Linear Quadratic Gaussian Control Design Research Articles

Fractional loop delays in adaptive optics modeling and control.

This paper revisits the problem of optimal (minimum variance) control for adaptive optics (AO) systems when measurement and command applications are asynchronous, resulting in a non-integer servo loop delay. When not properly accounted for, such fractional delays may severely degrade the AO performance, especially in the presence of high-frequency vibrations. We present evidence of this performance degradation thanks to in-lab experimental measurements on the Gran Telescopio Canarias Adaptive Optics (GTCAO) system controlled with standard suboptimal linear quadratic Gaussian (LQG) controllers. A constructive, easy to implement LQG control design is then proposed and validated in a simulation for vibrations affecting the tip-tilt modes. Our methodology is very interesting because it allows a performance assessment for any linear controller in terms of variance, rejection transfer functions, power spectral densities, and stability margins. We also show how the continuous-time disturbance model can be derived from standard discrete-time disturbance data-based modeling.

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.

Two Phase Linear Quadratic Gaussian Controller Design for Launch Vehicle Autopilot

The achievable payload of a launch vehicle is sensitive to the mass of the terminal stage which injects the payload into orbit, as well as to tracking errors introduced by the autopilot. The system is usually characterized by lightly damped slosh modes with uncertain parameters, whose stabilization is critical, while maintaining the overall performance of the system. Passive slosh stabilization involves introduction of mechanical baffles into the fluid tanks, which impacts the achievable payload mass. Optimal tracking performance along with active slosh stabilization is hence an ideal combination of autopilot design objectives. While optimal control methods are attractive for such systems, the lack of physical insight in the design procedure often limits the usefulness of these methods for launch vehicle autopilot design. A major challenge in stabilizing lightly damped slosh is the necessity to cater to very large mode magnitudes and phase swings exhibited by the system over the range of parameter perturbations. The significant contribution of this paper is the development of a two phase Linear Quadratic Gaussian approach, utilizing the physical insight into the system performance for tuning the weights in the performance index, to satisfy the time domain as well as frequency domain objectives. A robust design which exhibits superior time domain as well as frequency domain performance as compared to the benchmark classical controller is obtained, with near perfect phase stabilization of the lightly damped slosh dynamics.

Reduced Order LQG Control Design for Infinite Dimensional Port Hamiltonian Systems

This article proposes a method that combines linear quadratic Gaussian (LQG) control design and structure preserving model reduction for the reduced order control of infinite dimensional port Hamiltonian systems (IDPHS).For that purpose the weighting operators used in LQG control design are chosen such that the resulting dynamic controller is passive and the closed-loop system equivalent to control by interconnection. The method of Petrov-Galerkin is then used to approximate the balanced realization of the IDPHS by a finite dimensional port Hamiltonian system and to provide the associated reduced order LQG controller. The main advantages of the proposed method are that, first, both control and reduction are driven by closed-loop performances and that, second, due to the passivity properties of the controller the closed-loop stability is guaranteed when the finite dimensional controller is applied to the infinite dimensional system.

Linear quadratic gaussian control design with extended KALMAN filter

Linear quadratic gaussian control design with extended KALMAN filter

Performance assessment of distributed LQG control subject to communication delays

This paper deals with the control performance assessment of distributed networked control systems in the presence of communication delays. The best achievable steady-state performance of distributed networked control systems in the framework of distributed linear quadratic Gaussian (LQG) control is presented where communication delays serve as the most fundamental performance limitation. In the proposed distributed LQG control design, distributed controllers and distributed observers are designed simultaneously without using separation principle. And the non-applicability of separation principle is investigated and demonstrated in distributed networked control with communication delays. In order to handle time-varying communication delays, we propose to use lower and upper bounds to characterize the range of the best achievable control performance with respect to the range of the communication delays. The obtained results can be used to evaluate the potential performance improvement of an existing distributed networked control system. The proposed approach is illustrated through a numerical example.

Economic Performance Optimization by Set Point and Weighting Parameter Tuning based on LQG Controller Design

Several researches have formulated economic performance optimization problems taking account of a trade-off relation between process input and output variance. The present work introduces theoretical formulations that relate the weighting parameter with each input and output variance on the condition that the Linear Quadratic Gaussian (LQG) controllers are implemented as lower layer controllers. The proposed approach is applied to a two-input, two-output separation process model, and solves optimal weighting parameter based on LQG control. The numerical example also shows that the obtained optimal weighting parameter is effective for a MPC based learning algorithm.

On LQG control design for network systems with/without acknowledgments using a particle filtering technology

This paper focuses on the behavior of a linear quadratic Gaussian (LQG) controller for discrete-time systems utilizing industrial communication protocols. A new design of LQG problem is investigated for constrained networked control systems by using a new class of a quadratic cost function with a communication cost. This paper is considered two industrial communication protocols namely: the transportation control protocol (TCP), in which the sender should receive an acknowledgment regarding the delivery of the sending packets and the user datagram protocol (UDP) where the acknowledgment signal is absence. In the latter one, the driver (actuation) does not afford acknowledgment to inform the controller/estimator regarding the reception of the action packets. In such setting, the UDP-like protocol can react nonlinearly, where the absence of the acknowledgment creates a nonlinear optimization control law. In this sense, a LQG with standard Kalman filtering is failed because the separation principle can not reached. Under this setting, a suboptimal methodology can be successfully implemented to compensate the absence of communication and acknowledgment packets. The prescribed performance of networked system is sustained in the presence of communication constraints. The probabilities of the data signal dropouts are expressed in terms of random Bernoulli processes. Then, simulation results are provided to demonstrate the validity of the proposed schemes and to compare them with others from literature.

상태공간 모델링에 의한 오일쿨러의 Robust LQG 제어기 설계

상태공간 모델링에 의한 오일쿨러의 Robust LQG 제어기 설계

LQG controller design for a quadrotor UAV based on particle swarm optimisation

This paper deals with the modelling and the linear quadratic Gaussian (LQG) control design of a quadrotor unmanned aerial vehicle (UAV) using different particle swarm optimisation (PSO) variants. Such a PSO-designed LQG controller is optimised in order to stabilise the position and the heading of the studied vertical take-off and landing (VTOL) quadrotor. Both canonical and recent variants of PSO algorithm, with linearly decreasing of inertia weight (PSO-In) and perturbed updating strategy (PSO-gbest), are considered for the systematically design and tuning of the LQG weighting matrices. These effective control parameters of the LQG approach represent the decision variables of the PSO-based LQG optimisation problem. Such an optimisation problem is formulated to minimise various performance time-domain criteria, like the integral of absolute error (IAE) and the maximum overshoot (MO) index, under nonlinear constraints related to the step responses of the closed-loop quadrotor dynamics. All proposed PSO algorithms are compared with each other and with the well known harmony search algorithm (HSA) and water cycle algorithm (WCA) metaheuristics for the stabilisation problem of the position and heading dynamics of the VTOL drone. Demonstrative simulation results are carried out in order to show the effectiveness of the proposed PSO variants-tuned LQG control approach.

LQG controller design for a quadrotor UAV based on particle swarm optimisation

This paper deals with the modelling and the linear quadratic Gaussian (LQG) control design of a quadrotor unmanned aerial vehicle (UAV) using different particle swarm optimisation (PSO) variants. Such a PSO-designed LQG controller is optimised in order to stabilise the position and the heading of the studied vertical take-off and landing (VTOL) quadrotor. Both canonical and recent variants of PSO algorithm, with linearly decreasing of inertia weight (PSO-In) and perturbed updating strategy (PSO-gbest), are considered for the systematically design and tuning of the LQG weighting matrices. These effective control parameters of the LQG approach represent the decision variables of the PSO-based LQG optimisation problem. Such an optimisation problem is formulated to minimise various performance time-domain criteria, like the integral of absolute error (IAE) and the maximum overshoot (MO) index, under nonlinear constraints related to the step responses of the closed-loop quadrotor dynamics. All proposed PSO algorithms are compared with each other and with the well known harmony search algorithm (HSA) and water cycle algorithm (WCA) metaheuristics for the stabilisation problem of the position and heading dynamics of the VTOL drone. Demonstrative simulation results are carried out in order to show the effectiveness of the proposed PSO variants-tuned LQG control approach.

A Design of a Hybrid Non-Linear Control Algorithm

One of the high energy consuming devices in the buildings is the air-conditioning system. Designing a proper controller to consider the thermal comfort and simultaneously control the energy usage of the device will impact on the system energy efficiency and its performance. The aim of this study was to design a Multiple-Input and Multiple-Output (MIMO), non-linear, and intelligent controller on direct expansion air-conditioning system The control algorithm uses the Fuzzy Cognitive Map method as a main controller and the Generalized Predictive Control method is used for assigning the initial weights of the main controller. The results of the proposed controller shows that the controller was successfully designed and works in set point tracking and under disturbance rejection tests. The obtained results of the Generalized Predictive Control-Fuzzy Cognitive Map controller are compared with the previous MIMO Linear Quadratic Gaussian control design on the same direct expansion air-conditioning system under the same conditions. The comparative results indicate energy savings would be achieved with the proposed controller with long-term usage. Energy efficiency and thermal comfort conditions are achieved by the proposed controller.

Dynamics modeling and advanced metaheuristics based LQG controller design for a Quad Tilt Wing UAV

This paper deals with the modelling and advanced metaheuristics-based tuning of a Linear Quadratic Gaussian (LQG) controller for a particular class of convertible Unmanned Aerial Vehicles (UAVs), called Quad Tilt-Wing (QTW). A dynamical model for the vertical, transition and horizontal flights is firstly derived using the Newton–Euler formalism. Since the main design parameters in the LQG control approach are the weighting matrices which are usually selected by classical and hard trials-errors based procedures, an optimization problem under operating constraints is formulated for systematically tuning these decision variables. Such an optimization-based LQG control problem is systematically solved using advanced and recent metaheuristics such as the Harmonic Search Algorithm, Water Cycle Algorithm (WCA) and Fractional Particle Swarm Optimization-based Memetic Algorithm (FPSOMA). To assess the performance of the proposed algorithms and conclude about their control parameters choices, an empirical comparison study is performed for solving different test functions from the single-objective optimization literature. The classical Particle Swarm Optimization and Ant Bee Colony algorithms are retained as comparison tools. Value- and Friedmans rank-based statistical analyses are presented. After that, experiments are conducted to achieve optimal coefficients of weighting matrices of LQG controllers in solving QTW position and heading stabilization problem. Demonstrative simulations show that the WCA, outperforming each one of other metaheuristics, provides the best results in terms of robustness and performance for the problem in hand. Results verify the efficiency the proposed metaheuristics-tuned LQG control structures.

LQG Controller Design for Heavy Vehicle Active Suspension Based on OT-AHP Method

In order to develop more scientific LQG (Linear-Quadratic Gaussian) optimal controller of vehicle active suspension, based on vehicle systme dynamics and modern control theory, the LQG controller of one 4-dof active suspension vehicle model was presented. And the index weighting coefficiens in LQG controller were rationally determind by AHP (Analytic Hierarchy Process) method. Based on this, for furtherly improving vehicle performanc, the subjective important degrees in AHP method were optimized by OT (Othogonal Test) method which took the linear weighted sum of ride comfort and road friendliness index as the comprehensive performance evaluation index. The simulation results showed that, compared to AHP method, the LQG active suspension vehicle designed by OT-AHP (Orthogonal Test of Analytic Hierarchy Process) method could have better comprehensive performance, which could provide new ideas for the development of vehicle active suspension.

Time-Varying LQG Control for Vibration of Coupled Vehicle-Bridge System

Time-varying linear quadratic Gaussian (LQG) control for vibration of coupled vehicle-bridge system is studied. The vehicle is modeled as a moving mass model with three degrees of freedom, which consists of vehicle body, bogie and wheel. Active suspensions are adopted for the primary and secondary ones, and the control forces are produced by two actuators placed between the bogie and wheel, and between the vehicle body and the bogie, respectively. Vehicle-bridge coupling systems are time-dependent, which lead to the time-varying Riccati differential equation and the time-varying Kalman-Bucy filter equation in the LQG controller design. However, both of them are solved precisely via precise integration method and symplectic conservative perturbation method. In the example, the time history responses of the bridge and the vehicle were calculated respectively for the vehicle with passive suspensions or with active suspensions. Numerical results show that with active suspensions adopted, ride comfort can be improved when the vehicles passing through the bridge.

Design and Analysis of Robust Minimax LQG Controller for an Experimental Beam Considering Spill-Over Effect

In this brief the design and analysis of an optimal robust minimax linear quadratic Gaussian (LQG) control of vibration of a flexible beam is studied. The analysis is performed by transforming the minimax LQG control design problem to its equivalent mixed sensitivity design problem. The first six modes of the beam in the frequency range of 0-700 Hz are selected for control purpose. Among these modes, three modes in the frequency range of 100-400 Hz are used for control, while the other three modes are left as the uncertainty of modeling. Both the model and the uncertainty are measured based on experimental data. The nominal model is identified from frequency response data and the uncertainty is presented by frequency weighted multiplicative modeling method. For the augmented plant consisting of the nominal model and its accompanied uncertainty, a minimax LQG controller is designed. Analysis and tradeoff between robust stability and robust performance is shown by selecting two different choices of uncertainty modeling. Simulation results used to show how the uncertainty weights can be tuned so that the proposed robust controller increase the damping of the system in its resonance frequencies and maintain the robust stability of the feedback system at the same time.

Design of a genetic-algorithm-based self-tuning sliding fuzzy controller for an active suspension system

Due to the fixed damping coefficient of the passive suspension system, it is difficult to enhance ride comfort and driving quality. An active suspension system provides extra force through the actuator which allows it to effectively isolate energy from vibrations and improve passenger comfort. This paper investigates ride comfort of a quarter-vehicle active suspension system according to the ISO 2631-1 standard. Using feedback information about the sprung mass acceleration, unsprung mass acceleration, and suspension deflection, an extended Kalman filter is developed to estimate the six unknown state variables: the sprung mass displacement and velocity; unsprung mass displacement and velocity; actuating force; and spool valve displacement. In addition, the road surface irregularities are also estimated. As compared to conventional controllers, the hydraulic actuator has time-varying, uncertain, and highly non-linear characteristics; thus, this paper applies a genetic-algorithm-based self-tuning sliding fuzzy controller and feedback linearization technique to design the actuating force. Simulation results are presented that show that the proposed controller demonstrates significant improvements in the vibration suppression of the vehicle body and ride comfort compared to a linear quadratic Gaussian controller design.

Normalized problem of anisotropy-based stochastic H ∞ optimization for closed-loop system order reduction by balanced truncation

This paper addresses the normalized problem of anisotropy-based stochastic H∞ optimization for a linear discrete time-invariant system. The problem includes the problem of linear-quadratic Gaussian controller design and H∞ optimization problem as limiting particular cases. It is shown that the order of a cross-coupled nonlinear algebraic equation system defining the optimal controller realization matrices can be reduced. This equation system can be partially decoupled that results in its simplification.

The Design of LQG Controller for Active Suspension Based on Analytic Hierarchy Process

A full vehicle model with seven degrees of freedom based on active suspension control is established, and linear quadratic gaussian (LQG) is designed by applying optimal control theory. Especially, the methodology of Analytic Hierarchy Process (AHP) is used to make the selection of weighted coefficients of performance indexes, which can reduce ineffective job in contrast with experience method. From the simulation results, it is shown that ride quality of the vehicle with active suspension has been effectively improved in comparison with the vehicle of passive suspension by the methodology of AHP applying to the selection of the weights.

Finite Dimensional Optimal Control of Poiseuille Flow

In this paper we consider linear stabilization of plane, Poiseuille  ow using linear quadratic Gaussian optimal control theory. It is shown that we may signiŽ cantly increase the dissipation rate of perturbation energy, while reducing the required control energy, as compared with that reported using simple, integral compensator control schemes. Poiseuille  ow is described by the inŽ nite dimensional Navier–Stokes equations. Because it is impossible to implement inŽ nite dimensional controllers, we implement high but Ž nite order controllers. We show that this procedure in theory can lead to destabilization of unmodeled dynamics. We then show that this may be avoided using distributed control or, dually, distributed sensing. A problem in high plant order linear quadratic Gaussian controller design is numerical instability in the synthesis equations. We show a linear quadratic Gaussian design that uses an extremely low-order plant model. This low-order controller produces results essentially equivalent to the high-order controller.