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At least 973 records · Page 54

Optimal SCR Control Using Data-Driven Models

We present an optimal control solution for the urea injection for a heavy-duty diesel (HDD) selective catalytic reduction (SCR). The approach taken here is useful beyond SCR and could be applied to any system where a control strategy is desired and input-output data is available. For example, the strategy could also be used for the diesel oxidation catalyst (DOC) system. In this paper, we identify and validate a one-step ahead Kalman state-space estimator for downstream NOx using the bench reactor data of an SCR core sample. The test data was acquired using a 2010 Cummins 6.7L ISB production engine with a 2010 Cummins production aftertreatment system. We used a surrogate HDD federal test procedure (FTP), developed at Michigan Technological University (MTU), which simulates the representative transients of the standard FTP cycle, but has less engine speed/load points. The identified state-space model is then used to develop a tunable cost function that simultaneously minimizes NOx emissions and urea usage. The cost function is quadratic and univariate, thus the minimum can be computed analytically. We show the performance of the closed-loop controller in using a reduced-order discrete SCR simulator developed at MTU. Our experiments with the surrogate HDD-FTP data show that the strategy developed in this paper can be used to identify performance bounds for urea dose controllers.

diesel, emmissions, control, environment, modeling↗

Integrated controls-structures optimization of a large space structure

General-purpose control and structural codes are applied to a large detailed structural model including objective and constraint functions derived from actual design specifications. The approach is to divide the problem into a controls optimization step, a structural optimization step, and a system level coordination step. The objective is to minimize mass and power consumption with constraints on vibration characteristics, strength, and damping. This decomposition and optimization approach significantly enhances the design of a structure based on the COFS-I Mast Flight System, which is selected as a demonstration problem.

Pasula, S. L.↗

Optimal periodic control for spacecraft pointing and attitude determination

A new approach to autonomous magnetic roll/yaw control of polar-orbiting, nadir-pointing momentum bias spacecraft is considered as the baseline attitude control system for the next Tiros series. It is shown that the roll/yaw dynamics with magnetic control are periodically time varying. An optimal periodic control law is then developed. The control design features a state estimator that estimates attitude, attitude rate, and environmental torque disturbances from Earth sensor and sun sensor measurements; no gyros are needed. The state estimator doubles as a dynamic attitude determination and prediction function. In addition to improved performance, the optimal controller allows a much smaller momentum bias than would otherwise be necessary. Simulation results are given.

Pittelkau, Mark E.↗

Stability-Constrained Learning for Frequency Regulation in Power Grids With Variable Inertia

The increasing penetration of converter-based renewable generation has resulted in faster frequency dynamics, and low and variable inertia. As a result, there is a need for frequency control methods that are able to stabilize a disturbance in the power system at timescales comparable to the fast converter dynamics. This paper proposes a combined linear and neural network controller for inverter-based primary frequency control that is stable at time-varying levels of inertia. We model the time-variance in inertia via a switched affine hybrid system model. We derive stability certificates for the proposed controller via a quadratic candidate Lyapunov function. We test the proposed control on a 12-bus 3-area test network, and compare its performance with a base case linear controller, optimized linear controller, and finite-horizon Linear Quadratic Regulator (LQR). Our proposed controller achieves faster mean settling time and over 50% reduction in average control cost across 100 inertia scenarios compared to the optimized linear controller. Unlike LQR which requires complete knowledge of the inertia trajectories and system dynamics over the entire control time horizon, our proposed controller is real-time tractable, and achieves comparable performance to LQR.

data-driven control↗

Results of an integrated structure/control law design sensitivity analysis

A design sensitivity analysis method for Linear Quadratic Cost, Gaussian (LQG) optimal control laws, which predicts change in the optimal control law due to changes in fixed problem parameters using analytical sensitivity equations is discussed. Numerical results of a design sensitivity analysis for a realistic aeroservoelastic aircraft example are presented. In this example, the sensitivity of the optimally controlled aircraft's response to various problem formulation and physical aircraft parameters is determined. These results are used to predict the aircraft's new optimally controlled response if the parameter was to have some other nominal value during the control law design process. The sensitivity results are validated by recomputing the optimal control law for discrete variations in parameters, computing the new actual aircraft response, and comparing with the predicted response. These results show an improvement in sensitivity accuracy for integrated design purposes over methods which do not include changes in the optimal control law. Use of the analytical LQG sensitivity expressions is also shown to be more efficient than finite difference methods for the computation of the equivalent sensitivity information.

Gilbert, Michael G.↗

Exploring quantum control landscapes: Topology, features, and optimization scaling

Quantum optimal control experiments and simulations have successfully manipulated the dynamics of systems ranging from atoms to biomolecules. Surprisingly, these collective works indicate that the effort (i.e., the number of algorithmic iterations) required to find an optimal control field appears to be essentially invariant to the complexity of the system. The present work explores this matter in a series of systematic optimizations of the state-to-state transition probability on model quantum systems with the number of states N ranging from 5 through 100. The optimizations occur over a landscape defined by the transition probability as a function of the control field. Previous theoretical studies on the topology of quantum control landscapes established that they should be free of suboptimal traps under reasonable physical conditions. The simulations in this work include nearly 5000 individual optimization test cases, all of which confirm this prediction by fully achieving optimal population transfer of at least 99.9% on careful attention to numerical procedures to ensure that the controls are free of constraints. Collectively, the simulation results additionally show invariance of required search effort to system dimension N. This behavior is rationalized in terms of the structural features of the underlying control landscape. The very attractive observed scaling with system complexity may be understood by considering the distance traveled on the control landscape during a search and the magnitude of the control landscape slope. Exceptions to this favorable scaling behavior can arise when the initial control field fluence is too large or when the target final state recedes from the initial state as N increases.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Optimal cooperative control synthesis of active displays

A technique is developed that is intended to provide a systematic approach to synthesizing display augmentation for optimal manual control in complex, closed-loop tasks. A cooperative control synthesis technique, previously developed to design pilot-optimal control augmentation for the plant, is extended to incorporate the simultaneous design of performance enhancing displays. The technique utilizes an optimal control model of the man in the loop. It is applied to the design of a quickening control law for a display and a simple K/s(2) plant, and then to an F-15 type aircraft in a multi-channel task. Utilizing the closed loop modeling and analysis procedures, the results from the display design algorithm are evaluated and an analytical validation is performed. Experimental validation is recommended for future efforts.

Garg, S.↗

Optimal cooperative control synthesis of active displays

A technique is developed that is intended to provide a systematic approach to synthesizing display augmentation for optimal manual control in complex, closed-loop tasks. A cooperative control synthesis technique, previously developed to design pilot-optimal control augmentation for the plant, is extended to incorporate the simultaneous design of performance enhancing displays. The technique utilizes an optimal control model of the man in the loop. It is applied to the design of a quickening control law for a display and a simple K/(s squared) plant, and then to an F-15 type aircraft in a multichannel task. Utilizing the closed-loop modeling and analysis procedures, the results from the display design algorithm are evaluated and an analytical validation is performed. Experimental validation is recommended for future efforts.

Gary, Sanjay↗

A homotopy algorithm for digital optimal projection control GASD-HADOC

The linear-quadratic-gaussian (LQG) compensator was developed to facilitate the design of control laws for multi-input, multi-output (MIMO) systems. The compensator is computed by solving two algebraic equations for which standard closed-loop solutions exist. Unfortunately, the minimal dimension of an LQG compensator is almost always equal to the dimension of the plant and can thus often violate practical implementation constraints on controller order. This deficiency is especially highlighted when considering control-design for high-order systems such as flexible space structures. This deficiency motivated the development of techniques that enable the design of optimal controllers whose dimension is less than that of the design plant. A homotopy approach based on the optimal projection equations that characterize the necessary conditions for optimal reduced-order control. Homotopy algorithms have global convergence properties and hence do not require that the initializing reduced-order controller be close to the optimal reduced-order controller to guarantee convergence. However, the homotopy algorithm previously developed for solving the optimal projection equations has sublinear convergence properties and the convergence slows at higher authority levels and may fail. A new homotopy algorithm for synthesizing optimal reduced-order controllers for discrete-time systems is described. Unlike the previous homotopy approach, the new algorithm is a gradient-based, parameter optimization formulation and was implemented in MATLAB. The results reported may offer the foundation for a reliable approach to optimal, reduced-order controller design.

Collins, Emmanuel G., Jr.↗

Two neural network algorithms for designing optimal terminal controllers with open final time

Multilayer neural networks, trained by the backpropagation through time algorithm (BPTT), have been used successfully as state-feedback controllers for nonlinear terminal control problems. Current BPTT techniques, however, are not able to deal systematically with open final-time situations such as minimum-time problems. Two approaches which extend BPTT to open final-time problems are presented. In the first, a neural network learns a mapping from initial-state to time-to-go. In the second, the optimal number of steps for each trial run is found using a line-search. Both methods are derived using Lagrange multiplier techniques. This theoretical framework is used to demonstrate that the derived algorithms are direct extensions of forward/backward sweep methods used in N-stage optimal control. The two algorithms are tested on a Zermelo problem and the resulting trajectories compare favorably to optimal control results.

Plumer, Edward S.↗

Neural Networks-Based Inverter Control: Modeling and Adaptive Optimization for Smart Distribution Networks

The optimal voltage control of inverter-based resources, especially under the high penetration of solar photovoltaics, is critical to the stability of the distribution power system. However, the computational complexity as well as the coordinated operation performance of the voltage control optimization in the distribution power system limits the real-time applications. To mitigate this issue, a model-free based adaptive optimal control scheme for the smart inverter is proposed to maximize the active power generation, minimize the power loss, and maintain the bus voltages in smart distribution networks. An inverter-based optimization model for coordinated operation is first established, considering the uncertainties of renewable power generation. Subsequently, by collecting the data and control strategies, the neural networks (NNs) based algorithm is proposed to efficiently predict the best possible control strategy. The main objective of this scheme is to accurately predict candidate optimal solutions with near-negligible feasibility and optimization gaps, with the advantage of avoiding complicated iteration-based numerical algorithms. Thereafter, the co-simulation among OpenDSS, MATLAB, and Python is set up to fully take advantage of the three individual software. Experiments are conducted based on different control parameter characteristics and structures of NNs. Finally, the results reveal that an average mean squared error of 0.013 and 1 ms response time are achieved, which is lower than some state-of-the-art methods.

42 ENGINEERING↗

Combined control-structure optimization

An approach for combined control-structure optimization keyed to enhancing early design trade-offs is outlined and illustrated by numerical examples. The approach employs a homotopic strategy and appears to be effective for generating families of designs that can be used in these early trade studies. Analytical results were obtained for classes of structure/control objectives with linear quadratic Gaussian (LQG) and linear quadratic regulator (LQR) costs. For these, researchers demonstrated that global optima can be computed for small values of the homotopy parameter. Conditions for local optima along the homotopy path were also given. Details of two numerical examples employing the LQR control cost were given showing variations of the optimal design variables along the homotopy path. The results of the second example suggest that introducing a second homotopy parameter relating the two parts of the control index in the LQG/LQR formulation might serve to enlarge the family of Pareto optima, but its effect on modifying the optimal structural shapes may be analogous to the original parameter lambda.

Salama, M.↗

On stochastic control and optimal measurement strategies

The control of stochastic dynamic systems is studied with particular emphasis on those which influence the quality or nature of the measurements which are made to effect control. Four main areas are discussed: (1) the meaning of stochastic optimality and the means by which dynamic programming may be applied to solve a combined control/measurement problem; (2) a technique by which it is possible to apply deterministic methods, specifically the minimum principle, to the study of stochastic problems; (3) the methods described are applied to linear systems with Gaussian disturbances to study the structure of the resulting control system; and (4) several applications are considered.

Kramer, L. C.↗

Satellite tracking by combined optimal estimation and control techniques.

Combined optimal estimation and control techniques are applied for the first time to satellite tracking systems. Both radio antenna and optical tracking systems of NASA are considered. The optimal estimation is accomplished using an extended Kalman filter resulting in an estimated state of the satellite and of the tracking system. This estimated state constitutes an input to the optimal controller. The optimal controller treats a linearized system with a quadratic performance index. The maximum principle is applied and a steady-state approximation to the resulting Riccati equation is obtained. A computer program, RATS, implementing this algorithm is described. A feasibility study of real-time implementation, tracking simulations, and parameter sensitivity studies are also reported.

Dressler, R. M.↗

A Stochastic Maximum Principle for a Stochastic Differential Game of a Mean-Field Type

We construct a stochastic maximum principle (SMP) which provides necessary conditions for the existence of Nash equilibria in a certain form of N-agent stochastic differential game (SDG) of a mean-field type. The information structure considered for the SDG is of a possible asymmetric and partial type. To prove our SMP we take an approach based on spike-variations and adjoint representation techniques, analogous to that of S. Peng (SIAM J. Control Optim. 28(4):966-979, 1990) in the optimal stochastic control context. In our proof we apply adjoint representation procedures at three points. The first-order adjoint processes are defined as solutions to certain mean-field backward stochastic differential equations, and second-order adjoint processes of a first type are defined as solutions to certain backward stochastic differential equations. Second-order adjoint processes of a second type are defined as solutions of certain backward stochastic equations of a type that we introduce in this paper, and which we term conditional mean-field backward stochastic differential equations. From the resulting representations, we show that the terms relating to these second-order adjoint processes of the second type are of an order such that they do not appear in our final SMP equations. A comparable situation exists in an article by R. Buckdahn, B. Djehiche, and J. Li (Appl. Math. Optim. 64(2):197-216, 2011) that constructs a SMP for a mean-field type optimal stochastic control problem; however, the approach we take of using these second-order adjoint processes of a second type to deal with the type of terms that we refer to as the second form of quadratic-type terms represents an alternative to a development, to our setting, of the approach used in their article for their analogous type of term.

97 MATHEMATICS AND COMPUTING↗

Design, Optimization, and Control of Floating Offshore Wind Farms for Optimal Energy Production (Final report)

The uncertainty and irregularity of ocean waves and the ocean environment is a major factor in the development of commercial scale floating wind turbines as the operation of floating structures in such an environment can lead to irregular and unpredictable loading, fatigue, and ultimately a reduction in the operational life of the turbine system which affects energy production over the lifetime of the turbine. Control solutions that can limit float motions and mitigate stressful events on the structure become essential for extending lifetime and limiting the operational uncertainty of a floating wind turbine. Digital twins are computational replicas of physical systems that operate in parallel with the operation of the physical system. Given advanced knowledge of a systems input, digital twins have the ability to predict the behavior of a system in advance, which can be valuable in the control of that system. In this project, we developed and assessed potential digital twin models developed in house and openly available (OpenFast) for use in the real time control of the six degree of freedom response motions of a floating wind turbine in ocean waves. Coupling these models with near-field real time irregular sea surface (wve) measurement/sensings and prediction models, we used the digital twin to predict how the floating turbine will respond to the incoming waves. Applying this information to a motion control system of the float, one can limit and control float motions to prevent undesirable loading events/large angular motions, thus increasing system life and ultimately contributing to optimizing energy production. Due to the computational intensity of operating a digital twin in real time, we investigated the use of artificial intelligence techniques to speed-up the processes of the digital twin, as well as the wave reconstruction/prediction models. Model tank testing at the University of Rhode Island and University of Maine both validated and demonstrated the developed techniques on simple float geometries and a scale model of the NREL 15 MW reference turbine.

17 WIND ENERGY↗

Extended State Observer-Based Robust Model Predictive Velocity Control for Permanent Magnet Synchronous Motor

This article proposes an extended state observer based robust model predictive velocity control to decrease system prediction error under parameter uncertainties for permanent magnet synchronous motor (PMSM). We develop a new PMSM model that consists of velocity and acceleration to lump the system information and an external disturbance into a disturbance. The extended state observer (ESO) is designed to estimate the velocity, acceleration, and disturbance. By estimating the state variables and disturbance using the ESO, the model predictive control (MPC) finds the optimal control input by predicting future system behavior. Additionally, the direct current controller is designed so that the direct current converges to zero. Because the proposed method is not designed based on the cascade structure from the viewpoint of velocity control, the optimization control for the velocity and currents can be defined. Thus, the proposed method is robust against external disturbances and parameter uncertainties owing to feedback linearization, state feedback, and ESO-based MPC using the acceleration PMSM model. The proposed control algorithm was experimentally verified and it showed improved velocity tracking performance compared with ESO-based MPC using the conventional PMSM model.

42 ENGINEERING↗