

We report a theoretical study on laterally-coupled pairs of vertical-cavity surface-emitting lasers (VCSELs) operated under conditions that generate or suppress high-speed optical spiking regimes, and show their potential in exemplar functionalities for use in photonic neuromorphic computing systems. The VCSEL numerical analysis is based on a system of five coupled mode equations, which, for the case of weak coupling, are reduced to a set of three equations that predict the saddle-node stability boundary in terms of device parameters and operating conditions. These results guide numerical simulation to demonstrate multiple neuron-like dynamics, including single- and multiple-spike emission, spiking inhibition, and rebound spiking directly in the optical domain. Importantly, these behaviours are obtained at sub-nanosecond rates, hence multiple orders of magnitude faster than the millisecond timescales of biological neurons. The mechanisms responsible are explained by reference to appropriate phase portraits. The coupled VCSELs model is then used for demonstration of high-speed, all-optical digital-to-spiking encoding and for representation of digital image data using rate-coded spike trains

Simulated dynamics of optically pumped dilute nitride 1300 nm spin vertical-cavity surface-emitting lasers

The authors report a theoretical analysis of optically pumped 1300 nm dilute nitride spin-polarised vertical-cavity surface-emitting lasers (VCSELs) using the spin-flip model to determine the regions of stability and instability. The dependence of the output polarisation ellipticity on that of the pump is investigated, and the results are presented in twodimensional contour maps of the pump polarisation against the magnitude of the optical pump. Rich dynamics and various forms of oscillatory behaviour causing self-sustained oscillations in the polarisation of the spin-VCSEL subject to continuouswave pumping have been found because of the competition of the spin-flip processes and birefringence. The authors also reveal the importance of considering both the birefringence rate and the linewidth enhancement factor when engineering a device for high-frequency applications. A very good agreement is found with the experimental results reported by the authors' group. © The Institution of Engineering and Technology 2014

Nonlinear model predictive control for the ALSTOM gasifier.

In this work a nonlinear model predictive control based on Wiener model has been developed and used to control the ALSTOM gasifier. The 0% load condition was identified as the most difficult case to control among three operating conditions. A linear model of the plant at 0% load is adopted as a base model for prediction. A nonlinear static gain represented by a feedforward neural network was identified for a particular output channel—namely, fuel gas pressure, to compensate its strong nonlinear behaviour observed in open-loop simulations. By linearising the neural network at each sampling time, the static nonlinear model provides certain adaptation to the linear base model at all other load conditions. The resulting controller showed noticeable performance improvement when compared with pure linear model based predictive contr

Nonlinear model predictive control using automatic differentiation

Although nonlinear model predictive control (NMPC) might be the best choice for a nonlinear plant, it is still not widely used. This is mainly due to the computational burden associated with solving online a set of nonlinear differential equations and a nonlinear dynamic optimization problem in real time. This thesis is concerned with strategies aimed at reducing the computational burden involved in different stages of the NMPC such as optimization problem, state estimation, and nonlinear model identification. A major part of the computational burden comes from function and derivative evaluations required in different parts of the NMPC algorithm. In this work, the problem is tackled using a recently introduced efficient tool, the automatic differentiation (AD). Using the AD tool, a function is evaluated together with all its partial derivative from the code defining the function with machine accuracy. A new NMPC algorithm based on nonlinear least square optimization is proposed. In a first–order method, the sensitivity equations are integrated using a linear formula while the AD tool is applied to get their values accurately. For higher order approximations, more terms of the Taylor expansion are used in the integration for which the AD is effectively used. As a result, the gradient of the cost function against control moves is accurately obtained so that the online nonlinear optimization can be efficiently solved. In many real control cases, the states are not measured and have to be estimated for each instance when a solution of the model equations is needed. A nonlinear extended version of the Kalman filter (EKF) is added to the NMPC algorithm for this purpose. The AD tool is used to calculate the required derivatives in the local linearization step of the filter automatically and accurately. Offset is another problem faced in NMPC. A new nonlinear integration is devised for this case to eliminate the offset from the output response. In this method, an integrated disturbance model is added to the process model input or output to correct the plant/model mismatch. The time response of the controller is also improved as a by–product. The proposed NMPC algorithm has been applied to an evaporation process and a two continuous stirred tank reactor (two–CSTR) process with satisfactory results to cope with large setpoint changes, unmeasured severe disturbances, and process/model mismatches. When the process equations are not known (black–box) or when these are too complicated to be used in the controller, modelling is needed to create an internal model for the controller. In this thesis, a continuous time recurrent neural network (CTRNN) in a state–space form is developed to be used in NMPC context. An efficient training algorithm for the proposed network is developed using AD tool. By automatically generating Taylor coefficients, the algorithm not only solves the differentiation equations of the network but also produces the sensitivity for the training problem. The same approach is also used to solve online the optimization problem of the NMPC. The proposed CTRNN and the predictive controller were tested on an evaporator and two–CSTR case studies. A comparison with other approaches shows that the new algorithm can considerably reduce network training time and improve solution accuracy. For a third case study, the ALSTOM gasifier, a NMPC via linearization algorithm is implemented to control the system. In this work a nonlinear state–space class Wiener model is used to identify the black–box model of the gasifier. A linear model of the plant at zero–load is adopted as a base model for prediction. Then, a feedforward neural network is created as the static gain for a particular output channel, fuel gas pressure, to compensate its strong nonlinear behavior observed in open–loop simulations. By linearizing the neural network at each sampling time, the static nonlinear gain provides certain adaptation to the linear base model. The AD tool is used here to linearize the neural network efficiently. Noticeable performance improvement is observed when compared with pure linear MPC. The controller was able to pass all tests specified in the benchmark problem at all load conditions

Dynamic behaviour of VCSELs subject to optical injection with arbitrary polarization

We report novel theory and experiments for a 1550 nm VCSEL subject to different types of polarized optical injection. The theory combines the SFM with the bifurcation method to generate a new stability map in the plane of injection power and polarization angle. Very good agreement between theory and experiment is reported

Dynamic behaviour of spin vertical cavity surface emitting lasers

This research investigates the nonlinear dynamics and polarization properties of solitary and optically-injected spin-Vertical-Cavity Surface-Emitting Lasers (VCSELs). We report a first comprehensive theoretical analysis of optically-pumped spin-polarized VCSELs which combines the spin flip model (SFM) with both the Largest Lyapunov Exponent (LLE) and bifurcation analysis techniques to determine regions of stability and instability. The dependence of these regions on a wide range of fundamental device parameters is investigated and results are presented in a new form of contour maps. One aspect that this reveals is the importance of considering both the birefringence rate and the linewidth enhancement factor when engineering a device for high frequency applications. Also using the experimental characteristics of an optically pumped 1300 nm dilute nitride VCSEL to derive appropriate SFM parameters, we show very good agreement between simulation and experiment for the CW behaviour and stability. The SFM has been extended and generalized to allow for optical injection of arbitrary polarization. Measurements on conventional electrically-pumped 1550-nm VCSELs with different frequency spacing between the resonances of the orthogonal polarizations of the fundamental transverse mode have been used to estimate the model's parameters. Excellent agreement is found between experiment and theory for the stability and polarization properties of the optically-injected VCSELs. Finally, the results of theoretical investigations for optically-pumped spin- VCSELs subject to polarized optical injection have been presented. The new extended SFM is used in this study to show the effect of the optical injection on the steady-state characteristics, nonlinear dynamics and polarization of spin-VCSELs. New maps of nonlinear dynamics and output polarization have been generated using different values of device parameters and pumping power and ellipticity. Furthermore, controlling the circular polarization degree of a spin- VCSEL via the optical pumping or the external optical injection has been investigated and results from the two methods compared.EThOS - Electronic Theses Online ServiceGBUnited Kingdo