Linear Quadratic Gaussian Method Research Articles

Satellite Attitude Control System Design Taking into Account the Fuel Slosh and Flexible Dynamics

The design of the spacecraft Attitude Control System (ACS) becomes more complex when the spacecraft has different type of components like, flexible solar panels, antennas, mechanical manipulators and tanks with fuel. The interaction between the fuel slosh motion, the panel’s flexible motion and the satellite rigid motion during translational and/or rotational manoeuvre can change the spacecraft center of mass position damaging the ACS pointing accuracy. This type of problem can be considered as a Fluid-Structure Interaction (FSI) where some movable or deformable structure interacts with an internal fluid. This paper develops a mathematical model for a rigid-flexible satellite with tank with fuel. The slosh dynamics is modelled using a common pendulum model and it is considered to be unactuated. The control inputs are defined by a transverse body fixed force and a moment about the centre of mass. A comparative investigation designing the satellite ACS by the Linear Quadratic Regulator (LQR) and Linear Quadratic Gaussian (LQG) methods is done. One has obtained a significant improvement in the satellite ACS performance and robustness of what has been done previously, since it controls the rigid-flexible satellite and the fuel slosh motion, simultaneously.

SEMI-ACTIVE VIBRATION CONTROL FOR OFFSHORE PLATFORMS BASED ON LQG METHOD

The objective of this paper is to mitigate the wave-induced vibration of offshore platform with magneto-rheological (MR) damper. The model of the platform coupled with MR damper is established where the external wave force is approximated with a white noise via a designed filter. Based on Linear Quadratic Gaussian (LQG) method, the optimal control force is determined when taking the measurement noise into account. Semi-active control algorithm is applied to generate the MR damping force by comparing with the optimal control force. Numerical example demonstrates that the semi-active control strategy based on LQG method can reduce the responses of the platform effectively.

Beam structural system moving forces active vibration control using a combined innovative control approach

This study proposes an innovative control approach to suppress the responses of a beam structural system under moving forces. The proposed control algorithm is a synthesis of the adaptive input estimation method (AIEM) and linear quadratic Gaussian (LQG) controller. Using the synthesis algorithm the moving forces can be estimated using AIEM while the LQG controller offers proper control forces to effectively suppress the beam structural system responses. Active control numerical simulations of the beam structural system are performed to evaluate the feasibility and effectiveness of the proposed control technique. The numerical simulation results show that the proposed method has more robust active control performance than the conventional LQG method.

ACTIVE CONTROL OF BUILDINGS WITH BILINEAR HYSTERESIS AND TIME DELAY

In this paper, an active controller for buildings with bilinear hysteresis and time delay is studied. The bilinear hysteretic model is treated as a stiffness restoring force. By using specific transformation and augmentation of state parameters, the equation of motion of the system with an explicit time delay is transformed into a standard state space where there is no explicit time delay. A linear quadratic Gaussian control method is proposed for the controller design with time delay. The method is verified with numerical simulations of three-story and 20-story buildings. Comparison study of simulation results indicates that the control performance will deteriorate if the time delay is not taken into account in the control design. The proposed time-delay controller not only effectively compensate the time delay for better control effectiveness, but it also works well with both small and large time-delay problems.

Voltage control of emerging distribution systems with induction motor loads using robust LQG approach

Summary This paper identifies a new called “critical voltage mode in emerging distribution systems. The small-signal stability analysis indicates that load voltage dynamics significantly influence the damping of the newly identified mode. This has frequency of oscillation between the electromechanical and subsynchronous oscillation of power systems. A novel voltage controller is designed to damp this voltage of the system. The controller is designed using the linear quadratic Gaussian (LQG) method with norm-bounded uncertainty. The approach considered in this paper is to find the smallest upper bound on the H∞ norm of the uncertain system and to design an optimal controller based on this bound. The design method requires the solution of a linear matrix inequality. The performance of the designed controller is demonstrated on a distribution test system for different types of induction motors. Simulation results show that the proposed controller with a careful uncertainty modeling has significant performance to improve the voltage profile of the distributed generation system compared to the conventional excitation controller and standard LQG controller. Copyright © 2013 John Wiley & Sons, Ltd.

Augmented LQG Method for Optimal Control of Ship Shaft-Generatorfor

Abstract In order to maximize electrical energy from a marine propulsion engine in all operating conditions and to minimize the damage caused by mechanical fatigue, an optimal control method was applied to a ship shaft-generator driven by the marine propulsion engine. An augmented linear quadratic Gaussian (LQG) was proposed. The speed of ship shaft-generator was not stable due to high intensity of disturbances from the propeller. The augmented LQG controller regulated the ship shaft-generator torque, although the power output of the ship shaft-generator was dynamically uncertain. Hardwarein-the-loop simulation for ship shaft-generator based on Siemens Sinamics was carried out. The experimental results show that the proposed LQG controller strategies can effectively harmonize the rotor speed under highly stochastic turbulences from the propeller.

Active control to reduce the horizontal seismic response of buildings taking into account the soil-structure interaction

In this paper an active vibration control technique to reduce the seismic response of a soil-retaining structure interaction (SRSI) system is presented. The proposed control technique is a synthesis of the adaptive input estimation method (AIEM) and the linear quadratic Gaussian (LQG) controller. The AIEM can estimate online the unknown input. The LQG controller offers optimal control forces to suppress the SRSI system vibration. The control performance of the proposed control technique is numerically evaluated. The obtained results show that the proposed method is more robust than the conventional LQG method.

Optimal LQG Controller for Variable Speed Wind Turbine Based on Genetic Algorithms

Linear Quadratic Gaussian (LQG) control methodology shows useful properties of good performance and robust-ness in controller design applied to wind turbine. Typically, in the design procedure LQG method is necessary to select weighting matrices in order to solve the Algebraic Riccati Equations and then get the matrices Kalman Filter gain and optimal state-feedback. In order to optimize a LQG control applied to Double-Fed Induction Generator in wind power system, a Genetic Algorithms (GA) adapted to get the best values of the element of weighting matrices is proposed in this paper. The performance indices ISE and ITSE are a good alternative to obtain the fitness function to design LQG controllers with GA. The simulation results show the high effectiveness of this optimal design method.

Lateral Flight Technical Error Estimation Model for Performance Based Navigation

Flight technical error (FTE) combined with navigation system error (NSE) is the main part of total system error (TSE) in performance based navigation (PBN). The implementation of PBN requires pre-flight prediction and en-route short-term dynamical prediction of the TSE. Once the sum of predicted lateral FTE and NSE is greater than the specified PBN value, the PBN cannot operate. Thus, accurate modeling and thorough analysis of lateral FTE are indispensible. Multiple-input multiple-output (MIMO) lateral track control system of a transport aircraft is designed using linear quadratic Gaussian and loop transfer recovery (LQG/LTR) method, and the lateral FTE of a turbulence disturbed approach operation is analyzed. The error estimation mapping function of latera FTE and its bound estimation algorithm are proposed based on singular value theory. According to the forming mechanism of lateral FTE, the algorithm considers environmental turbulence fluctuation disturbance, aircraft dynamics and control system parameters. Real-data-based Monte-Carlo simulation validates the theoretical analysis of FTE. It also shows that FTE is mainly caused by turbulence fluctuation disturbance when automatic flight control system (AFCS) is engaged and would increase with escalating environmental turbulence intensity.

Stochastic optimal control of state constrained systems

In this article we consider the problem of stochastic optimal control in continuous-time and state-action space of systems with state constraints. These systems typically appear in the area of robotics, where hard obstacles constrain the state space of the robot. A common approach is to solve the problem locally using a linear-quadratic Gaussian (LQG) method. We take a different approach and apply path integral control as introduced by Kappen (Kappen, H.J. (2005a), ‘Path Integrals and Symmetry Breaking for Optimal Control Theory’, Journal of Statistical Mechanics: Theory and Experiment, 2005, P11011; Kappen, H.J. (2005b), ‘Linear Theory for Control of Nonlinear Stochastic Systems’, Physical Review Letters, 95, 200201). We use hybrid Monte Carlo sampling to infer the control. We introduce an adaptive time discretisation scheme for the simulation of the controlled dynamics. We demonstrate our approach on two examples, a simple particle in a halfspace and a more complex two-joint manipulator, and we show that in a high noise regime our approach outperforms the iterative LQG method.

Optimal control of fuel processing system using generalized linear quadratic Gaussian and loop transfer recovery method

This paper proposes an optimal control system that consists of both feedforward and state-feedback controllers designed using a generalized linear quadratic Gaussian and loop transfer recovery (GLQG/LTR) method for a fuel processing system (FPS). This FPS uses natural gas as fuel and reacts with atmospheric air through a catalytic partial oxidation (CPO) response. The control objective is focused on the regulatory performance of the output vector in response to a desired stack current command in the face of load variation. The proposed method provides another degree of freedom in the optimal control design and gives the compensated system a prescribed degree of stability. Finally, the numerical simulations of compensated FPS reveal that the proposed method displays better performance and robustness properties in both time-domain and frequency-domain responses than those obtained by the traditional LQ Method. Copyright © 2010 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society

A model-driven multivariable controller for vapor compression refrigeration systems

A model-driven controller for vapor compression refrigeration systems is presented herein. Mathematical sub-models were developed for each of the system components: heat exchangers (condenser and evaporator), variable-speed compressor and variable-orifice electric expansion device. The overall system simulation model was used to design a MIMO controller based on the linear-quadratic Gaussian method using a state observer of the Kalman filter type. A purpose-built testing apparatus comprised of a variable-speed compressor and a pulse-width modulated expansion valve was used to collect data for the system identification and model validation exercises. It was found that the model reproduces the experimental trends of the working pressures in conditions far from the operation point (±30%) with a maximum deviation of ±5%. Additional experiments were also performed to verify the ability of the controller of tracking reference changes and rejecting thermal load disturbances as high as 15%.

Stochastic control of reservoir systems using indicator functions: New enhancements

In our previous works, deterministic release policies were considered for the development of approximations of the two lower moments of the storage volume defined by the dynamic equation of the reservoir in discrete time but in continuous state space. Important innovation in that work was the incorporation of the lower and upper bounds of reservoir systems into the dynamic equation for the storage volume using indicator functions. The current work, which also does not use discretization, looks at an extension of previous developments that incorporates standard operating policies, and also a new randomized release policy, both of which make the moments calculations exact under the assumptions that (1) the sum of current random inflow and the previous storage volume can be described by just the two lower moments and (2) only the means and variances of the inflows are known. First‐ and second‐moment expressions are derived for the stochastic storage state variable and include terms for the failure probabilities (probabilities of spills or deficits). Expected values of the storage state, variances of storage, release policies, and failure probabilities are obtained by solving the optimal reservoir operations problem using nonlinear programming. The various statistics thus obtained from this optimization compare extremely well with those obtained from simulation for the single‐reservoir monthly operations problem studied. The exact characterization of the mean and variance of the storage state variable is derived, which is a difficulty in existing formulations based on linear quadratic Gaussian methods. For example, the latter methods have been unable to estimate these moments reasonably accurately, especially for long‐term operations, whereas the traditional storage theory based on discretization brings on the “curse of dimensionality.” The presentation herein is directed to both traditional reservoir storage theorists who are interested in the design of a reservoir where estimating the probabilities of spills and deficits is important and modern reservoir analysts who are interested in multiperiod optimal release decisions in the operations of reservoirs.

Optimal control design of fuel processing system by linear quadratic Gaussian and loop transfer recovery method

This paper presents an optimal control system which consists of both feedforward and state‐feedback controllers designed using a well‐developed linear quadratic Gaussian and loop transfer recovery (LQG/LTR) method for a fuel processing system (FPS). This FPS uses natural gas as fuel and reacts with atmospheric air through a catalytic partial oxidation (CPO) response. The control objective is focused on the regulatory performance of output vector in response to a desired stack current command in face of load variation. First, a Kalman filter is designed to provide an optimal estimation of state variables and to shape the target feedback loop function. And then an optimal two‐degree‐of‐freedom controller is designed subject to a linear quadratic performance index in the LTR process. Finally, the numerical simulations of compensated FPS reveal that the proposed method achieves better performance and robustness properties than presently accepted methods, in both time‐domain and frequency‐domain responses.

Optimal Control of Fuel Processing System Using Generalized Linear Quadratic Gaussian and Loop Transfer Recovery Method

This paper originally proposes an optimal control system which consists of both feedforward and statefeedback controllers using a generalized linear quadratic Gaussian and loop transfer recovery (GLQG/LTR) method. The control objective is focused on the regulatory performances of output vector in response to a desired stack current command in face of load variation. The proposed method provides another degree-of-freedom in optimal controller design and makes the compensated system have a prescribed degree of stability. Finally, the numerical simulations of a compensated fuel processing system reveal that the proposed method achieves better performance and robustness properties in both time-domain and frequency-domain responses than those obtained by the traditional LQ Method.

Joint control for flexible‐joint robot with input‐estimation approach and LQG method

AbstractIn this work, the input‐estimation (IE) algorithm and the linear quadratic Gaussian (LQG) controller are adopted to design a control system. The combined method can maintain higher control performance even when the system variation is unknown and under the influence of disturbance input. The IE algorithm is an on‐line inverse estimation method involving the Kalman filter (KF) and the least‐square method, which can estimate the system input without additional torque sensor, while the LQG control theory has the characteristic of low sensitivity of disturbance. The design and analysis processes of the controller will also be discussed in this paper. The joint control of the flexible‐joint robot system is utilized to test and verify the effectiveness of the control performance. According to the simulation results, the IE algorithm is an effective observer for estimating the disturbance torque input, and the LQG controller can effectively cope with the situation that the disturbance exists. Finally, higher control performance of the combined method for joint control of the robotic system can be further verified. Copyright © 2007 John Wiley & Sons, Ltd.

Polynomial Linear Quadratic Gaussian and Sliding Mode Observer for a Quadrotor Unmanned Aerial Vehicle

A polynomial Linear quadratic Gaussian method is used to compute a controller which is mixed with feedback linearization to control altogether a non linear Quadrotor UAV. A dual criterion involving the minimization of the error and control signal variances is analyzed. The introduction of the feedback linearization is seen to be useful to transform the MIMO system into a non interacting one. This will facilitate the computation of spectral factorization where the behavior is like SISO system. An algorithm is developed in this context. A sliding mode observer is added to feedback loop to estimate the unmeasured states necessary to the inner loop controller. The convergence of output state vector is obtained despite the non-robustness exact linearization when uncertainties on system parameters and disturbances occur. However the sensitivity and complementary sensitivity are presented to confirm the performance and robustness theory and validate the efficiency of results. The weighting functions choice is analyzed through frequency domain. The whole observer-estimator-control constitutes an original suggestion of control system with minimum sensors used. The robustness study has been realized on simulation taking into account uncertainties, disturbances, with a corrupted measured state by noise, and the actuator saturation. The results obtained show the convergence in finite time of estimated values and a satisfying tracking error of desired trajectories.

Multidisciplinary design optimization of mechatronic vehicles with active suspensions

A multidisciplinary optimization method is applied to the design of mechatronic vehicles with active suspensions. The method is implemented in a GA-A’GEM-MATLAB simulation environment in such a way that the linear mechanical vehicle model is designed in a multibody dynamics software package, i.e. A’GEM, the controllers and estimators are constructed using linear quadratic Gaussian (LQG) method, and Kalman filter algorithm in Matlab, then the combined mechanical and control model is optimized simultaneously using a genetic algorithm (GA). The design variables include passive parameters and control parameters. In the numerical optimizations, both random and deterministic road inputs and both perfect measurement of full state variables and estimated limited state variables are considered. Optimization results show that the active suspension systems based on the multidisciplinary optimization method have better overall performance than those derived using conventional design methods with the LQG algorithm.

Wind tunnel verification of actively controlled high-rise building in along-wind motion

Recently, the newly developed technology towards lighter and more strengthened material has facilitated more and more construction of high-rise buildings in many urban areas where the efficiency of space usage is demanding. Though the strength capacity of these buildings is adequate for safety requirement under wind excitation, the stiffness lessened might cause excessive displacements and accelerations on which building serviceability and comfort of occupants depend. In the last decade, many research efforts have demonstrated that the use of structural control is able to achieve remarkable results in reducing the wind-induced vibration for high-rise buildings. However, most of them are accomplished using numerical simulation. In this paper, a feasible and reliable design process for active control is proposed through wind tunnel tests. A four degree-of-freedom scaled (1:300) model of a high-rise building equipped with active mass driver is constructed on a wind tunnel to experimentally verify its applicability for wind-induced along-wind motion. A system identification scheme, which is capable of taking into account the interaction among wind, control device and structure, is presented to construct the nominal system. For the controller design, the advanced control strategy, linear quadratic Gaussian (LQG) method with acceleration feedback, is employed. From the experimental results, it is shown that the performance of the active controller following the design process proposed is remarkable in reducing the along-wind responses of high-rise buildings. Furthermore, despite of the fact that nominal system itself contains system uncertainty, the performance of active control using LQG control law remains quite promising and robust.

THE MODELLING AND VIBRATION CONTROL OF BEAMS WITH ACTIVE CONSTRAINED LAYER DAMPING

The finite element method (FEM) is combined with the Golla–Hughes–McTavish (GHM) model of viscoelastic materials (VEM) to model a cantilever beam with active constrained layer damping treatments. This approach avoids time-consuming iteration in solving modal frequencies, modal damping ratios and responses. But the resultant finite element (FE) model has too many degrees of freedom (d.o.f.s) from the point of view of control, nor is it observable and controllable. A new model reduction procedure is proposed. An iterative dynamic condensation is performed in the physical space, and Guyan condensation is taken as an initial iteration approximation. A reduced order model (ROM) of suitable size emerges, but it is still not observable and controllable. Accordingly, a robust model reduction method is then employed in the state space. A numerical example proves that this procedure reduces the model and assures the stability, controllability and observability of the final reduced order model (FROM). Finally, a controller is designed by linear-quadratic Gaussian (LQG) method based on the FROM. The vibration attenuation is evident