Publications
197 results found
Thammawichai M, Kerrigan EC, 2017, Energy-efficient real-time scheduling for two-type heterogeneous multiprocessors, Real-Time Systems, Vol: 54, Pages: 132-165, ISSN: 0922-6443
We propose three novel mathematical optimization formulations that solve the same two-type heterogeneous multiprocessor scheduling problem for a real-time taskset with hard constraints. Our formulations are based on a global scheduling scheme and a fluid model. The first formulation is a mixed-integer nonlinear program, since the scheduling problem is intuitively considered as an assignment problem. However, by changing the scheduling problem to first determine a task workload partition and then to find the execution order of all tasks, the computation time can be significantly reduced. Specifically, the workload partitioning problem can be formulated as a continuous nonlinear program for a system with continuous operating frequency, and as a continuous linear program for a practical system with a discrete speed level set. The latter problem can therefore be solved by an interior point method to any accuracy in polynomial time. The task ordering problem can be solved by an algorithm with a complexity that is linear in the total number of tasks. The work is evaluated against existing global energy/feasibility optimal workload allocation formulations. The results illustrate that our algorithms are both feasibility optimal and energy optimal for both implicit and constrained deadline tasksets. Specifically, our algorithm can achieve up to 40% energy saving for some simulated tasksets with constrained deadlines. The benefit of our formulation compared with existing work is that our algorithms can solve a more general class of scheduling problems due to incorporating a scheduling dynamic model in the formulations and allowing for a time-varying speed profile.
Cantoni M, Farokhi F, Kerrigan EC, et al., 2017, Structured computation of optimal controls for constrained cascade systems, International Journal of Control, Vol: 93, Pages: 30-39, ISSN: 0020-7179
Constrained finite-horizon linear-quadratic optimal control problems are studied within the context of discrete-time dynamics that arise from the series interconnec- tion of subsystems. A structured algorithm is devised for computing the Newton-like steps of primal-dual interior-point methods for solving a particular re-formulation of the problem as a quadratic program. This algorithm has the following properties: (i) the computation cost scales linearly in the number of subsystems along the cascade; and (ii) the computations can be distributed across a linear proces- sor network, with localized problem data dependencies between the processor nodes and low communication overhead. The computation cost of the approach, which is based on a fixed permutation of the primal and dual variables, scales cubically in the time horizon of the original optimal control problem. Limitations in these terms are explored as part of a numerical example. This example involves application of the main results to model data for the cascade dynamics of an automated irrigation channel in particular.
Shukla H, Khusainov B, Kerrigan EC, et al., 2017, Software and hardware code generation for predictive control using splitting methods, IFAC World Congress 2017, Publisher: IFAC / Elsevier, Pages: 14386-14391
This paper presents SPLIT, a C code generation tool for Model Predictive Control (MPC) based on operator splitting methods. In contrast to existing code generation packages, SPLIT is capable of generating both software and hardware-oriented C code to allow quick prototyping of optimization algorithms on conventional CPUs and field-programmable gate arrays (FPGAs). A Matlab interface is provided for compatibility with existing commercial and open-source software packages. A numerical study compares software, hardware and heterogeneous implementations of splitting methods and investigates MPC design trade-offs. For the considered testcases the reported speedup of hardware implementations over software realizations is 3x to 11x.
Khusainov B, Kerrigan EC, Suardi A, et al., 2017, Nonlinear predictive control on a heterogeneous computing platform, IFAC World Congress 2017, Publisher: IFAC / Elsevier, Pages: 11877-11882
Nonlinear Model Predictive Control (NMPC) is an advanced control technique that often relies on computationally demanding optimization and integration algorithms. This paper proposes and investigates a heterogeneous hardware implementation of an NMPC controller based on an interior point algorithm. The proposed implementation provides flexibility of splitting the workload between a general-purpose CPU with a fixed architecture and a field-programmable gate array (FPGA) to trade off contradicting design objectives, namely performance and computational resource usage. A new way of exploiting the structure of the Karush-Kuhn-Tucker (KKT) matrix yields significant memory savings, which is crucial for reconfigurable hardware. For the considered case study, a 10x memory savings compared to existing approaches and a 10x speedup over a software implementation are reported. The proposed implementation can be tested from Matlab using a new release of the Protoip software tool, which is another contribution of the paper. Protoip abstracts many low-level details of heterogeneous hardware programming and allows quick prototyping and processor-in-the-loop verification of heterogeneous hardware implementations.
Bachtiar V, Manzie C, Kerrigan EC, 2017, Nonlinear model-predictive integrated missile control and Its multiobjective Tuning, Journal of Guidance Control and Dynamics, Vol: 40, Pages: 2961-2970, ISSN: 1533-3884
Ge M, Kerrigan EC, 2017, Noise covariance identification for nonlinear systems using expectation maximization and moving horizon estimation, Automatica, Vol: 77, Pages: 336-343, ISSN: 0005-1098
In order to estimate states from a noise-driven state space system, the state estimator requires a priori knowledge of both process and output noise covariances. Unfortunately, noise statistics are usually unknown and have to be determined from output measurements. Current expectation maximization (EM) based algorithms for estimating noise covariances for nonlinear systems assume the number of additive process and output noise signals are the same as the number of states and outputs, respectively. However, in some applications, the number of additive process noises could be less than the number of states. In this paper, a more general nonlinear system is considered by allowing the number of process and output noises to be smaller or equal to the number of states and outputs, respectively. In order to estimate noise covariances, a semi-definite programming solver is applied, since an analytical solution is no longer easy to obtain. The expectation step in current EM algorithms rely on state estimates from the extended Kalman filter (EKF) or smoother. However, the instability and divergence problems of the EKF could cause the EM algorithm to converge to a local optimum that is far away from true values. We use moving horizon estimation instead of the EKF/smoother so that the accuracy of the covariance estimation in nonlinear systems can be significantly improved.
Picciau A, Inggs G, Wickerson J, et al., 2017, Balancing locality and concurrency: solving sparse triangular systems on GPUs, 23rd IEEE International Conference on High Peformance Computing, Data, and Analytics (HiPC), Publisher: IEEE, Pages: 183-192
Many numerical optimisation problems rely onfast algorithms for solving sparse triangular systems of linearequations (STLs). To accelerate the solution of such equations,two types of approaches have been used: on GPUs, concurrencyhas been prioritised to the disadvantage of data locality, whileon multi-core CPUs, data locality has been prioritised to thedisadvantage of concurrency.In this paper, we discuss the interaction between data localityand concurrency in the solution of STLs on GPUs, and we presenta new algorithm that balances both. We demonstrate empiricallythat, subject to there being enough concurrency available in theinput matrix, our algorithm outperforms Nvidia’s concurrencyprioritisingCUSPARSE algorithm for GPUs. Experimental resultsshow a maximum speedup of 5.8-fold.Our solution algorithm, which we have implemented inOpenCL, requires a pre-processing phase that partitions thegraph associated with the input matrix into sub-graphs, whosedata can be stored in low-latency local memories. This preliminaryanalysis phase is expensive, but because it depends onlyon the input matrix, its cost can be amortised when solving formany different right-hand sides.
Khusainov B, Kerrigan EC, Constantinides GA, 2017, Multi-objective Co-design for Model Predictive Control with an FPGA, European Control Conference 16, Publisher: IEEE, Pages: 110-115
In order to achieve the best possible performanceof a model predictive controller (MPC) for a given set ofresources, the software algorithm and computational platformhave to be designed simultaneously. Moreover, in practicalapplications the controller design problem has a multi-objectivenature: performance is traded off against computational hardwareresource usage, namely time, energy and space. Thispaper proposes formulating an MPC design problem as a multiobjectiveoptimization (MOO) problem in order to explore thedesign trade-offs in a systematic way.Since the design objectives in the resulting MOO problem areexpensive to evaluate, i.e. evaluation requires time consumingsimulations, most of the classical and evolutionary MOOalgorithms cannot be employed for this class of design problems.For this reason a practical MOO algorithm that can deal withexpensive-to-evaluate functions is presented. The algorithm isbased on Kriging and the hypervolume criterion that wasrecently proposed in the expensive optimization literature. Anumerical example for a fast gradient-based controller designshows that the proposed approach can efficiently exploreoptimal performance-resource trade-offs.
Ge M, Kerrigan EC, 2016, Relations between Full Information and Kalman-Based Estimation, 55th IEEE Conference on Decision and Control, Publisher: IEEE
For nonlinear state space systems with additivenoises, sometimes the number of process noise signals couldbe less than the dimension of the state space. In order toimprove the accuracy and stability of nonlinear state estimation,this paper provides for the first time the derivation of thefull information estimator (FIE) for such nonlinear systems.We verify our derivation of the FIE by firstly proving theunbiasedness and minimum-variance of the FIE for linear timevarying (LTV) systems, then showing the equivalence betweenthe Kalman filter/smoother and the FIE for LTV systems.Finally, we prove that the FIE will provide more accurate stateestimates than the extended Kalman filter (EKF) and smoother(EKS) for nonlinear systems.
Thammawichai M, Kerrigan EC, 2016, Feedback Scheduling for Energy-Efficient Real-Time Homogeneous Multiprocessor Systems, 55th IEEE Conference on Decision and Control, Publisher: IEEE
Real-time scheduling algorithms proposed in theliterature are often based on worst-case estimates of taskparameters and the performance of an open-loop scheme cantherefore be poor. To improve on such a situation, one caninstead apply a closed-loop scheme, where feedback is exploitedto dynamically adjust the system parameters at run-time. Wepropose an optimal control framework that takes advantageof feeding back information of finished tasks to solve a realtimemultiprocessor scheduling problem with uncertainty intask execution times, with the objective of minimizing thetotal energy consumption. Specifically, we propose a linearprogramming-based algorithm to solve a workload partitioningproblem and adopt McNaughton’s wrap around algorithmto find the task execution order. Simulation results for aPowerPC 405LP and an XScale processor illustrate that ourfeedback scheduling algorithm can result in an energy savingof approximately 40% compared to an open-loop method.
Ge M, Kerrigan EC, 2016, Short-term ocean wave forecasting using an autoregressive moving average model, Control 2016 - 11th International Conference on Control, Publisher: IEEE
In order to predict future observations of a noisedrivensystem, we have to find a model that exactly or atleast approximately describes the behavior of the system sothat the current system state can be recovered from pastobservations. However, sometimes it is very difficult to modela system accurately, such as real ocean waves. It is thereforeparticularly interesting to analyze ocean wave properties inthe time-domain using autoregressive moving average (ARMA)models. Two ARMA/AR based models and their equivalent statespace representations will be used for predicting future oceanwave elevations, where unknown parameters will be determinedusing linear least squares and auto-covariance least squaresalgorithms. Compared to existing wave prediction methods, inthis paper (i) an ARMA model is used to enhance the predictionperformance, (ii) noise covariances in the ARMA/AR model arecomputed rather than guessed and (iii) we show that, in practice,low pass filtering of historical wave data does not improve theforecasting results.
Lee KW, Moase W, Ooi A, et al., 2016, Optimization Framework for Codesign of Controlled Aerodynamic Systems, AIAA Journal, Vol: 54, Pages: 3149-3159, ISSN: 1533-385X
Optimization studies of dynamic systems using high-fidelity numerical models necessitate a tradeoff between fidelity and the total computational time required during design. A gradient-based optimization framework is proposed for the aerodynamic shape and controller design of aerodynamic systems using computationally intensive high-fidelity models. Subject to some general properties, the framework offers flexibility in the types of simulation models used and provides guarantees regarding closeness to an optimal design. A nested optimization loop that allows for the partitioning of controller and plant architecture is implemented. The proposed framework exploits time-scale properties of the dynamic system model, closeness properties of partially converged iterative solutions of computational fluid dynamics models, and the continuous adjoint method. It is shown that combining these methods can improve the total computational time relative to finite differencing. An example of optimizing the aerodynamic body and control gains of a tail-fin controlled supersonic missile is presented.
Ge M, Kerrigan EC, 2016, Noise Covariance Identification for Time-varying and Nonlinear Systems, International Journal of Control, Vol: 90, Pages: 1903-1915, ISSN: 1366-5820
Kalman-based state estimators assume a priori knowledge of the covariance matrices of the process and observation noise. However, in most practical situations, noise statistics and initial conditions are often unknown and need to be estimated from measurement data. This paper presents an auto-covariance least-squares-based algorithm for noise and initial state error covariance estimation of large-scale linear time-varying (LTV) and nonlinear systems. Compared to existing auto-covariance least-squares based-algorithms, our method does not involve any approximations for LTV systems, has fewer parameters to determine and is more memory/computationally efficient for large-scale systems. For nonlinear systems, our algorithm uses full information estimation/moving horizon estimation instead of the extended Kalman filter, so that the stability and accuracy of noise covariance estimation for nonlinear systems can be guaranteed or improved, respectively.
Cantoni M, Farokhi F, Kerrigan EC, et al., 2016, A scalable QP solver for optimal control of cascades with constraints, Australian Control Conference
Bachtiar V, Manzie C, Moase WH, et al., 2016, Analytical results for the multi-objective design of model-predictive control, Control Engineering Practice, Vol: 56, Pages: 1-12, ISSN: 0967-0661
In model-predictive control (MPC), achieving the best closed-loop performance under a given computational capacity is the underlying design consideration. This paper analyzes the MPC tuning problem with control performance and required computational capacity as competing design objectives. The proposed multi-objective design of MPC (MOD-MPC) approach extends current methods that treat control performance and the computational capacity separately – often with the latter as a fixed constraint – which requires the implementation hardware to be known a priori. The proposed approach focuses on the tuning of structural MPC parameters, namely sampling time and prediction horizon length, to produce a set of optimal choices available to the practitioner. The posed design problem is then analyzed to reveal key properties, including smoothness of the design objectives and parameter bounds, and establish certain validated guarantees. Founded on these properties, necessary and sufficient conditions for an effective and efficient optimizer are presented, leading to a specialized multi-objective optimizer for the MOD-MPC being proposed. Finally, two real-world control problems are used to illustrate the results of the tuning approach and importance of the developed conditions for an effective optimizer of the MOD-MPC problem.
Kerrigan EC, Khusainov B, Constantinides GA, 2016, What Is Different about Embedded Optimization?, European Control Conference (ECC), Publisher: IEEE, Pages: 600-600
Suardi A, Longo S, Kerrigan EC, et al., 2015, Explicit MPC: hard constraint satisfaction under low precision arithmetic, Control Engineering Practice, Vol: 47, Pages: 60-69, ISSN: 1873-6939
MPC is becoming increasingly implemented on embedded systems, where low precision computation is preferred either to reduce costs, speedup execution or reduce power consumption. However, in a low precision implementation, constraint satisfaction cannot be guaranteed. To enforce constraint satisfaction under numerical errors, we adopt tools from forward error analysis to compute an error bound on the output of the embedded controller. We treat this error as a state disturbance and use it to inform the design of a constraint-tightening robust controller. The technique is validated via a practical implementation on an FPGA evaluation board.
Kerrigan EC, Constantinides GA, Suardi A, et al., 2015, Computer Architectures to Close the Loop in Real-time Optimization, 54th IEEE Conference on Decision and Control, Publisher: IEEE, Pages: 4597-4611
Many modern control, automation, signal processing and machine learning applications rely on solving a sequence of optimization problems, which are updated with measurements of a real system that evolves in time. The solutions of each of these optimization problems are then used to make decisions, which may be followed by changing some parameters of the physical system, thereby resulting in a feedback loop between the computing and the physical system. Real-time optimization is not the same as `fast' optimization, due to the fact that the computation is affected by an uncertain system that evolves in time. The suitability of a design should therefore not be judged from the optimality of a single optimization problem, but based on the evolution of the entire cyber-physical system. The algorithms and hardware used for solving a single optimization problem in the office might therefore be far from ideal when solving a sequence of real-time optimization problems. Instead of there being a single, optimal design, one has to trade-off a number of objectives, including performance, robustness, energy usage, size and cost. We therefore provide here a tutorial introduction to some of the questions and implementation issues that arise in real-time optimization applications. We will concentrate on some of the decisions that have to be made when designing the computing architecture and algorithm and argue that the choice of one informs the other.
Palma V, Suardi A, Kerrigan EC, 2015, Sensitivity-based multistep MPC for embedded systems, 5th IFAC Conference on Nonlinear Model Predictive Control 2015 (NMPC'15), Publisher: Elsevier, Pages: 360-365, ISSN: 1474-6670
In model predictive control (MPC), an optimization problem is solved every sampling instant to determine an optimal control for a physical system. We aim to accelerate this procedure for fast systems applications and address the challenge of implementing the resulting MPC scheme on an embedded system with limited computing power. We present the sensitivity-based multistep MPC, a strategy which considerably reduces the computing requirements in terms of floating point operations (FLOPs), compared to a standard MPC formulation, while fulfilling closed- loop performance expectations. We illustrate by applying the method to a DC-DC converter model and show how a designer can optimally trade off closed-loop performance considerations with computing requirements in order to fit the controller into a resource-constrained embedded system.
Kerrigan EC, 2015, Feedback and time are essential for the optimal control of computing systems, 5th IFAC Conference on Nonlinear Model Predictive Control, Publisher: Elsevier, Pages: 380-387, ISSN: 1474-6670
The performance, reliability, cost, size and energy usage of computing systems can be improved by one or more orders of magnitude by the systematic use of modern control and optimization methods. Computing systems rely on the use of feedback algorithms to schedule tasks, data and resources, but the models that are used to design these algorithms are validated using open-loop metrics. By using closed-loop metrics instead, such as the gap metric developed in the control community, it should be possible to develop improved scheduling algorithms and computing systems that have not been over-engineered. Furthermore, scheduling problems are most naturally formulated as constraint satisfaction or mathematical optimization problems, but these are seldom implemented using state of the art numerical methods, nor do they explicitly take into account the fact that the scheduling problem itself takes time to solve. This paper makes the case that recent results in real-time model predictive control, where optimization problems are solved in order to control a process that evolves in time, are likely to form the basis of scheduling algorithms of the future. We therefore outline some of the research problems and opportunities that could arise by explicitly considering feedback and time when designing optimal scheduling algorithms for computing systems.
Suardi A, Kerrigan EC, Constantinides GA, 2015, Fast FPGA prototyping toolbox for embedded optimization, European Control Conference (ECC), Publisher: IEEE, Pages: 2589-2594
Traditionally compute-intensive optimisation algorithms have been implemented on CPU based machines, primarily in order to reduce development time, but sacrificing computing speed and energy consumption. However, recent advancements in FPGA technologies are making the design effort comparable to that of CPUs, making them an increasingly viable option. This paper presents FPGA IP prototyping toolbox (PROTOIP), which is an Open Source framework conceived to enable researchers and engineers to design, validate and prototype algorithms quickly on FPGA platforms. Abstracting many low-level FPGA design details, PROTOIP provides custom templates, scripts, example designs and tutorials specifically tailored for embedded optimization applications.
Thammawichai M, Kerrigan EC, 2015, Energy-efficient scheduling for homogeneous multiprocessor systems, Publisher: arXiv
We present a number of novel algorithms, based on mathematical optimizationformulations, in order to solve a homogeneous multiprocessor schedulingproblem, while minimizing the total energy consumption. In particular, for asystem with a discrete speed set, we propose solving a tractable linearprogram. Our formulations are based on a fluid model and a global schedulingscheme, i.e. tasks are allowed to migrate between processors. The new methodsare compared with three global energy/feasibility optimal workload allocationformulations. Simulation results illustrate that our methods achieve bothfeasibility and energy optimality and outperform existing methods forconstrained deadline tasksets. Specifically, the results provided by ouralgorithm can achieve up to an 80% saving compared to an algorithm without afrequency scaling scheme and up to 70% saving compared to a constant frequencyscaling scheme for some simulated tasksets. Another benefit is that ouralgorithms can solve the scheduling problem in one step instead of using arecursive scheme. Moreover, our formulations can solve a more general class ofscheduling problems, i.e. any periodic real-time taskset with arbitrarydeadline. Lastly, our algorithms can be applied to both online and offlinescheduling schemes.
Bachtiar V, Kerrigan EC, Moase WH, et al., 2015, Continuity and Monotonicity of the MPC Value Function with respect to Sampling Time and Prediction Horizon, Automatica, Vol: 63, Pages: 330-337, ISSN: 1873-2836
The digital implementation of model predictive control (MPC) is fundamentally governed by two design parameters; samplingtime and prediction horizon. Knowledge of the properties of the value function with respect to the parameters can be used fordeveloping optimisation tools to find optimal system designs. In particular, these properties are continuity and monotonicity.This paper presents analytical results to reveal the smoothness properties of the MPC value function in open- and closed-loopfor constrained linear systems. Continuity of the value function and its differentiability for a given number of prediction stepsare proven mathematically and confirmed with numerical results. Non-monotonicity is shown from the ensuing numericalinvestigation. It is shown that increasing sampling rate and/or prediction horizon does not always lead to an improved closedloopperformance, particularly at faster sampling rates.
Jones CN, Kerrigan E, 2015, Predictive control for embedded systems, OPTIMAL CONTROL APPLICATIONS & METHODS, Vol: 36, Pages: 583-584, ISSN: 0143-2087
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Feng Z, Kerrigan EC, 2015, Latching-Declutching Control of Wave Energy Converters Using Derivative-Free Optimization, IEEE Transactions on Sustainable Energy, Vol: 6, Pages: 773-780, ISSN: 1949-3029
We consider predictive control of a wave energy converter(WEC) that can switch between three modes: 1) powergeneration; 2) declutched with no power generation; or 3) latchedwith zero velocity. We propose a formulation that turns the optimalcontrol problem into a small dimensional discrete optimizationproblem, where the only decision variables are bounds onthe latching time and power take-off (PTO) time, whereas theobjective function is computed from the trajectory of a hybridsystem with linear dynamics in each sample interval. The optimizationproblem is solved using a novel derivative-free algorithmthat exploits the quantization of the decision variables in orderto reduce the number of function evaluations. Two closed-loopformulations are also studied within a receding horizon implementation:the first one uses past wave information and can double theenergy generation compared to the uncontrolled case, while thesecond formulation uses predictions of future waves and is able toresult in a further increase in energy generation. The benefits ofcodesigning the physical system and controller is compared to thesequential approach of first optimizing the physical system withoutcontrol, followed by controller design.
Jones BL, Heins PH, Kerrigan EC, et al., 2015, Modelling for robust feedback control of fluid flows, Journal of Fluid Mechanics, Vol: 769, Pages: 687-722, ISSN: 0022-1120
This paper addresses the problem of designing low-order and linear robust feedback controllers that provide a priori guarantees with respect to stability and performance when applied to a fluid flow. This is challenging, since whilst many flows are governed by a set of nonlinear, partial differential–algebraic equations (the Navier–Stokes equations), the majority of established control system design assumes models of much greater simplicity, in that they are: firstly, linear; secondly, described by ordinary differential equations (ODEs); and thirdly, finite-dimensional. With this in mind, we present a set of techniques that enables the disparity between such models and the underlying flow system to be quantified in a fashion that informs the subsequent design of feedback flow controllers, specifically those based on the H∞ loop-shaping approach. Highlights include the application of a model refinement technique as a means of obtaining low-order models with an associated bound that quantifies the closed-loop degradation incurred by using such finite-dimensional approximations of the underlying flow. In addition, we demonstrate how the influence of the nonlinearity of the flow can be attenuated by a linear feedback controller that employs high loop gain over a select frequency range, and offer an explanation for this in terms of Landahl’s theory of sheared turbulence. To illustrate the application of these techniques, an H∞ loop-shaping controller is designed and applied to the problem of reducing perturbation wall shear stress in plane channel flow. Direct numerical simulation (DNS) results demonstrate robust attenuation of the perturbation shear stresses across a wide range of Reynolds numbers with a single linear controller.
Bachtiar V, Kerrigan EC, Moase WH, et al., 2015, Smoothness Properties of the MPC Value Function with respect to Sampling Time and Prediction Horizon, 10th Asian Control Conference (ASCC)
Liu Y, Van Schijndel J, Longo S, et al., 2015, UAV Energy Extraction With Incomplete Atmospheric Data Using MPC, IEEE TRANSACTIONS ON AEROSPACE AND ELECTRONIC SYSTEMS, Vol: 51, Pages: 1203-1215, ISSN: 0018-9251
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- Citations: 12
Ng BF, Palacios R, Kerrigan EC, et al., 2015, Aerodynamic load control in horizontal axis wind turbines with combined aeroelastic tailoring and trailing-edge flaps, Wind Energy, Vol: 19, Pages: 243-263, ISSN: 1095-4244
This paper presents an aeroservoelastic modeling approach to investigate dynamic load alleviation in large wind turbines with composite blades and trailing-edge aerodynamic surfaces. The tower and rotating blades are modeled using geometrically non-linear composite beams and linearized about reference rotating conditions with potentially arbitrarily large structural displacements. The aerodynamics of the rotor are represented using a linearized unsteady vortex lattice method, and the resulting aeroelastic system is written in a state-space description that is both convenient for model reductions and control design. A linear model of a single blade is then used to design an inline image regulator, capable of providing load reductions of up to 13% in closed loop on the full wind turbine non-linear aeroelastic model. When combined with passive load alleviation through aeroelastic tailoring, dynamic loads can be further reduced to 35%. While the separate use of active flap controls and passive mechanisms for load alleviation has been well-studied, an integrated approach involving the two mechanisms has yet to be fully explored and is the focus of this paper. Finally, the possibility of exploiting torsional stiffness for active load alleviation on turbine blades is also considered.
Jerez JL, Constantinides GA, Kerrigan EC, 2015, A Low Complexity Scaling Method for the Lanczos Kernel in Fixed-Point Arithmetic, IEEE TRANSACTIONS ON COMPUTERS, Vol: 64, Pages: 303-315, ISSN: 0018-9340
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- Citations: 9
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