Linear Quadratic Gaussian Method Research Articles

A fuzzy based intelligent scheme for enhancing the performance of the optimal controllers by online weighting matrix selection in seismically excited nonlinear buildings

In the present work, an effective strategy is proposed to improve the efficiency of the optimal controllers that are based on minimizing a performance index by using a fuzzy controller. In the used fuzzy system, the weighting matrices of the optimal controller are tuned online according to the response of the structural system. In order to assess the effectiveness of the proposed control scheme, its function is investigated in two phases on a 3-story nonlinear benchmark building equipped with MR dampers. In the first phase, a linear quadratic Gaussian (LQG) controller is combined with a fuzzy logic system (Fuzzy-LQG) and the efficiency of the used technique is compared with three different cases of the conventional LQG controllers. The results show that the Fuzzy-LQG, in addition to using an optimal level of demand energy, has a better performance than the conventional LQG methods in controlling the maximum responses of the structure. In the second phase, the performance of a polynomial optimal controller that is a summation of polynomials in nonlinear states in combination with the fuzzy system is investigated. At this stage, the effectiveness of the designed control system (Fuzzy Polynomial) in terms of seismic performance criteria with the results of a conventional LQG active control system, an optimal adaptive neuro-fuzzy inference system (ANFIS) and a neural network predictive control (NNPC) system is evaluated. The results show that this method is successful in improving the structural performance of a nonlinear building subjected to earthquakes.

Laboratory demonstration of the prediction of wind-blown turbulence by adaptive optics at 8 kHz with use of LQG control.

The low-latency adaptive optical mirror system (LLAMAS) is designed to push the limits on achievable latencies and frame rates. It has 21 subapertures across its pupil. A reformulated version of the linear quadratic Gaussian (LQG) method predictive Fourier control is implemented in LLAMAS; for all modes, it takes just 30µs to compute. In the testbed, a turbulator mixes hot and ambient air to produce wind-blown turbulence. Wind prediction clearly improves correction when compared to an integral controller. Closed-loop telemetry shows that wind-predictive LQG removes the characteristic "butterfly" and reduces temporal error power by up to a factor of three for mid-spatial frequency modes. Strehl changes seen in focal plane images are consistent with telemetry and the system error budget.

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.

Data Driven Linear Quadratic Gaussian Control Design

The implementation of the Linear Quadratic Gaussian (LQG) scheme is often considered problematic as it requires a dynamic model of the system as a whole. The challenges come from state variables without a physical representation and the interference factors that affect the reading process. This paper presents and assesses a combination of methods to adapt the LQG scheme to a discrete-time linear system. The method KalmanNet constructed by the Long-Short Term Memory architecture (LSTM) is employed to replace the role of Kalman Filter (KF). The Value Iteration (VI) algorithm supersedes the role of the Linear Quadratic Regulator (LQR) controller in solving quadratic regulation issues. The assessment of the proposed algorithm on a cart-pole system and batch distillation column with a disturbance factor in uncorrelated Gaussian white noise is carried out in a simulated way under a discrete-time linear system. The result indicates that the solving of regulation problems through the conventional LQG method is not conclusive as the output response oscillation is still in progress. The combination of the KalmanNet and VI algorithm, as aforementioned, provides better results as it proves to solve the regulation problem as well as to compel the system output to converge.

Control of inventory system with random demand and product damage during delivery using the linear quadratic gaussian method

This study formulates a dynamical system for the control of a single product inventory system in accordance with the random value of demand and the percentage of damaged product during the delivery process. The formulated model has the form of a linear state-space system comprising of two disturbances, which represents the random value of demand and the percentage of the damaged product during delivery. The optimal value of the product amount ordered to the supplier is properly calculated by using the linear quadratic gaussian (LQG) method. The controller is used by the manager to make inventory level decisions under the uncertainty of demand and damaged items during the product delivery process. The result showed that the optimal product order for each review time was achieved, and the inventory level was used to obtain the right set point properly. Moreover, based on comparison with other research results, the proposed model was well performed.

An LQG Controller Based on Real System Identification for an Active Hydraulically Interconnected Suspension

Rollover prevention is always one of the research hotspots in vehicle design. Active hydraulically interconnected suspension (HIS) is a promising technology to reduce vehicle body roll angle caused by different driving inputs and road conditions. This paper proposes a novel actuator of the active HIS system. The actuator consists of two cylinders, a ball screw, and only one motor. The actuator proposed can reduce the number of motors needed in the system. Meanwhile, forced vibration identification (FVI) is used to identify the transfer function of a half-car physical model and a Kalman state observer is applied to eliminate the influence of sensor noise. The FVI method can eliminate most model uncertainties and hidden variables. Aggressive and moderate optimal linear quadratic Gaussian (LQG) methods are implemented to control the motion of the vehicle body based on the identified transfer function of the physical model. The performance of an active HIS system with an aggressive and moderate LQG controller is compared with that of a passive HIS system. The effectiveness of the LQG controller is validated by simulation and experimental results. Also, the obtained results show that the stabilization speed of the active HIS system is 20% faster than that of the passive HIS system and the roll angle can be reduced up to 55% than that of the passive HIS system.

Lateral-vertical coupled active suspension on railway vehicle and optimal control methods

Plenty of studies focused on single-direction active suspensions on railway vehicles; at least four actuators per vehicle are needed forconventional active secondary suspensions in both lateral and vertical directions, leading to a sharp increase in costs and reduction inreliability. This paper proposes a novel configuration, lateral-vertical coupled (LVC) active secondary suspension, with only two actuators and two accelerometers per vehicle. To deal with the coupled dynamics, linear quadratic Gaussian (LQG) method and optimal skyhook damping (OSD) method are developed for achieving optimal control. OSD method has similar advantages as LQG method and is easier to implement. Then, linearised vehicle dynamics is modelled to design the controllers and observer, and a more complete nonlinear simulation model is established for verification. Theoretical analysis and simulation results show that LVC active suspension reduces car body vibration in one direction at the cost of negative effects in the other. LQG control fails to provide satisfying performance compared with passive suspensions, whereas OSD control can effectively improve lateral and vertical vibration and ride comfort by applying reasonable actuator forces. Besides, actuator dynamics is important to the effectiveness of LVC active suspension, and OSD controller is robust to measurement noise and model errors to some extent.

LQG Controller for the Control of Active and Reactive Power of DFIG Operating Under Inter-turn Short Circuit Fault

Objective: This article presents a comparative study between the direct control for a Doubly- Fed Induction Generator (DFIG) in the healthy and faulty mode. Methods: First with classical IP controller then Linear Quadratic Gaussian (LQG) controller which propose an ensemble of Linear Quadratic Regulator and Kalman filter for the state estimation. The developed model of the machine allows the simulation of the inter-turn short circuit in the stator. The use of the LQG method provides very good performance for motor operation and robustness of the control law despite the external perturbation. The performance of the control is compared to a classical controller's PI. Results: The obtained results demonstrate that this type of controller allows the alleviation of the mechanical stress and it ensures good performances under fault, the continuity of this system is ensured. Conclusion: The simulation has been carried out using a MATLAB script and the results are presented.

Modeling and control of magnetorheological 6-DOF stewart platform based on multibody systems transfer matrix method

A 6-DOF vibration isolation system with magneto-rheological damper (MRD) based on Stewart mechanism was designed to reduce the mechanical vibration more effectively. To make the isolation system perform well, an effective control method was also proposed. Using the linear multibody systems transfer matrix method (MSTMM), the dynamic model of the MRD 6-DOF vibration isolation system was established to obtain the dynamic characteristics. Firstly, based on the test mechanical property of magnetorheological damper, the electromagnetic coupling model of magnetorheological damper was established. Secondly, the transfer equation of 6-DOF vibration isolation system was established by linear MSTMM. And the state space equation was derived using the modal superposition method, which was based on the augmented eigenvector and body dynamics equation. Thirdly, the linear quadratic Gaussian control method of MRD 6-DOF vibration isolation system was designed. Finally, the numerical simulation was carried out. The results showed that MRD 6-DOF vibration isolation system with optimal control improved the dynamic performance of mechanical equipment effectively. Compared with passive vibration isolation system, the translation of the vibration isolation system in the X, Y, and Z directions, as well as the rotation around the X axis, Y axis and Z axis were reduced by 51.85%, 58.71%, 64.43%, 75.43%, 66.45% and 52.87%, respectively. Similarly, the percentage drops were 50.00%, 56.16%, 34.94%, 53.09%, 38.14% and 46.76% compared to the PID control based vibration isolation system, respectively. The established dynamic model and control strategy provided theoretical basis for relevant vibration isolation tests.

A Practical Approach to Optimal Control Problem for Atomic Clocks.

Linear quadratic Gaussian (LQG) control is one of the known techniques used for steering atomic clocks to external references. Complexity of the use of the LQG method is caused by uncertainty in selection of the weight coefficients of the cost function. Therefore, modeling of the steering algorithm for particular noises of reference and controlled clock (oscillator) is required. In this article, we propose the algorithm, which allows us to calculate weight coefficients and, consequently, gain coefficients of the control loop without modeling, by using initial information about frequency stability of reference signal and steered oscillator. An analysis of the LQG algorithm is supplemented with the results for two other strategies for control loop gain coefficients calculation.

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.

Tracking of square reference signals using internal model‐based LQG robust controller for positioning of a micro‐electro‐mechanical systems micromirror

This work studies the Lorentz force-based polymer hard-magnetic micromirror for optical switch application. For this purpose, a robust control design is proposed, which is based on the linear quadratic gaussian method incorporating with the well-known internal model principle. The proposed scheme can simultaneously be easily implemented and it can improve the positioning performances and noise rejection ability. The effectiveness is verified by experimental results.

Optimal estimation and scheduling in aquifer management using the rapid feedback control method

Abstract Management of water resources systems often involves a large number of parameters, as in the case of large, spatially heterogeneous aquifers, and a large number of “noisy” observations, as in the case of pressure observation in wells. Optimizing the operation of such systems requires both searching among many possible solutions and utilizing new information as it becomes available. However, the computational cost of this task increases rapidly with the size of the problem to the extent that textbook optimization methods are practically impossible to apply. In this paper, we present a new computationally efficient technique as a practical alternative for optimally operating large-scale dynamical systems. The proposed method, which we term Rapid Feedback Controller (RFC), provides a practical approach for combined monitoring, parameter estimation, uncertainty quantification, and optimal control for linear and nonlinear systems with a quadratic cost function. For illustration, we consider the case of a weakly nonlinear uncertain dynamical system with a quadratic objective function, specifically a two-dimensional heterogeneous aquifer management problem. To validate our method, we compare our results with the linear quadratic Gaussian (LQG) method, which is the basic approach for feedback control. We show that the computational cost of the RFC scales only linearly with the number of unknowns, a great improvement compared to the basic LQG control with a computational cost that scales quadratically. We demonstrate that the RFC method can obtain the optimal control values at a greatly reduced computational cost compared to the conventional LQG algorithm with small and controllable losses in the accuracy of the state and parameter estimation.

LQG based model predictive control for gust load alleviation

A linear quadratic Gaussian (LQG) based model predictive control (MPC) method is proposed to alleviate the dynamic gust loads of flexible aircrafts flying through turbulence, utilizing look-ahead information of the turbulence via light detection and ranging (LIDAR) systems or on board alpha probe. The new method features both infinite prediction horizon and infinite control horizon. The forepart of the infinite control sequence consists of a few online optimized variables, and the rest are outputs of an LQG controller, designed offline using an improved LQG method. The advantages of the proposed method are twofold. Firstly, the stability property of the controlled system is improved due to application of the infinite prediction horizon and the LQG controller. Secondly, adoption of an infinite control horizon not only improves the control performance, but also greatly reduces the number of online optimized control variables whilst retaining control performance. Furthermore, a technique to tackle the effects of control delay is also designed. The effectiveness and advantages of the proposed approach are demonstrated through numerical results using a general transport aircraft model.

Parameter-robust linear quadratic Gaussian technique for multi-agent slung load transportation

This paper copes with parameter-robust controller design for transportation system by multiple unmanned aerial vehicles. The transportation is designed in the form of string connection. Minimal state-space realization of slung-load dynamics is obtained by Newtonian approach with spherical coordinates. Linear quadratic Gaussian / loop transfer recovery (LQG/LTR) is implemented to control the position and attitude of all the vehicles and payloads. The controller's robustness against variation of payload mass is improved using parameter-robust linear quadratic Gaussian (PRLQG) method. Numerical simulations are conducted with several transportation cases. The result verifies that LQG/LTR shows fast performance while PRLQG has its strong point in robustness against system variation.

Improved LQG Method for Active Gust Load Alleviation

AbstractAgainst a background of various techniques for gust load alleviation (GLA), this paper aims at proposing an improved linear quadratic Gaussian (LQG) method, which is robust to variations of...

Stability Enhancement of a DC-Segmented AC Power System

This paper proposes and investigates a new line-commutated current-sourced converter (LCC)-high voltage dc current (HVDC) global supplementary control (GSC) strategy for stabilizing and enhancing the dynamic performance of a large ac system that is segmented by LCC-HVDC links. The GSC is designed based on a linear quadratic Gaussian (LQG) method and enables coordinated supplementary control action of multiple HVDC links that participate in segmentation. The GSC can stabilize the ac system while either minimizing the propagation of oscillatory dynamics from one segment to other segments (GSC1) or enabling their controlled transfer from a disturbed segment to other segments (GSC2). The study results show that in a fully-dc-segmented system: 1) GSC1 and GSC2 are able to stabilize the system; 2) under GSC1, each segment can experience major disturbances without causing adjacent segments to experience the disturbances with the same degree of severity; and 3) GSC2 enables controlled transfer of the oscillations among the segments and, depending on the system configuration, can further reduce the magnitude and duration of oscillatory dynamics. The studies are conducted on a three-segment ac system including three interconnecting LCC-HVDC links.

Active linear quadratic Gaussian control of the vibration of a flexible beam with a time-varying mass

A linear quadratic Gaussian method for active vibration control of a flexible beam with a time-varying mass is studied in this article. As the time-varying mass can change the resonance frequencies of system and induce instability of system, the vibration control of time-varying mass systems using piezoelectric actuators has been the subject of recent interest. The equation of motion of a beam with a time-varying concentrated mass is obtained by using admissible functions and the principle of separation of variables. Then, active control using piezoelectric actuators is simulated for the time-varying mass system. The linear quadratic Gaussian control strategy is employed for the suppression of transverse vibration of the beam with time-varying mass under different conditions. The numerical results show that the proposed scheme can attenuate the vibration of the variable mass system effectively in the interested frequency range. The control method can be used for the beam with constant mass or time-varying mass.

Satellite Attitude Control System Design considering the Fuel Slosh Dynamics

The design of the satellite attitude control system (ACS) becomes more complex when the satellite structure has different type of components like, flexible solar panels, antennas, mechanical manipulators, and tanks with fuel. A crucial interaction can occur between the fuel slosh motion and the satellite rigid motion during translational and/or rotational manoeuvre since these interactions can change the satellite centre of mass position damaging the ACS pointing accuracy. Although, a well-designed controller can suppress such disturbances quickly, the controller error pointing may be limited by the minimum time necessary to suppress such disturbances thus affecting the satellite attitude acquisition. As a result, the design of the satellite controller needs to explore the limits between the conflicting requirements of performance and robustness. This paper investigates the effects of the interaction between the liquid motion (slosh) and the satellite dynamics in order to predict what the damage to the controller performance and robustness is. The fuel slosh dynamics is modelled by a pendulum which parameters are identified using the Kalman filter technique. This information is used to design the satellite controller by the linear quadratic regulator (LQR) and linear quadratic Gaussian (LQG) methods to perform a planar manoeuvre assuming thrusters are actuators.