Linear Quadratic Gaussian Optimal Control Research Articles

Robust stabilization of LTI negative imaginary systems using the nearest negative imaginary controller

AbstractThis paper considers the problem of robust stabilization of linear time‐invariant systems with respect to unmodelled dynamics and structure uncertainties. To that end, a methodology to find the nearest negative imaginary system for a given non‐negative imaginary system is presented first. Then, this result is employed to construct a near optimal linear quadratic Gaussian controller achieving desired performance measures. The problem is formulated using port‐Hamiltonian method and the required conditions are defined in terms of linear matrix inequalities. The technique is presented using the fast gradient method to solve the problem systematically. The designed controller satisfies a negative imaginary property and guarantees a robust feedback loop. The effectiveness of the approach is demonstrated by a simulation on a numerical example.

A data-driven LQG method for linear time-varying systems to monitor the controller performance in the batch process

PurposeThe flexibility of batch process enables its wide application in fine-chemical, pharmaceutical and semi-conductor industries, whilst its complexity necessitates control performance monitoring to ensure high operation efficiency. This paper proposes a data-driven approach to carry out controller performance monitoring within batch based on linear quadratic Gaussian (LQG) method.Design/methodology/approachA linear time-varying LQG method is proposed to obtain the joint covariance benchmark for the stochastic part of batch process input/output. From historical golden operation batch, linear time-varying (LTV) system and noise models are identified based on generalized observer Markov parameters realization.FindingsOpen/closed loop input and output data are applied to identify the process model as well as the disturbance model, both in Markov parameter form. Then the optimal covariance of joint input and output can be obtained by the LQG method. The Hotelling's Tˆ2 control chart can be established to monitor the controller.Originality/value(1) An observer Markov parameter approach to identify the time-varying process and noise models from both open and closed loop data, (2) a linear time-varying LQG optimal control law to obtain the optimal benchmark covariance of joint input and output and (3) a joint input and output multivariate control chart based on Hotelling's T2 statistic for controller performance monitoring.

LQG Reference Tracking With Safety and Reachability Guarantees Under Unknown False Data Injection Attacks

We investigate a linear quadratic Gaussian (LQG) tracking problem with safety and reachability constraints in the presence of an adversary who mounts a false data injection attack on an unknown set of sensors. For each possible set of compromised sensors, we maintain a state estimator disregarding the sensors in that set, and calculate the optimal LQG control input at each time based on this estimate. We propose a control policy which constrains the control input to lie within a fixed distance of the optimal control input corresponding to each state estimate. The control input is obtained at each time step by solving a quadratically constrained quadratic program. We prove that our policy can achieve a desired probability of safety and reachability using the barrier certificate method. Our control policy is evaluated via a numerical case study.

Active Vibration Control of Timoshenko Sigmoid Functionally Graded Porous Composite Beam with Distributed Piezoelectric Sensor/Actuator in a Thermal Environment

This work presents the study of the dynamics and active control of a cantilever sigmoid FGM beam with porosities in a thermal environment. During this study, we considered the Timoshenko beam’s theory combined with the finite element method (FEM). This work also presents a comparative study with an experimental study for the vibration of a functionally graded piezoelectric beam (FGPM) to validate the numerical model. Linear quadratic Gaussian (LQG) optimal control with a Kalman filter was used for the vibration control using piezoelectric sensors and actuators as symmetrical layers to eliminate membrane effects. The controlled and uncontrolled responses are presented, considering the influence of thermal effect, the porosity of the FGM material, and the location of the sensor pair on the smart structure. The results indicate that the porosity effect of the FGM material, as well as the application of the thermal effect, involves an increase in vibration frequencies, in contrast to the increase in the power law index. The study also shows that the thermal and porosity effects result in an increase in vibration amplitudes.

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.

Active Flutter Suppression of a Two-Dimensional Wing Using Linear Quadratic Gaussian Optimal Control

This paper aims to utilize the modern control theory in designing an active flutter suppression controller for a two-dimensional wing with a flap. In this study, the wing’s pitch–plunge linear aeroelastic response, in addition to the control flap motion, was modeled using Lagrange’s energy method, and Theodorsen’s classic unsteady aerodynamic theory. The derived mathematical model was represented in state-space so the modern control techniques can be implemented. The open-loop system was analyzed, and the flutter speed for a selected experimental-wing model was calculated. For model verification purposes, the open-loop simulation results were compared to an experimental study from the literature. Next, a linear quadratic Gaussian (LQG) compensator with integral action was designed and tuned using MATLAB®simulation environment to reach the best possible performance at a selected speed in the flutter region, where the results have proven excellent performance for this kind of controller in flutter suppression, as the stable flight region has successfully been extended by 29%.

Optimal linear quadratic Gaussian control based frequency regulation with communication delays in power system

<p>In this paper, load frequency regulator based on linear quadratic Gaussian (LQG) is designed for the MAPS with communication delays. The communication delay is considered to denote the small time delay in a local control area of a wide-area power system. The system is modeled in the state space with inclusion of the delay state matrix parameters. Since some state variables are difficult to measure in a real modern multi-area power system, Kalman filter is used to estimate the unmeasured variables. In addition, the controller with the optimal feedback gain reduces the frequency spikes to zero and keeps the system stable. Lyapunov function based on the LMI technique is used to re-assure the asymptotically stability and the convergence of the estimator error. The designed LQG is simulated in a two area connected power network with considerable time delay. The result from the simulations indicates that the controller performed with expectation in terms of damping the frequency fluctuations and area control errors. It also solved the limitation of other controllers which need to measure all the system state variables.</p>

Machine Learning Methods to Investigate Drug Delivery in Infusion Pump

In the current scenario, usage of the smart medical pump is predominant in the medical field. The precise drug dosage, flow accuracy should be maintained to increase the performance of an infusion pump. In this work, an attempt has been made to predict and control the speed of the infusion pump for suitable infusion flowrate using machine learning technique and Linear Quadratic Gaussian (LQG) controller. The data for this study is considered from the publicly available online database, electronic Medicines Compendium (eMC). The speed of the infusion pump has been calculated using the drug dosage and flow rate for two different drugs. The prediction of infusion pump speed is achieved using Linear regression with Principal Component analysis (PCR) and Support Vector Machine Regression (SVR). The performance of the prediction schemes is evaluated using standard metrics. To validate the optimal control of the predicted speed, two different medical graded motors are considered. Further, the optimal control of the pump speed is investigated using Proportional–Integral–Derivative (PID), Linear Quadratic Regulator (LQR), and LQG controllers for its stability criteria. The prediction of the pump speed using regression models PCR, SVR has been verified and then the transient response analysis with rise time, settling time for both the motors have been examined. Results demonstrate that the LQG optimal control strategy achieves fast rise time, settling time of motor1 with 0.653s, 1.15s, and 0.22, 0.392s for motor2 respectively.

NSGA-II algorithm-based LQG controller design for nuclear reactor power control

The design of reactor power control system is closely related to the safety and economy of nuclear power plants. To improve its power control performance, this study takes a pressurized water reactor as the research object. The nonlinear dynamic mathematical model and its state space model were first derived; Then the Linear Quadratic Gaussian (LQG) optimal control method was adopted to design the reactor power controller; Furthermore, the multi-objective optimization of the linear quadratic regulator (LQR) weighting coefficient is carried out based on the elitist nondominated sorting genetic algorithm version II (NSGA-II). The results show that the LQG controller optimized based on NSGA-II method not only has fast response, high control accuracy and good stability, but also has good robustness and can obtain superior reactor power control performance.

Optimal control and learning for cyber‐physical systems

Optimal control and learning for <scp>cyber‐physical</scp> systems

Kalman-filter-based robust control for hypersonic flight vehicle with measurement noises

This paper investigates the tracking control problem of hypersonic flight vehicle (HFV) with measurement noises and system uncertainties. The system states of HFV are usually difficult to be accurately measured due to sensor noises and complex flight environment, which makes the controller design extremely difficult. To deal with such a problem, a linear quadratic Gaussian (LQG) optimal control algorithm and a robust back-stepping control strategy are proposed using Kalman filter. Firstly, the Kalman filter is used as a state observer for HFV to estimate the true states polluted by noises. Then, a linear LQG controller is proposed to realize the tracking control with the estimated states. In addition, to deal with the more practical case that the system suffers from both measurement noises and system uncertainties, a robust back-stepping control scheme based on Kalman filter and disturbance observer is presented. Different from the existing results, the proposed control scheme can guarantee the tracking performance under measurement noises and uncertainties. Finally, simulation results of HFV are carried out to demonstrate the effectiveness of the two proposed controllers.

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.

Proximity Operations and Three Degree-of-Freedom Maneuvers Using the Smartphone Video Guidance Sensor

This paper presents the first demonstration of NASA’s Smartphone Video Guidance Sensor (SVGS) as real-time position and attitude estimator for proximity and formation maneuvers. An optimal linear quadratic Gaussian controller was used, combining a linear quadratic regulator and a Kalman filter. The system was demonstrated controlling the 3-degree of freedom planar motion of the RINGS ground units (Resonant Inductive Near-field Generation Systems). A state-space model of the system’s 3-DOF motion dynamics was derived, and model parameters extracted using a system identification technique. The system’s motion control performance is experimentally demonstrated in both tracking and formation maneuvers. The results highlight the capabilities and performance of the Smartphone Video Guidance Sensor (SVGS) as a vision-based real-time position and attitude sensor for motion control, formation flight and proximity operations. A leader-follower formation maneuver approach is demonstrated, as well as position hold and path following.

Optimal control for networked control systems with multiple delays and packet dropouts

This article focuses on the problem of optimal linear quadratic Gaussian control for networked control systems with multiple delays and packet dropouts. The main contributions are twofold. Firstly, based on the introduced maximum principle for linear quadratic Gaussian system with multiple input delays and packet dropouts, a nonhomogeneous relationship between the state and costate is obtained, which is the key technical tool to solve the problem. Secondly, a necessary and sufficient condition for the optimal networked control problem is given in virtue of the coupled Riccati equations, and the explicit expression of the optimal controller is presented. Numerical examples are shown to illustrate the proposed algorithm.

Optimal linear quadratic Gaussian control for discrete time‐varying system with simultaneous input delay and state/control‐dependent noises

SummaryThis article focuses on the problem of linear quadratic Gaussian (LQG) control for discrete time‐varying system with input delay and state/control‐dependent noises. When the state variables can be exactly observed, first, we obtain the maximum principle by applying the method of variation. Second, a nonhomogeneous relationship between the state and the costate is developed in virtue of the obtained maximum principle and the mathematical induction. It is noted that the nonhomogeneous relationship is the solution to the forward and backward stochastic difference equations (FBSDEs). Finally, based on the solution to the FBSDEs, a necessary and sufficient condition for the optimal LQG control is derived in terms of coupled Riccati equations. Moreover, the analytical expression of the optimal controller is presented. The derived results are applied in networked control systems with packet dropout. Numerical examples are shown to illustrate the effectiveness of the proposed algorithm.

LQG control on mixed H2/H∞ problem: the discrete-time case

ABSTRACTIn this paper, we are concerned with linear quadratic Gaussian (LQG) control on the mixed problem. The mixed problem can be formulated as a kind of constraint optimisation problems where the control input is to minimise the -norm subject to the -constraint dealt with by the disturbance. The main contributions are twofold. First, when the state variables can be obtained exactly, necessary and sufficient conditions are given to guarantee the existence of the strategies. Second, the optimal LQG controller in terms of three decoupled equations (two Riccati equations and one Lyapunov equation) is obtained. The key technique is to apply the Stackelberg game approach by treating the disturbance as the follower and the control input as the leader respectively. A practical example is given to verify the efficiency of the proposed approach.

Time-varying linear quadratic Gaussian optimal control for three-degree-of-freedom wave energy converters

This paper presents a time-varying linear quadratic control for a three-degree-of-freedom (3-DoF) wave energy converter (WEC). The dynamic model for a heave-surge-pitch WEC has a linear coupling between pitch and surge modes, as well as a nonlinear coupling between the heave and pitch modes that affect the pitch motion. It is observed, however, that the heave motion is decoupled from the other two modes, and that the heave effect on the pitch motion can be recognized as a time-varying stiffness. Hence it is proposed in this paper to design a time-varying linear quadratic control for the coupled pitch-surge modes. The goal is to maximize the energy harvested over a receding time horizon. Prediction of the excitation forces is needed and is obtained based an estimate of the excitation force at the current time. The latter is obtained using an extended Kalman filter. The WEC motion is assumed constrained in this study. The results show that the energy harvested using this 3-DoF WEC is about three-fold higher than the energy extracted in heave mode, depending on the sea state. The paper also shows, with proper design of the control, it is possible to exploit this coupling to harvest more energy.

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.

Feasibility study of using a semiactive electromagnetic friction damper for seismic response control of horizontally curved bridges

Semiactive control systems have been found to be more effective than passive and active control systems for seismic protection of bridges because of their reliable and adaptable characteristics. This paper presents a comprehensive investigation on the modeling and design of a semiactive electromagnetic friction damper (SEMFD) for the seismic response control of horizontally curved bridges. The proposed SEMFD possesses a simple configuration consisting of a ferromagnetic plate and two arrays of ferromagnetic core coils (FCs) attached to the two sides of the ferromagnetic plate through two friction pads. The attractive magnetic interaction between the FCs arrays and the ferromagnetic plate creates the normal force, which generates friction force as the friction pads and the ferromagnetic plate move relative to each other. The magnitude of this force can be controlled by varying the control current passing through the FCs. This semiactive controller, designed based on the optimal linear quadratic Gaussian control method, is capable of reducing the undesirable effects of stick–slip motion in the damper, while restoring the piston of the SEMFD to its initial position at the end of the excitation. The capability of the proposed SEMFD to mitigate the rigid-body motion of decks of horizontally curved bridges is demonstrated by implementing it into the dynamic model of a horizontally curved bridge prototype. The numerical results indicate that the proposed SEMFD is effective in limiting the motion of the deck and thereby preventing it from unseating, which is one of the most common modes of failure among horizontally curved bridges.

Active vibration control of motorized spindle based on mixed /Kalman filter robust state feedback control

In its working process, a high-speed motorized spindle bearing-rotor system is affected by a variety of vibration excitations, which severely affect the machining precision and reliability. In view of the problems in the active vibration control of current smart-material-based bearing-rotor systems and based on the structural layout of a piezoelectric device and a controlled bearing-rotor system, a bearing was directly connected to a piezoelectric actuator via a sleeve, which improved the working efficiency of the piezoelectric stack actuator. Furthermore, to improve the robustness of the system’s vibration control performance under different external excitations (e.g., cutting force and mass unbalance), uncertainties in internal parameters (changes in bearing stiffness and stiffness nonlinearity of piezoelectric materials), process and measure noises, a mixed state feedback algorithm based on norm optimization and a Kalman filter observer with state disturbance estimation was established. The dynamic and robust performance of the proposed method was compared with that of the linear quadratic Gaussian optimal control methods and output feedback control method through both simulation and experiment by changing the piezoelectric stacks without changing the control program.