Conventional Linear Quadratic Gaussian 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.

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.

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.

A robust linear-quadratic-gaussian controller for the real-time hybrid simulation on a benchmark problem

Abstract During a real-time hybrid simulation (RTHS), inevitable time delay of actuators when responding to a command will reduce the accuracy of test results and sometimes even cause unstable testing. The inner-loop controller of an actuator is generally capable of eliminating the effects due to small time-delays. However, if a test specimen behaves nonlinearly, accuracy of RTHS results will be impaired. In addition to the uncertainty of test specimens and transfer system, measurement noises of the displacement and force sensors also require a robust external controller for RTHS. In this paper, a robust linear-quadratic-gaussian (LQG) controller with a Loop Transfer Recovery (LTR) procedure and a polynomial-based feedforward prediction (FP) algorithm is proposed to compensate the adverse effects due to time delay and uncertainties within the RTHS testing system. The stability and robustness of the proposed controller are analysed in the frequency domain using the Nyquist curve and the Bode diagrams. Numerical simulations are then carried out on the benchmark problem using both the proposed robust and the conventional LQG controllers and their performance is compared using the nine evaluation criteria. It is demonstrated that the robust LQG (RLQG) controller outperforms the conventional LQG controller in terms of compensating the parameter uncertainties in the testing system and achieving accurate RTHS results.

Control Performance Assessment for ILC-Controlled Batch Processes in a 2-D System Framework

In this paper, control performance assessment (CPA) is studied for batch processes controlled by iterative learning control (ILC). A 2-D linear quadratic Gaussian (LQG) benchmark is proposed to assess the performance of ILC in a 2-D framework. Based on the 2-D theory, an ILC-controlled batch process is first converted into a 2-D Roesser model. Subsequently, in order to assess the control performance of the converted 2-D system, the conventional LQG tradeoff curve is upgraded to the LQG performance assessment tradeoff surface. However, the complete knowledge of the system model is required to obtain the LQG tradeoff surface. For system without accurate model knowledge, a novel data-driven CPA method is further proposed. In this case, a novel 2-D closed-loop subspace identification method is proposed to identify the converted 2-D Roesser system. Based on the identified model, the LQG tradeoff surface can be obtained and utilized to assess the control performance. Overall, several simulation examples verified the feasibility and effectiveness of the proposed method.

Varying Charge Voltage in the Steps Control Method of ABS for In-Wheel Motors Driven Electric Vehicles Based on an Improved LQG Scheme

This paper explores a coordinated control strategy of the anti-lock braking system (ABS) for in-wheel motors driven electric vehicles to recover more braking energy while satisfying the target of slip ratio control based on a newly varying charge voltage in steps control (VCVISC). The novel VCVISC method is proposed on the existing battery management system to change the charging voltage by choosing the number of batteries in the series to substitute for the converter. The reason that the conventional linear quadratic Gaussian (LQG) control employed in ABS control does not function is examined by theoretical derivation, and an improved LQG scheme is presented to calculate the real-time required braking torque by adding virtual damping and infinitely small terms in the Riccati equation. A distributing strategy of braking torque is presented to maximize the energy recovery, which is realized by using the VCVISC method to regulate the regenerative braking torque in real time. Simulation results under different braking road scenarios demonstrate that the proposed ABS control strategy can achieve not only an outstanding response for tracking ideal slip ratio, but also an efficient braking energy recovery efficiency.

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.

Adaptive Semiactive Cable Vibration Control: A Frequency Domain Perspective

An adaptive solution to semiactive control of cable vibration is formulated by extending the linear quadratic Gaussian (LQG) control from time domain to frequency domain. Frequency shaping is introduced via the frequency dependent weights in the cost function to address the control effectiveness and robustness. The Hilbert-Huang transform (HHT) technique is further synthesized for online tuning of the controller gain adaptively to track the cable vibration evolution, which also obviates the iterative optimal gain selection for the trade-off between control performance and energy in the conventional time domain LQG (T-LQG) control. The developed adaptive frequency-shaped LQG (AF-LQG) control is realized by collocated self-sensing magnetorheological (MR) dampers considering the nonlinear damper dynamics for force tracking control. Performance of the AF-LQG control is numerically validated on a bridge cable transversely attached with a self-sensing MR damper. The results demonstrate the adaptivity in gain tuning of the AF-LQG control to target for the dominant cable mode for vibration energy dissipation, as well as its enhanced control efficacy over the optimal passive MR damping control and the T-LQG control for different excitation modes and damper locations.

Transcale control for a class of discrete stochastic systems based on wavelet packet decomposition

In this paper, a wavelet packet decomposition (WPD) based real-time transcale linear-quadratic-Gaussian (LQG) tracking control algorithm is given for a class of discrete stochastic systems, which is developed with the state-space models of wavelet packet coefficients at the coarsest scale decomposition layer established by Haar WPD. The WPD-based transcale control algorithm provides a compromise between performance index and computational efficiency compared with the conventional LQG tracking control algorithm, and it is an improvement of the wavelet transform based algorithm previously proposed. Simulation results are presented to demonstrate the effectiveness of the proposed algorithm.

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.

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.

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.

Robust Performance of Fuzzy Supervisory Control for Seismically Excited Cable-Stayed Bridge

This paper investigates the robust performance of fuzzy supervisory control (FSC) technique for seismically excited cable-stayed bridge. The FSC technique utilizes fuzzy logic-based decision-making process to incorporate a set of pre-designed static control gains into a time-varying optimal control gain. To demonstrate the excellent robustness of the FSC technique on response control of earthquake-excited cable-stayed bridge, a conventional linear quadratic Gaussian (LQG) controller with single static gain and two fuzzy supervisory controllers are designed for the benchmark cable-stayed bridge, and their robust performances are examined under uncertainty in bridge model and against failures in actuators and sensors. Under the presence of uncertainty in the bridge model, the FSC system successfully reduces the seismic responses of the bridge without significant increase in the total amount of power and stroke required by the control system, while the LQG system exhibits a substantial increase in the seismic responses. Under conditions of sensor or actuator failures, the FSC system guarantees a more enhanced robust performance than the LQG system as well.

Designing active flutter suppression for high-dimensional aeroelastic systems involving a control delay

Many linear control laws, such as optimal controllers and classical controllers, have seen their applications to suppressing the aeroelastic vibrations of the high-dimensional aeroelastic system. However, those conventional control laws may not work effectively if the high-dimensional aeroelastic system involves a control delay. The paper reveals the effect of input time delay on the stability of a controlled high-dimensional aeroelastic system in an incompressible flow field and presents a new optimal control law to suppress the flutter of the high-dimensional aeroelastic system with an input time delay in the control loop. The procedure of designing the proposed control law includes three steps as follows. The first step is to convert the system described by a set of differential equations with a time delay into a set of difference equations involving discrete delay terms by using zero-order holder. The second step, exhibiting the novelty of the study, is to transform the difference equations with delay terms into a set of delay-free difference equations via a state transformation. The third step is to use the theory of linear control, say, the theory of Linear Quadratic Gaussian (LQG), to complete the design of controller by solving an equivalent Riccati equation. The paper demonstrates the efficacy of proposed method in designing the flutter suppression controller for a wind-tunnel model of Multiple-Actuated Wing. The new method works much better than classical feedback and conventional LQG controllers, both of which do not take the input time delay into account and may induce instability, when the input time delay becomes significant.

Robust Aeroelastic Control of a Thin-Walled Wing Structure with Model Uncertainty

AbstractThe robust vibration control and dynamic response analysis of an advanced aircraft wing structure are addressed in this paper. The wing structure is modeled as a thin-walled beam with fiber-reinforced composite materials featuring a circumferentially asymmetric stiffness (CAS) configuration that completely splits into two coupled groups of motion. The time-dependent external loads are considered with unsteady aerodynamics in an incompressible flow field. To demonstrate the robust characteristics of the sliding mode methods, both the conventional linear quadratic Gaussian (LQG) regulator and the proposed method are compared with respect to model uncertainty and external excitation. The numerical results demonstrate that the sliding mode control (SMC) on the basis of the sliding mode observer (SMO) is an efficient way to control the unstable dynamic response subjected to various external loads associated with model uncertainty.

New decentralized control technique based on substructure and LQG approaches

Decentralized control is more suitable for structural control of large-scale structures. In this paper, a new decentralized control technique is proposed based on the linear quadratic Gaussian (LQG) and substructure approaches. A large-scale structure is divided into a set of smaller substructures. Each substructure is controlled by its own local controller with interaction forces at substructural interfaces, which are considered as “unknown external inputs” to the substructure concerned. An algorithm of recursive least squares estimation for the unknown excitation is proposed. A numerical example of the decentralized control of a tall building is studied to illustrate the new proposed algorithm. Simulation results show that the proposed decentralized control provides satisfactory control performance when comparing with the conventional centralized LQG control algorithm and is viable for the future structural control of large-scale structures.

Human simulated intelligent control of vehicle suspension system with MR dampers

This paper presents vibration control responses of a controllable magnetorheological (MR) suspension system of a passenger car. The MR damper is designed and manufactured on the basis of the mixed-mode operation, and its time response is experimentally evaluated to integrate with the suspension model. After formulating the dynamic model of a half-car MR suspension system, a human simulated intelligent control (HSIC) scheme is developed to attenuate unwanted vibrations such as pitch angle acceleration. After verifying the effectiveness of the HSIC via computer simulation, the road test of the passenger car installed with four MR dampers is undertaken. The power spectrum densities of dynamic motions such as body acceleration and pitch angle acceleration are measured and analyzed. In addition, the control results obtained from the proposed HSIC are compared with those obtained from a conventional linear quadratic Gaussian (LQG) control method.

Active vibration control of structural systems by a combination of the linear quadratic Gaussian and input estimation approaches

This study proposes an active control method to suppress the responses of structural systems. The present control method is a synthesis algorithm of the linear quadratic Gaussian (LQG) and input estimation approaches. By using the synthesis method, structural vibrations can be suppressed more effectively due to the actions of the proper control forces. In this work, numerical simulations of active vibration control of lumped-mass systems are performed to verify the feasibility and effectiveness of the proposed algorithm. The simulation results demonstrate that the control performance of the present method for structures with external excitation forces is better than that of the conventional LQG approach.

Aeroelastic Response of Flapped-Wing Systems Using Robust Estimation Control Methodology

This paper concerns the active aeroelastic control of 3-D flap-wing systems exposed to gust and/or sonic boom in an incompressible flow field. This is achieved via implementation of a robust estimation capability (sliding mode observer: SMO), and of the use of the deflected flap as to suppress the flutter instability or enhance the subcritical aeroelastic response to gust or blast loads. To this end, a control methodology using LQG(Linear Quadratic Gaussian) in conjunction with SMO is implemented, and its performance toward suppressing flutter and reducing the vibrational level in the subcritical flight speed range is demonstrated. Moreover, its performances are compared with the ones provided via implementation of conventional LQG with Kalman filter.

An assessment of fuzzy logic vessel path control

A fuzzy logic controller for ship path control in restricted waters is developed and evaluated. The controller uses inputs of heading, yaw rate, and lateral offset from the nominal track to produce a commanded rudder angle. Input variable fuzzification, fuzzy associative memory rules, and output set defuzzification are described. Two maneuvering situations are evaluated: track keeping along a specified path where linearized regulator control is valid; and larger maneuvers onto a specified path where nonlinear modeling and control are required. For the track keeping assessment, the controller is benchmarked against a conventional linear quadratic Gaussian (LQG) optimal controller and Kalman filter control system. The Kalman filter is used to produce the input state variable estimates for the fuzzy controller as well. An initial startup transient and regulator control performance with an external hydrodynamic disturbance are evaluated using linear model simulations of a crude oil tanker. A fully nonlinear maneuvering model for a smaller product tanker is used to assess the larger maneuvers. The fuzzy controller exhibits promising performance and application flexibility.