Linear Quadratic Gaussian Regulator Research Articles

Output Feedback Stabilization of Doubly Fed Induction Generator Wind Turbines under Event-Triggered Implementations

The robust stabilization of doubly fed induction generators in wind turbines against external disturbances is considered in this study. It is assumed that the angular speeds of wind turbines can only be measured and sent to the controller in a discrete-time fashion over a network. To generate the sampling times, three different triggering schemes were developed: time-triggering, static event-triggering, and dynamic event-triggering mechanisms; moreover, performance comparisons were conducted between such approaches. The design methodology is based on emulation, such that the plant is first stabilized in continuous-time where a robust feedback law is constructed based on the linear quadratic Gaussian regulator (LQG) approach. Then, the impact of the network is taken into account, and an event-triggering mechanism is built so that closed-loop stability is maintained and the Zeno phenomenon is avoided by using temporal regularization. The necessary stability constraints are framed as a linear matrix inequality, and the whole system is modeled as a hybrid dynamical system. A numerical simulation is used to demonstrate the effectiveness of the control strategy. The results show that the event-triggering mechanisms achieve a significant reduction of around 50% in transmissions compared to periodic sampling. Moreover, numerical comparisons with existing approaches show that the proposed approach provides better performance in terms of the stability guarantee and number of transmissions.

Integral linear quadratic Gaussian regulator subject to unknown inputs: application in photovoltaic systems

Integral linear quadratic Gaussian regulator subject to unknown inputs: application in photovoltaic systems

Linear feedback control of spreading dynamics in stochastic nonlinear network models: epileptic seizures.

The development of models and approaches for controlling the spreading dynamics of epileptic seizures is an essential step towards new therapies for people with pharmacologically resistant epilepsy. Beyond resective neurosurgery, in which epileptogenic zones (EZs) are the target of surgery, closed-loop control based on intracranial electrical stimulation, applied at the very early stage of seizure evolution, has been the main alternative, e.g. the RNS system from NeuroPace (Mountain View, CA). In this approach the electrical stimulation is delivered to target brain areas after detection of seizure initiation in the EZ. Here, we examined, on model simulations, some of the closed-loop control aspects of the problem. Seizure dynamics and spread are typically modeled with highly nonlinear dynamics on complex brain networks. Despite the nonlinearity and complexity, currently available optimal feedback control approaches are mostly based on linear approximations. Alternative machine learning control approaches might require amounts of data beyond what is commonly available in the intended application. We thus examined how standard linear feedback control approaches perform when applied to nonlinear models of neural dynamics of seizure generation and spread. In particular, we considered patient-specific epileptor network models for seizure onset and spread. The models incorporate network connectivity derived from (diffusion MRI) white-matter tractography, have been shown to capture the qualitative dynamics of epileptic seizures and can be fit to patient data. For control, we considered simple linear quadratic Gaussian (LQG) regulators. The LQG control was based on a discrete-time state-space model derived from the linearization of the patient-specific epileptor network model around a stable fixed point in the regime of preictal dynamics. We show in simulations that LQG regulators acting on the EZ node during the initial seizure period tend to be unstable. The LQG solution for the control law in this case leads to global feedback to the EZ-node actuator. However, if the LQG solution is constrained to depend on only local feedback originating from the EZ node itself, the controller is stable. In this case, we demonstrate that localized LQG can easily terminate the seizure at the early stage and prevent spread. In the context of optimal feedback control based on linear approximations, our results point to the need for investigating in more detail feedback localization and additional relevant control targets beyond epileptogenic zones.

Linear Quadratic Gaussian with noise signals for lateral and longitudinal of F-16

Today, classical control methods are still widely used because of their excellent performance in a working enviroment with noise signals. Besides, they are suitble for functiions of the system : operations to control a machine are more flexible, easy to perform, less unwanted risks occur, the efficiency of controlling a system better. In the early years of the 21st century, traditional algorithms still promote their effects. Besides the traditional control methods, the author has applied more moderm and smarter algorithms such as adjusting Linear Quadratic Gaussian (LQG) to control a system on the ground or a system moving in the air. In the paper, LQG regulator is applied to a flight model to demonstrate its effectiveness in all cases. LQG regulator has not been applied before for this model. Results are as expected by the author for the working enviroment with noise signals affecting the system. Kalman filter used in this paper has shown its usefulness in the problem of dealing with unwanted signals. Simulation is done by Matlab.

중형기동 회전익기 진동 하중 감소를 위한 선형 개별 블레이드 제어 법칙 설계 및 시뮬레이션

In the recent decades, rotorcrafts have been examined and subjected to experimentation for higher harmonic control (HHC) for hub vibratory load reduction through hydraulic swashplate actuation, or individual blade control (IBC). This paper presents a design of a linear quadratic Gaussian (LQG) regulator based on the LTI representation of HART-II rotor and evaluate its controlled stability and sensitivity. Specifically, a linear quadratic control synthesis for vibration reduction using the revised IBC control inputs of N/rev and (N±1)/rev, which will enable a linear time-invariant identification of a rotor, is presented. The following aspects are detailed: (1) a multi-body aeroelasitc rotor analysis of the baseline HART-II and UH-60A rotor; (2) the LTI identification method; and (3) the design and simulation of LQG closed-loop vibratory load control law.

Guaranteed Stability Margins for Decentralized Linear Quadratic Regulators

It is well-known that linear quadratic regulators (LQR) enjoy guaranteed stability margins, whereas linear quadratic Gaussian regulators (LQG) do not. In this letter, we consider systems and compensators defined over directed acyclic graphs. In particular, there are multiple decision-makers, each with access to a different part of the global state. In this setting, the optimal LQR compensator is dynamic, similar to classical LQG. We show that when sub-controller input costs are decoupled (but there is possible coupling between sub-controller state costs), the decentralized LQR compensator enjoys similar guaranteed stability margins to classical LQR. However, these guarantees disappear when cost coupling is introduced.

Optimal Control Approach for Robot System Using LQG Technique

A two-wheeled self-balancing robot system bases on the physical problem of an inverted pendulum. Stabilization of this type of mobile robot requires applying an active control approach. This paper proposes an efficient Linear Quadratic Gaussian (LQG) optimal control for the two-wheeled robot system. The LQG (a combination of a Kalman Filter (KF) and Linear Quadratic Regulator (LQR)) controller is designed to stabilize the robot while reducing the effect of the process and measurement noises on its performance. The LQG controller parameters (elements of state and control weighting matrices of the LQR and KF) are optimally tuned using the Particle Swarm Optimization (PSO) optimization method. The robot stabilization scheme is simulated utilizing MATLAB software to validate the proposed PSO-LQG controller system. The effectiveness of the proposed controller is validated based on the control criteria parameters, which are rise time, settling time, maximum overshoot, and steady-state error. The results prove that the proposed PSO-LQG controller can give very good movement performance in terms of both transient and steady-state responses.

Neural Networks Application for the Data of LQG Regulator for the Flexible Joint Robot

This paper describes the investigation of a flexible robotic arm with Degree of Freedom (DOF) through Linear Quadratic Gaussian (LQG) regulator under the influence of noise signals with using diagrams below. The derived model is based on the Euler-Lagrange approach while LQG mode is proposed as a modern control method. A flexible robotic arm that is test in the modern regulator is essential for applications. This is even more interesting while these arms have joints that work independently of each other, but they still ensure a tight connection between the joints. Testing the stability characteristics of the system through this regulator helps readers determine the output signals of a system exactly. From here, the author came up with strategies the match the requirements. Although the initial stage of the operating cycle is not stable with the use of LQG regulator, most of later stages of this process of closed systems of robotic systems gradually become stable. In particular, adjusting LQG for flexible joint robot gives satisfactory simulation results. This promises a positive result of other joint robot. Neural networks applied in this paper have proven its effectiveness in information security issues. It is also very useful for tight control of possible situations such as a large scale attack on network systems, automated control systems. The main contributions of this paper have been clearly demonstrated through two strategies that need to be addressed: LQG, neural networks for the data of LQG regulator.The methods described above have not been previously published for this model. Therefore, this article was born to outline the above objectives and the plans have been satisfactorily implemented. These studies are important because they serve as a necessary database in the selection of control strategies according to the requirements. Simulation results are done by Matlab. The purpose of the study of this paper: the author has searched for a stability of the system through the above methods. The applied method is a thorough study of the structure of the system as well as the construction of algorithms to form the regulator. The result ia a reliable simulation of events after the system is controlled by these regulators.

Optimal Secondary Control to Suppress Voltage Fluctuations in an HVDC-Linked Wind Farm Grid

High-voltage direct-current (HVDC) systems using voltage source converters (VSCs) have been developed to suppress voltage fluctuations in offshore grids due to the intermittent power generation of offshore wind farms (OWFs). This paper proposes a new strategy for the optimal secondary voltage control of HVDC-linked OWFs. In the proposed strategy, optimal coordinated control of an HVDC system and OWFs is achieved to minimize real-time voltage fluctuations throughout an offshore grid. A full-order dynamic model of HVDC-linked OWFs is implemented, and its unobservable and uncontrollable state variables are then eliminated using a model reduction algorithm. Given the dynamic model, a linear quadratic Gaussian regulator is designed for optimal coordinated control, and an eigenvalue analysis is conducted focusing on the effects of communication time delays on the stability of the proposed strategy. Simulation case studies are also carried out to verify that the proposed strategy more effectively improves real-time regulation of offshore grid voltages, compared to conventional strategies, while ensuring voltage stability even for relatively large delays in communications systems.

Practical implementable controller design with guaranteed asymptotic stability for nonlinear systems

Establishing the stability of model predictive control formulation is challenging. Using a combination of the terminal cost term and the terminal inequality constraint i.e. terminal set results in nominal asymptotic stability. Larger terminal set results in shorter minimum prediction horizon length required for feasibility from identical initial condition. Current work presents novel linear quadratic Gaussian regulator based approach for the terminal set characterization for the discrete time model predictive control scheme. Proposed approach provides large degrees of freedom in the form of additive matrices as tuning parameters for enlarging the terminal sets as against a single scalar for the literature approaches. Efficacy of the novel approach is demonstrated using a benchmark four tank system. It was observed that the average computation time reduces to significantly when compared to the approaches from the literature for identical initial conditions. This makes the controller design suitable for practical implementation.

Polynomial Wiener LQG Controllers based on Toeplitz Matrices

This paper re-examines the discrete-time Linear Quadratic Gaussian (LQG) regulator problem. The normal approach to this problem is to use a Kalman filter state estimator and Kalman control state feedback. Though quite successful, an alternative approach in the frequency domain was employed later. That method used z-transfer functions or polynomials in the z-domain. The transfer function approach is similar to the method used in Wiener filtering and requires the use of Diophantine equations (sometimes bilateral) to find the optimal controller. The contribution here uses a similar approach but uses lower triangular Toeplitz matrices instead of polynomials to gain advantage of eliminating the use of Diophantine equations. This is because the single Diophantine equation approach fails when the system has non-relative prime polynomials and the need for bilateral Diophantine equations is computationally far more complex.

Linear Quadratic Gaussian Regulator for the Nonlinear Observer-Based Control of a Dynamic Base Inverted Pendulum

The inverted pendulum is a non-linear control problem permanently tending towards instability. The main aim of this study is to design a controller capable enough to work within the given conditions while also keeping the pendulum erect given the impulsive movement of the cart to which it is joint via a hinge. The first half of the paper presents the mathematical modelling of the dynamic system, together with the design of a linear quadratic regulator (LQR). This paper also discusses a novel adaptive control mechanism employing a Kalman filter for the mobile inverted pendulum system (MIPS). In the second half of the paper, a Gaussian Quadratic Linear Controller (LQG) is adapted to improve on previous deficiencies. The simulation is done through Simulink and results show that both controllers are capable of managing the multiple output model. However, data from simulations clearly showed that an LQG controller is a better choice.

The Remote Control of the Artillery Rocket Set as a Strongly Nonlinear System Subject to Random Loads

On the modern battlefield, fighting capabilities, such as speed, target detection range, target identification capabilities, and shooting effectiveness, of short-range artillery rocket sets (ARSs) are constantly being improved. Problems arise when attempting to successfully fire such kits in the face of disruption from both the cannon and the moving platform on which the cannon is mounted. Furthermore, the set is a variable mass system since it can fire anywhere from a few to dozens or even hundreds of missiles in a brief period of time, implying that the ARS is a highly nonlinear system of variable parameters (non-stationary). This work shows how to control such a system. If the ARS is placed on a moving basis where there is both a system and measurement noise, the state variables must be restored, and the ARS data must be filtered. Therefore, in addition to the LQR regulator, an extended Kalman filter was used. As a consequence of this synthesis, an LQG (linear quadratic Gaussian) regulator of ARS was obtained, which was used to follow the target along the line of sight. The key goal of this paper is to develop control algorithms that will increase the performance of ARS control in elevation and azimuth, as well as the accuracy of achieving and eliminating maneuverable air targets. Moreover, through the quality criterion adopted, we hope to affect control energy costs while maintaining control precision. Graphical representations of certain computational simulation results are provided.

An optimized LQG servo controller design using LQI tracker for VSP-based AC/DC interconnected systems

This paper proposes a novel application for the optimal Linear Quadratic Gaussian (LQG) servo controller to enable a proper coordination of the AC/HVDC interconnected system with Virtual Synchronous Power (VSP) based inertia emulation. Particularly, the proposed control design takes the process disturbances and measurement noise of the studied VSP-HVDC system into account, while few studies have focused on this perspective. The proposed LQG controller with modifications is designed by means of a combination of Kalman Filter (state estimator) and an added Linear Quadratic Integrator (LQI) to observe the system model’s states and track the reference commands while rejecting the effects of system noise. Besides, we utilize a swarm-based optimization algorithm to operate as the search process for the tuning of the elements in the weighting matrices involved in the controller design. The role of the proposed optimal LQG controller is to stabilize such AC/DC interconnected system with VSP-based inertia emulator while minimizing the associated performance index. According to the obtained simulation results, in addition to the advancement from the VSP-based approach for damping frequency oscillations excited by faults, application of the proposed LQG servo controller can achieve the targets on both estimating the state variables and tracking the reference signals with satisfactory performance, comparing with the conventional LQG regulator.

On-sky results for adaptive optics control with data-driven models on low-order modes

ABSTRACT Dedicated tip–tilt loops are commonly implemented on adaptive optics (AO) systems. In addition, a number of recent high-performance systems feature tip–tilt controllers that are more efficient than the integral action controller. In this context, linear–quadratic–Gaussian (LQG) tip–tilt regulators based on stochastic models identified from AO telemetry have demonstrated their capacity to effectively compensate for the cumulated effects of atmospheric disturbance, windshake and vibrations. These tip–tilt LQG regulators can also be periodically retuned during AO operations, thus allowing to track changes in the disturbances’ temporal dynamics. This paper investigates the potential benefit of extending the number of low-order modes to be controlled using models identified from AO telemetry. The global stochastic dynamical model of a chosen number of turbulent low-order modes is identified through data-driven modelling from wavefront sensor measurements. The remaining higher modes are modelled using priors with autoregressive models of order 2. The loop is then globally controlled using the optimal LQG regulator build from all these models. Our control strategy allows for combining a dedicated tip–tilt loop with a deformable mirror that corrects for the remaining low-order modes and for the higher orders altogether, without resorting to mode decoupling. Performance results are obtained through evaluation of the Strehl ratio computed on H-band images from the scientific camera, or in replay mode using on-sky AO telemetry recorded in 2019 July on the CANARY instrument.

Actuator and sensor placement for closed-loop control of convective instabilities

This work deals with the characterization of the closed-loop control performance aiming at the delay of transition. We focus on convective wavepackets, typical of the initial stages of transition to turbulence, starting with the linearized Kuramoto–Sivashinsky equation as a model problem representative of the transitional 2D boundary layer; its simplified structure and reduced order provide a manageable framework for the study of fundamental concepts involving the control of linear wavepackets. The characterization is then extended to the 2D Blasius boundary layer. The objective of this study is to explore how the sensor–actuator placement affects the optimal control problem, formulated using linear quadratic Gaussian (LQG) regulators. This is carried out by evaluating errors of the optimal estimator at positions where control gains are significant, through a proposed metric, labelled as $$\gamma $$ . Results show, in quantitative manner, why some choices of sensor–actuator placement are more effective than others for flow control: good (respectively, bad) closed-loop performance is obtained when estimation errors are low (respectively, high) in the regions with significant gains in the full-state-feedback problem. Unsatisfactory performance is further understood as dominant estimation error modes that overlap spatially with control gains, which shows directions for improvement of a given set-up by moving sensors or actuators. The proposed metric and analysis explain most trends in closed-loop performance as a function of sensor and actuator position, obtained for the model problem and for the 2D Blasius boundary layer. The spatial characterization of the $$\gamma $$ -metric provides thus a valuable and intuitive tool for the problem of sensor–actuator placement, targeting here transition delay but possibly extending to other amplifier-type flows.

Closed-Loop Control of a Piezo-Fluidic Amplifier

Fluidic valves based on the Coanda effect are increasingly being considered for use in aerodynamic flow control applications. A limiting factor is their variation in switching time, which often precludes their use. The purpose of this paper was to demonstrate the closed-loop control of a recently developed novel piezo-fluidic valve that reduces response time uncertainty at the expense of operating bandwidth. Use is made of the fact that a fluidic jet responds to a piezo tone by deflecting away from its steady-state position. A control signal used to vary this deflection is amplitude modulated onto the piezo tone. Using only a pressure measurement from one of the device output channels, an output-based linear quadratic Gaussian regulator was designed to follow a desired reference deflection, achieving control of a . Finally, the controller’s performance in terms of disturbance rejection and response time predictability is demonstrated.

Welcome to 2020 and the Future of Control

Welcome to 2020 and the Future of Control

X-ray pulsar-based GNC system for formation flying in high Earth orbits

In this paper, comprehensive pulsar-based Guidance, Navigation and Control (GNC) system is designed and applied to satellites formation flying. The complete autonomy of the X-ray pulsar navigation technology provides both absolute and relative positioning information for spacecraft in or even beyond the solar system, and provides an interesting alternative solution to classical navigation techniques such as Global Navigation Satellite System (GNSS). The navigation measurements are studied using a relative time of arrival (RTOA) estimating method, which takes advantage of the noise-filtered pulsar profiles in the cross-correlation estimator to achieve robustness. An adaptive Kalman filter is exploited to minimise the effect of processing noises caused by the primary satellite. A linear Quadratic Gaussian regulator is then applied to control the formation. Two different configurations are studied in high Earth orbits (HEOs). Simulation results show that the designed GNC algorithms can fulfill the required accuracy (10% of the baseline) of the Magnetospheric Multiscale Mission, with the position root-mean-square error of ~1.6 km. . The excellent robustness of the designed GNC system on the positioning errors of the primary satellite suggests a role for X-ray pulsar-based formation flying technique in HEOs and the solar system.

Optimal Data-Driven Control of an LCC HVDC System for Real-Time Grid Frequency Regulation

Recent advances in data sensing and processing technologies enable data-driven control of high-voltage direct-current (HVDC) systems for improving the operational stability of interfacing power grids. This paper proposes an optimal data-driven control strategy for an HVDC system with line-commutated converters (LCCs), wherein the dc-link voltage and current are optimally regulated at distinct HVDC terminals to improve frequency regulation (FR) in both rectifier- and inverter-side grids. Each HVDC converter is integrated with feedback loops for regulation of grid frequency and dc-link voltage in a localized manner. For optimal FR in both-side grids, a data-driven model of the HVDC-linked grids is then developed to design a data-driven linear quadratic Gaussian (LQG) regulator, which is incorporated with the converter feedback loops. Case studies on two different LCC HVDC systems are performed using the data-driven models, which are validated via comparisons with physics-based models and comprehensive Matlab/Simulink models. The results of the case studies confirm that the optimal data-driven control strategy successfully exploits the fast dynamics of HVDC converters; moreover, cooperation of the HVDC system and synchronous generators in both-side grids is achieved, improving real-time FR under various HVDC system specifications, LQG parameters, and inertia emulation and droop control conditions.