Optimal LQG Research Articles

Infinite Horizon Optimal LQG Control of Interconnected Systems With Application to Multiarea Power Systems

Infinite Horizon Optimal LQG Control of Interconnected Systems With Application to Multiarea Power Systems

Vibration control of FGM plate using optimally placed piezoelectric patches

The aim of this study is to propose a methodology to actively control the vibration of functionally graded plates, with the help of piezoelectric actuators and sensors. The study relays on the classical plate theory to analytically formulate the governing equation of motion, which is then expanded to derive a space state equation of the model. The material properties of the FG plate are assumed to vary along the thickness direction. In order to improve the damping effectiveness, the location of the piezoelectric sensors and actuators is optimally determined using the H2 norm. The necessary control voltage was determined based on optimal LQR and LQG controllers.

Dynamic Control of Non-Linearly Tapering FGM Beams

This work presents the dynamics and active vibration control of a non-uniform functionally graded beam. Thanks to the strong use of beams and specifically with non-uniform section, in the different industrial applications, such as helicopter rotor blades, wind turbines, space and marine structures, we present in this article, a comparison of linearly and non-linearly tapering beams. The FGM beam is equipped with four layers of piezoelectric materials as sensors and actuators, bonded on the upper and lower surfaces of the main structure, on different finite elements to see the influence of its location on the dynamics and active control. In this study, the Timoshenko beam’s theory combined with FEM is applied to a beam divided into a finite number of elements. Hamilton's principle is applied to generate the equation of motion. The structure is modeled analytically and numerically and the simulation results are presented at the end. The optimal LQG control with Kalman filtering is applied.

Optimal LQG Control of Networked Systems Under Traffic-Correlated Delay and Dropout

Transmission delay and packet dropout are inevitable network-induced phenomena that severely compromise the control performance of network control systems. The real-time network traffic is a major dynamic parameter that directly influences delay and reliability of transmission channels, and thus, acts as an unavoidable source of induced coupling among all network sharing systems. In this letter, we analyze the effects of traffic-induced delay and dropout on the finite-horizon quality-of-control of an individual stochastic linear time-invariant system, where quality-of-control is measured by an expected quadratic cost function. We model delay and dropout of the channel as generic stochastic processes that are correlated with the real-time network traffic induced by the rest of network users. This approach provides a pathway to determine the required networking capabilities to achieve a guaranteed quality-of-control for systems operating over a shared-traffic network. Numerical evaluations are performed using realistic stochastic models for delay and dropout. As a special case, we consider exponential distribution for delay with its rate parameter being traffic-correlated, and traffic-correlated Markov-based packet drop model.

Optimal control of interconnected systems with time-correlated noises: Application to vehicle platoon

This paper studies the optimal state-feedback LQG control (OSLC) of interconnected systems (ISs) with time-correlated process noises. In an IS, the information is transmitted among subsystems via the network, and the transmission time is proportional to the distance of the corresponding subsystem pairs. This means that the information received by a subsystem includes the non-real-time information, and that the information from different subsystems may be of different time indexes. This makes the optimal controller design challenging. The OSLC of ISs with time-uncorrelated process noises is studied by an independence decomposition method in the existing literature. However, the existing independence decomposition method strongly relies on the condition that the process noises are time-uncorrelated, and fails for the time-correlated process noises case. In this paper, the globally optimal LQG controller of ISs with time-correlated process noises is successfully designed. In particular, a new cost function decomposition is obtained based on the Bellman equation. Both the system state and the control input are decomposed into two independent parts by the orthogonal decomposition technique. The proposed decomposition method leads to the successful design of the globally optimal controller. The proposed theoretical results are applied to a vehicle platoon system. The simulation shows that the platoon maintains a desired state and achieves a good performance under the proposed controller.

Optimal LQG controller to adjust the rudder supplying water to the turbine of small and medium hydro power plants

Introduction: This paper is the result of the research “Optimal LQG controller to open rudder supplying water to turbine of small and medium hydro power plants” developed in the Electric Power University in Vietnam in 2019.
 Problem: To maintain the frequency of the emitted voltage of the generator at the nominal value of 50 Hz, the authors present a solution to apply the optimal control theory to create a command to control the rudder angle to adjust the water flow into the turbine.
 Objective: The article presented about the order value formation algorithm, to stabilize the frequency of transmission voltage at 50 Hz standard value.
 Methodology: In this paper, the laws to control the rudder supplying water to turbine of small and medium hydro power plants are synthesized by optimal control theory. To establish optimal control rules, the paper proposes using the Kalman filter to estimate the state of the object. By that, the frequency of generated voltage will be stabilized under changing load. The efficacy of the steady and dynamic performance of the control strategy was verified using Matlab/Simulink software.
 Results: The proposed system can compensate for power fluctuations and is effective in terms of power regulation.
 Conclusion: The algorithm presented in the paper is the basis for setting up the software when when designing and manufacturing the turbine - generator combination. Applying this algorithm, the process of adjusting the transmitted power according to the required load will be performed with quality.
 Originality: This paper’s contribution lies in its employment of an effective optimal LQG control for varying operating conditions.
 Limitations: The authors need to spend more time to the development and and test this algorithm and and implementing it in practice.

Optimal LQG control for discrete time-varying system with multiplicative noise and multiple state delays

Optimal LQG control for discrete time-varying system with multiplicative noise and multiple state delays

Dynamic control of Euler Bernoulli FG porous beam under thermal loading with bonded piezoelectric materials

In order to develop a mathematical modeling of the smart structure, the study consists of using, in first time, the finite element method and Euler-Bernoulli theory applied to a flexible beam divided into a finite number of elements. For this purpose, we define the beam represented by the imperfect FG material, partially bonded on both surfaces, four thin layers of piezoelectric materials used as sensors/actuators. The effects of temperature and porosity on the dynamics and the active control are studied and discussed. The equations of motion are obtained via Hamilton principle. The structure is modeled analytically and numerically and the optimal LQG control with Kalman filtering is applied. The results of the simulation are presented to visualize the states of the dynamics of the several cases.

Finite element model based on an efficient layerwise theory for dynamics and active vibration control of smart functionally graded beams

In this work, we present a two-noded efficient finite element (FE) model incorporating the layer-wise mechanics for the dynamics and active vibration control of smart functionally graded (FG) beams. The material properties in the FG beam are assumed to vary smoothly in the thickness direction according to power law variation. The effective properties are computed using Mori-Tanaka homogenization scheme. Electric potential profile in the electroded piezoelectric layers/patches is assumed quadratic across its thickness. The equations of motion are derived using extended Hamilton’s principle. Due to the complex algebraic expressions involved in the effective properties of FG system, the inertia and stiffness parameters are computed numerically using six point Gauss integration method. To fulfill the convergence requirements for weak integration of various energy terms in the variational formulation, the transverse displacement is interpolated with Hermite interpolation function possessing C1-continuity while the inplane displacement, shear rotation and quadratic component of the electric potential are interpolated with linear Lagrangian functions of C0-continuity. The equipotential condition of the electroded piezoelectric sensors and actuators is conveniently modelled using electric node concept. The control system is designed for constant gain velocity feedback (CGVF), and optimal LQR and LQG control strategies for a reduced order model using state space approach. The control performance is studied for single-input-single-output (SISO) and multi-input-multi-output (MIMO) configurations under various excitations. The effect of material inhomogeneity on stability/instability of the closed-loop response in the CGVF control has been discussed.

F-16/MATV; Optimal Position Controller Design using Robust and Discrete Linear Quadrature Gaussian [RLQG] Controller

This paper presents the robust controller design for nonlinear F-16/MATV (Multi–Axis – Thrust - Vectoring) position control system. The linearization of nonlinear flight position system is guaranteed by feedback linearization using Taylor series expansion and the optimal LQG controllers are designed to achieve the steady state flight condition. The comparison of the using continuous and discrete LQG is fully discussed for control system. First the continuous optimal LQG controller is designed for continuous time state space represented flight dynamic system based on separation principle. But the designed optimal LQG controller requires a very large controller gain to achieve the design objective, which lacks high sensitivity and leads to highly cost system. This leads to design a controller using discrete LQG controller for discrete time state space represented flight control system. After implementing this controller into the system in MATLAB Simulink environment, using singular value decomposition technique, it is founded that the performance and robustness of the design objective is satisfied.

Optimal LQG Control for Networked Control Systems with Remote and Local Controllers

We consider the finite horizon optimal LQG control problem for networked control systems with a remote controller, a local controller and communication channels with packet dropouts and transmission delays. The local controller can directly observe state signals and send them to the remote controller via a packet-dropout channel. Then the remote controller sends the received measurement signals to the local controller. Afterwards, the two controllers operate the plant through a delayed channel. The contributions of this paper are as follows: Firstly, at the side of the remote controller, we develop an optimal estimator to show that the separation principle holds. Secondly, we derive a non-homogeneous relationship between the state and the costate of systems in virtue of the maximum principle. Finally, a necessary and sufficient condition for the optimal control problem is derived in terms of the two coupled Riccati equations. Numerical examples are employed to illustrate the theoretical results.

Approximate solution to optimal linear quadratic Gaussian control over non-acknowledgment networks

This paper investigates the solution of the optimal linear quadratic Gaussian control (LQG) problem for systems with packet losses over non-acknowledgment networks. The acknowledgment refers to acknowledgment signals, which are sent by the actuator to notify the controller whether the control packets are successfully received or not. Systems without acknowledgment for packet losses are usually called user-diagram-protocol-like (UDP-like) systems. It is known that for general UDP-like systems, there is no analytical solution to the optimal LQG problem and the computational efforts of numerical solutions will exponentially grow with time. By using a moment-preserving Gaussian approximation approach, this paper develops an efficient algorithm to approximately estimate system states. Based on approximate state estimates, an analytical solution to the optimal LQG problem for general UDP-like systems is obtained by using a dynamic programming approach. It is an approximate solution, and it becomes an exact solution under special conditions. Some simulation examples are given to illustrate the effectiveness of the proposed methods.

Hybrid Optimal LQG Tracking Control for Linear Discrete-Time Systems by Simultaneous Optimization Approach of System States and Mode Distributions

In this paper, we study optimal LQG tracking control problems for linear discrete-time hybrid systems. We adopt an approach to prepare some candidates of mode distributions and minimize value functions at each time for the systems and performance indices. By the approach, system states and mode distributions are simultaneously optimized so that performance indices are minimized for causal information of reference signals. We consider optimization problems for averaged systems and averaged performance indices throughout mode distributions. Finally, we give numerical examples and verify that we can obtain both optimal tracking performance and optimal candidate of mode distributions by the algorithm presented in this paper.

Globally Optimal State-Feedback LQG Control for Large-Scale Systems With Communication Delays and Correlated Subsystem Process Noises

This paper studies the optimal decentralized state-feedback control of large-scale systems. The large-scale system is composed of subsystems and defined over a connected digraph. One step time is required for information to travel across an edge in the graph. Under the above-mentioned setup, when subsystem process noises are uncorrelated, the explicit optimal state-feedback controller can be designed by independence decomposition based on information hierarchy graph. However, this decomposition method fails when the subsystem process noises are correlated. In this paper, we propose a new decomposition method for system state and control input, and split the optimal state-feedback control problem with correlated process noises into two subproblems that can be solved separately. The solution to the first subproblem can be obtained by solving a linear matrix equation. The second subproblem is solved by algebraic Ricatti equation.

High Order Approximations for LQR Control and LQG Estimation of Convection Diffusion Systems

In this paper we discuss higher order methods for approximating linear control systems governed by convection diffusion equations. In particular, we employ a hp - finite element method to construct low order approximations of the Riccati equations that arise in linear quadratic control and optimal state estimation. The method is based on using high order piecewise polynomial approximations that achieves accuracy by combining mesh refinement (h → 0) with high order polynomials (p → +∞). By employing high order methods one can obtain accuracy with fewer degrees of freedom than can be achieved with mesh refinement alone. These methods are well known in the simulation community and can be used to achieve high order simulations, but hp – methods have not been investigated as potential methods for approximating control systems governed by partial differential equations. We employ the hp – finite element method to develop approximations of the infinite dimensional Riccati operators that define optimal LQR and LQG controllers. Convergence and rates of convergence are presented. A numerical example is provided to illustrate the convergence rates for the hp – method and we close with a discussion of how such methods might be used to enhance the development of reduced order models.

Optimal Decentralized Output-Feedback LQG Control With Random Communication Delay.

This paper is concerned with the optimal decentralized output-feedback control of the large-scale systems. A random information pattern is considered, where the information is transmitted among the subsystems with random communication delays. For the random information pattern, the optimal LQG problems for both global estimation case and local estimation case are studied. It is difficult to derive the optimal controller under random framework, because the gains of the controller must be designed to satisfy the random sparse structure constraints. In this paper, we design the optimal controller by Hadamard product method. For global estimation case, the gains of the controller are obtained by solving linear matrix equation. For local estimation case, an iterative algorithm is exploited to compute the gains. In addition, the value of the cost function achieved by the designed controller is found and shown to monotonically increase with the increase of the delay probability for both global and local estimation cases. Finally, the theoretical results are illustrated by two numerical examples.

Hybrid Optimal Tracking Control for Linear Continuous-Time Systems by Simultaneous Optimization Approach of System States and Mode Distributions

In this paper, we study optimal LQG tracking control problems for linear continuous-time hybrid systems. We adopt an approach to prepare some candidates of mode distributions and minimize value functions at each time for the systems and performance indices. By the approach, system states and mode distributions are simultaneously optimized so that the performance indices are minimized for available information of reference signals. We consider optimization problems for averaged systems and averaged performance indices throughout mode distributions. Finally we give numerical examples and verify that we can obtain both optimal tracking performance and optimal candidate of mode distributions by the algorithm presented in this paper.

Stochastic optimal control of a heave point wave energy converter based on a modified LQG approach

The optimal control constrain problem of a wave energy point absorber is constrained due to limited stroke and saturation of the control force actuator. The basic idea of this paper is to control the motion of the absorber by a modified LQG control where the constraints on the displacement and actuator force are approximately considered by counteracting the absorbed power in the objective quadratic functional. Based on rational approximations to the radiation force and the wave load, the integrated dynamic system can be reformulated as a linear stochastic differential equation which is driven by a unit intensity Gaussian white noise. The optimal LQG control force becomes a linear function of the state vector of the integrated system, which can only be partially observed. In order to remedy this problem, the control is combined with a Kalman filter observer. The obtained sub-optimal solution has been compared to the numerical optimal solution obtained by nonlinear programming. With suitable calculated gain parameters, the LQG controller can provide approximately the amount of the averaged absorbed power as that of the numerical optimum.

Vibration control of rotating piezo-composite blade beam with CUS configuration based on optimal LQG controller

Vibration control of rotating composite blade beam with piezoelectric patch embedded is investigated. Stall flutter of piezo-composite blade driven by nonlinear aerodynamic forces is analyzed based on anisotropic circumferentially uniform stiffness (CUS) configuration. The blade is modeled as single-cell thin-walled beam structure, exhibiting the couplings among three displacements of vertical bending, lateral bending and transverse shear deformation, with structural tailoring implemented. The transversely piezoelectric actuating element is embedded in a manner such that its surface is parallel to the mid-surface of the blade beam. Piezoelectric damping ratios of rotating piezo-composite blade are described, with influences of different ply angles and rotating speeds illustrated. The flutter suppression for stall aeroelastic behavior based on an optimal LQG controller (OLC) with a dynamic regulator is highlighted with obvious effects demonstrated. In contrast with conventional LQG controller, the superiority of OLC controller is apparently demonstrated by time response and piezoelectric feedback voltage. Analytical proof of the structural modeling and feasibility analysis of the physical realization of the OLC algorithm are also investigated by comparisons of different modeling theories, and demonstrated by experimental platform.

An Optimal LQG Controller for Stochastic Event-triggered Scheduling over a Lossy Communication Network

Abstract We consider a networked control loop in which the sensors acquire partial state information and communicate to a remote controller through a lossy communication network. A scheduler, collocated with the sensors, decides to transmit a locally estimated state to the controller based on an event-triggered transmission policy with stochastic thresholds. Assuming that the local estimator either senses the communication channel or receives an ideal acknowledgment from the remote estimator, then the optimal control law can be shown to be a linear function of the conditional expectation of the state. However, the probability distribution of the state conditioned on the information available to the controller based on the mentioned transmission policy and network is not Gaussian, but rather described by a sum of Gaussians with an increasing number of terms at every time-step. We show that the optimal LQG control law can be determined without tracking this probability distribution for finding its expected value. Moreover, we establish that the stochastic event-triggered scheduler can be appropriately regulated in order to achieve a desired triggering probability at every time-step.