Linear Quadratic Regulator Controller Research Articles

Active Vibration Control of Flexible Structures with Super-Coiled Actuators

Flexible structures show low natural frequencies and light damping and often suffer from various dynamic loads, leading to low-frequency vibrations. Active vibration control is necessary for precision operation and long-term service of such structures, and a flexible actuator with a large actuation force and stroke is a key limitation. In this paper, super-coiled (SC) actuators, fabricated from fibers by twisting and inserting, were introduced to actively suppress the low-frequency vibration of flexible structures. Two SC actuators were symmetrically mounted on both surfaces of a cantilever beam to generate actuation forces. The force model of thermally driven SC actuators was developed, and a dynamic model of a cantilever beam with SC actuators was then proposed and validated via experimental actuation. Three types of control strategies, open loop, velocity negative feedback, and linear quadratic regulator (LQR), were adopted for vibration suppression. The results show that the proposed model fits quite well with the experimental data, and the maximum error between the experiment and the prediction is 3.90% among various driven currents. In velocity negative feedback control and LQR control, a 91.83% reduction of dynamic response is achieved, which validates the feasibility of using the actuator for low-frequency vibration control.

A Model-Based Control of Self-Driving Car Trajectory for Lanes Change Maneuver in a Smart City

High-quality computer control of autonomous vehicles in various environments is a priority for cyber-physical systems (CPS), Industry 4.0, and the global economy as a whole. The paper discusses the linearized control model of a Self-Driving Car (SDC) with a weight of 1160 kg. For safe maneuvering with obstacle avoidance, we employ an optimal control by Linear Quadratic Regulator (LQR) using a Simulink/MATLAB environment that is capable to demonstrate the satisfiability of LQR control for this maneuver using a 3D simulation environment under changing urban conditions in a smart city. This controller is easy for engineering implementation.

Microvibration Control of Hybrid Platform for High-Tech Equipment in Buildings Using Brain Emotional Learning-Based Intelligent Controller

In the semiconductor industry, the vulnerability of high-tech facilities installed on platforms to ground excitations induced by nearby traffic is significantly pronounced, primarily due to their small-scale dimensions. Consequently, it is imperative to design a smart control technique by effectively utilizing model-free controllers. Recently, adaptive intelligent control algorithms have emerged as a viable alternative to conventional model-based control algorithms. To address this issue, this study meticulously designed a hybrid platform using the adaptive intelligent controller known as the brain emotional learning-based intelligent controller, along with a Sugano fuzzy inference system to effectively optimize the controller’s learning parameters. These learning and intelligent-based algorithms offer notable advantages, including the ability to handle nonlinearity, uncertainty, and training capabilities within the control systems. To assess the effectiveness of the proposed controller in mitigating vibrations induced by traffic on high-tech facilities, a three degree-of-freedom structure is employed along with the hybrid platform. Finally, the performance of the hybrid platform in terms of microvibration control levels is meticulously validated using the Bolt Beranek Newman vibration criteria. Simulation results unequivocally demonstrate that the proposed controller outperforms both an uncontrolled system and a traditional linear quadratic regulator controller in terms of reducing the traffic-induced response of the hybrid platform and second floor, respectively. Through the integration of learning and intelligent-based controllers, the velocity levels of both the hybrid platform and the second floor are reduced to approximately 49.02% and remain well within the acceptable standard criteria curves.

A novel collaborative control algorithm for maximum power point tracking of wind energy hydraulic conversion system

AbstractWind has been admitted as one of the most promising renewable energy resources in multinational regionalization policies. However, the energy conversion and utilization are challenging due to the technique reliability and cost issues. Hydraulic wind turbine (HWT) may solve the above problems. HWT is taken as a research object, and the maximum power point tracking (MPPT) control strategy is proposed collaborating with active disturbance rejection control (ADRC) and linear quadratic regulator (LQR) control methods, to solve multiplicative nonlinearity problems in the plant models and the influence of external disturbance on control performance in the MPPT control process. A nonlinear simulation model is built to explain the main findings from the experiments and obtain a better understanding of the effect of time‐varying system parameters and random fluctuation in wind speed. The collaborative control algorithm is experimentally verified on a 24‐kW HWT semi‐physical test platform that results in a promising energy conversion rate, plus the hydraulic parameters can satisfy the demand, accordingly. Ultimately, the potential challenges of implementing this technique in a smart wind energy conversion system are discussed to give a further design guidance, either theoretically or practically.

Strong fixed-time dynamic inverse adaptive LQR integrated control strategy for dynamic positioning of ship

To ensure compositive capacities for dynamic positioning ship, a dynamic inverse adaptive linear quadratic regulator (DI-ALQR) control strategy is proposed for dynamic positioning ship based on strong fixed-time prescribed performance function (SFPPF) and cascaded fixed-time extended state observer (CFESO). Firstly, a high-fidelity four degree of freedom ship motion model including roll motion is constructed, and an inverse system of the ship is proposed to realize decoupling of variables and pseudo linearization of control systems. Next, the SFPPF is employed to ensure prescribed performance with predefined convergence. The DI-ALQR control strategy is presented to achieve integrated control of position, roll and heading of ship considering the balance between energy consumption and control accuracy. Simulation results and analysis prove that the proposed control strategy makes the position, roll and heading of ship reach in predefined-time and maintain the desired values, which ensures prescribed performance.

Optimal guidance law design for three-dimensional trajectory tracking of missiles based on fixed-gain disturbance observer

To address the trajectory tracking problem of missiles, an optimal disturbance rejection guidance law (ODRGL) in three dimensions is proposed under the premise of uncontrollable speed. Error models of the actual and the reference trajectory are built in channels of pitch and yaw, respectively. In the yaw channel, a modeling error is introduced as the model cannot be built directly. According to the separation theorem, the controller and the observer are designed respectively. A fixed-gain disturbance observer (FGDO) is proposed to estimate the disturbance such as wind disturbances and modeling errors, and the disturbance is compensated for feed-forward. The nominal error models of pitch and yaw channels are linearized by the differential geometric linearization theory, and then linear quadratic regulator (LQR) controllers are designed for the linearized models. The simulation results show that in the presence of wind disturbances and modeling errors, the optimal guidance law proposed in this paper can stabilize the original nonlinear system and ensure energy optimization.

Finding the LQR Weights to Ensure the Associated Riccati Equations Admit a Common Solution

This paper addresses the problem of finding the linear quadratic regulator (LQR) weights such that the associated discrete-time algebraic Riccati equations admit a common optimal stabilising solution. Solving such a problem is key to designing LQR controllers to stabilise discrete-time switched linear systems under arbitrary switching, or stabilise polytopic systems (e.g., Takagi-Sugeno fuzzy systems and linear parameter varying systems) in the entire operating region. To ensure problem tractability and reduce the searching space, this paper proposes an efficient framework of finding only the state weights based on the given input weights. Linear matrix inequality conditions are derived to conveniently check feasibility of the problem. An iterative algorithm with quadratic convergence and low computational complexity is developed to solve the problem. Efficacy of the proposed method is illustrated through numerical simulations of systems with various sizes.

Optimal Coordinated Control for Speed Tracking and Torque Synchronization of Rigidly Connected Dual-Motor Systems

Dual-motor systems have been broadly used to drive large inertia loads. In this article, the optimal coordinated control problem of rigidly connected permanent magnet synchronous motor (PMSM) systems is investigated to enhance the speed tracking and torque synchronization performance. First, the mathematical model of rigidly connected dual-PMSM systems is established in terms of the model of the PMSM and the characteristics of gear transmission drive. Second, to minimize the speed tracking and torque synchronization errors, a novel optimal coordinated control scheme is proposed for rigidly connected dual-PMSM systems by combining the conventional master–slave control structure and the linear–quadratic regulator control strategy. Then, taking into account the inherent two-time-scale characteristics, a composite suboptimal coordinated controller is devised through optimal problems of slow and fast subsystems. Furthermore, the closed-loop stability is proved by singular perturbation theory. Finally, simulation and experimental studies are provided to corroborate our theoretical results. It is shown that the proposed method can effectively improve the speed tracking and torque synchronization performance of the rigidly connected dual-PMSM system simultaneously.

Lnertia Weight-free Particle Swarm Optimization in Optimal Control Design for Vehicle Active Suspension Systems

Vehicle active suspension systems play an important role in ride comfort and driving safety. This study considers the problem of an efficient control scheme design for vehicle active suspension systems. The active suspension systems aim to get more comfortable riding and good handling for random road disturbances. The purpose of this work is to reduce the driver’s entire body acceleration and thereby improve ride comfort. The inertial weight-free particle swarm optimization (PSO) method is utilized to obtain weighting matrices of the optimal control namely linear quadratic regulator (LQR) for the active suspension systems. The designed state-feedback controller is applied to the quarter-car suspension system under different road profiles. Simulation results of the inertia weight-free PSO-tuned LQR are compared with the results of the classical-tuned controller and standard PSO-tuned LQR controller to show the effectiveness.

Design of Active Disturbance Rejection Controller for Trajectory-Following of Autonomous Ground Electric Vehicles

In this paper, the concept of symmetry is utilized in the promising trajectory-following control design of autonomous ground electric vehicles—that is, the construction and the solution of active disturbance rejection controllers are symmetrical. This paper presents an active disturbance rejection controller (ADRC) for improving the trajectory-following performance of autonomous ground electric vehicles (AGEV) with an advanced active front steering system. Since AGEV trajectory dynamics are inherently affected by complex traffic conditions, various driving maneuvers, and other road environment, the main control objective is to deal with the AGEV trajectory control challenges of system uncertainties, system nonlinearities, and external disturbance. First, the vehicle dynamics trajectory-following model and its state space representation system are established. Then, the augmented control-oriented vehicle-trajectory-following system with dynamic error is developed. The resulting active disturbance rejection controller of the vehicle-trajectory-following system is finally designed using the trajectory performance index and active disturbance compensation, and the stability of the active disturbance rejection controller is also analyzed and derived via Lyapunov stability theory. The effectiveness of the proposed controller is validated through double lane change and serpentine maneuvers under the co-simulation platform of MATLAB/Simulink-Carsim®. Simulation results show that the designed controller provides enhanced vehicle-trajectory-following performance compared to the linear quadratic regulator controller (LQR) and model predictive controller (MPC). It will provide a certain guidance for the controller engineering design of the AGEV trajectory-following system.

Integrated optimal control of distributed in-wheel motor drive electric vehicle in consideration of the stability and economy

From the perspective of handling stability and economy, this paper brings forward an integrated optimal control scheme of distributed in-wheel motor drive electric vehicles (IWMDEV). A linear quadratic regulator (LQR) controller is presented according to nominal model and ideal motions firstly. To tackle the uncertain parameters and random disturbance, a novel robust optimal (RO) control strategy is further proposed to design the top level controller by employing the combination of optimal control and high order sliding mode control. By virtue of the integral and terminal sliding mode surface, the resulting robust optimal control method can not only achieve better performance, but also converge in finite time without chattering phenomenon. As for the bottom level controller, an optimal algorithm is developed to determine the weights for each term in objective function of torque allocation dynamically and coordinate the relationship between driving safety and energy-saving performance timely. Finally, joint simulations are carried out. In comparison with LQR control strategy, the results demonstrate that the proposed control scheme could ensure the robustness and effectiveness in the presence of parametric perturbation and external disturbance. Moreover, the torque allocation algorithm, which considers both handling stability and energy consumption, proves to be an effectual approach.

Research on High-Speed Catamaran Motion Reduction with Semi-Active Control of Flexible Pontoon

A high-speed catamaran with a suspension system and flexible pontoons to reduce motion is proposed, and the vertical motion characteristics of the vessel are investigated. The results demonstrate that altering the stiffness of the flexible pontoon can significantly alter the motion characteristics of a high-speed vessel when subjected to wave excitation. The maximum relative error between the theoretical and experimental values of the vertical dynamic characteristics of the flexible pontoon, considered as a gas spring, is 10.5%. The vertical force exerted by the pontoon exhibits nonlinear behavior in response to compression, yet displays approximately linear behavior within its primary operational range. The design of the Linear Quadratic Regulator controller, utilizing genetic algorithm optimization, avoids the issue of subjectively setting weight coefficients typically found in traditional control systems. This approach achieves the objective of determining the optimal feedback matrix within specified constraints. Simulation results illustrate that the LQR controller developed using genetic algorithm significantly enhance the semi-active suspension performance compared to the passive suspension system. The Root Mean Square value of the main cabin acceleration is reduced by 85.82%, simultaneously reducing the RMS value of the suspension dynamic travel by 85.03% and the RMS value of the pontoon dynamic displacement by 24.42%. These outcomes thoroughly substantiate the effective reduction in vertical motion, effectively attenuating the motion of high-speed vessels under wave excitation.

Initial validation of a closed loop filter and controller approach for active stabilization of thermomechanical distortions

Increasing technological progress in space technology is accompanied by an increased demand for accuracy. The alignment of optical instruments or antennas on the satellite platform requires structural stability that can no longer be achieved with traditional, passive methods, such as the use of materials with high stiffness or low coefficient of thermal expansion. Within the Infrared Astronomy Satellite Swarm Interferometry (IRASSI) project, an approach to actively stabilizing structures against low-frequency periodic heat induced deformations has been developed and simulated. In this study, the basic functionality of that thermomechanical FEM model is demonstrated by means of the thermal transfer functions between the changes in the applied heat and the resulting temperature changes, as well as a closed loop filter and controller approach consisting of a Linear Quadratic Regulator (LQR) and a Kalman filter. For this purpose, an experimental setup consisting of an aluminum plate with 14 temperature sensors, four heating elements for controlling the structure and one heating element for simulating the perturbation is used. The evaluation of the thermal transfer functions in the model compared to the experimental setup shows a deviation of the phase shift of less than 0.6% and an amplitude shift of less than 3.5% on average. A Kalman filter processes the temperature measurement in order to obtain an optimal estimate for the LQR controller, which then calculates the necessary change in the heating power of the four control heating elements to minimize the displacements at the desired two positions in x- and y-direction. The verification is performed by a camera system as an external validation tool, which is able to resolve micron-scale displacements by measuring the spatial displacement of a speckle pattern applied to the structure using sub-pixel accurate image correlation algorithms. While the range of values of the amplitudes of the displacements is 8.93 μ in the uncontrolled case, an improvement of more than 4.6dB could be achieved by applying the filter and controller system. Thus, it is demonstrated that this method has the potential to further improve already highly stable structures or to make lighter and cheaper materials with poorer passive stability values usable through active structural stabilization.

Intelligent Power Control of Inverter Air Conditioners in Power Systems: A Brain Emotional Learning-Based Approach

Inverter air-conditioning (IAC) units have been proved to be effective in frequency regulation by providing flexible capacities. This paper proposes a brain emotional learning (BEL)-based controller to provide the IACs with control signals to be efficiently involved in the frequency regulation in power systems. The BEL-based controller can learn quick-auto, making it appropriate in systems facing uncertainty. To assess the BEL controller performance in realistic conditions, the uncertainties as a consequence of variations in system parameters and load level are considered. The goal is to use the BEL controller to increase the IAC units' ability to track regulation signals accurately in uncertain circumstances. The controller is compared to a fuzzy-PI control, a proportional control scheme, a model predictive control and a linear quadratic regulator control. A delay-dependent stability criterion is used to calculate the highest time delay in the IACs response under which the system maintains stability. In addition, this paper presents an BEL-based coordinator to coordinate the IACs and traditional generation units for compensating considerable frequency variations caused by the time delays. Case studies are accomplished on a multi-area power system in MATLAB/Simulink environment. Eventually, real-time verifications by OPAL-RT real-time digital simulator on the simulated power system are executed to assess the control method.

Stability Analysis of Lane-Keeping Assistance System for Trucks under Crosswind Conditions

To enhance the control accuracy of lane-keeping assistance systems for trucks encountering crosswind-induced lateral deviations to improve the lateral stability of the vehicle, this study proposes a control strategy based on a linear quadratic regulator (LQR) using a path-tracking preview model. First, the lateral deviation is calculated using the path-tracking preview model. Then, an observer for the vehicle’s sideslip angle is designed using a vehicle lateral tracking deviation model and a Kalman filter controller, and this is used to solve the deviation of the sideslip angle. Finally, a feedforward controller is designed based on the LQR controller and a linear two-degrees-of-freedom vehicle model to eliminate steady-state errors arising from LQR optimization, thereby obtaining the steering angle of the vehicle when subjected to crosswind conditions. Comparing the test results of the sideslip angle, yaw rate, and lateral acceleration demonstrates that this strategy effectively improves the control accuracy of lane-keeping under crosswind conditions. The proposed method is validated through hardware-in-the-loop experiments on a test bench, yielding results consistent with simulations.

Design of Linear Quadratic Regulator Based on Genetic Model Reference Adaptive Control

As the conventional control system is a controller that controls or regulates the dynamics of any other process. From time to time, this control system may not behave appropriately online; this is because of many factors like some variation in the dynamics of the process itself or unexpected changes in the environment, or even undefined parameters of the system model. To overcome the problem above, an adaptive controller is designed and implemented. This paper discusses the design of a controller for a ball and beam system with Genetic Model Reference Adaptive Control (GMRAC) for adaptive mechanism with the MIT rule. Parameter adjustment (selection) should be done using optimization methods in order to obtain an optimal performance, so genetic algorithm. (GA) will be used as an optimization method to obtain the optimum values for these parameters. As the controller, a Linear quadratic regulator (LQR) controller will be used as it is one of the most popular controllers, the performance of the proposed controller with the ball and beam system will be carried out with MATLAB Simulink in order to evaluate its effectiveness. The results show satisfactory performance where the position of the ball tracks the desired model reference.

Tracking and Vibration Control with a Parallel Structure Controller Based on a Flexible Ball Screw Drive System

In this paper, we present a parallel structure controller for flexible ball screw drive systems with dynamic variations mainly caused by variations in table position and workpiece mass. The controller consists of two parts: a linear quadratic regulator (LQR) controller with the aim of tracking reference trajectories with high response and accuracy and an interpolated gain-scheduled controller used to restrain system vibration. To damp out the varied resonant modes, the controller is obtained by a set of μ-synthesis linear time-invariant (LTI) controllers interpolated via Youla parameterization. Comparison experiments are conducted to confirm the performance of the proposed controller with a ball screw drive experimental setup. We demonstrate that the parallel structure controller achieves high performance in tracking, vibration suppression and disturbance rejection.

A Generalized Hamilton Robust Control Scheme of Trajectory Tracking for Intelligent Vehicles.

To ensure the accuracy and stability of intelligent-vehicle-trajectory tracking, a robust trajectory-tracking control strategy based on generalized Hamilton theory is proposed. Firstly, a dynamic Hamilton dissipative controller (DHDC) and trajectory-tracking Hamilton dissipative controller (TTHDC) were designed based on the established vehicle-dynamics control system and trajectory-tracking control system using the orthogonal decomposition method and control-switching method. Next, the feedback-dissipative Hamilton realizations of the two systems were obtained separately to ensure the convergence of the system. Secondly, based on the dissipative Hamilton system designed by TTHDC, a generalized Hamilton robust controller (GHRC) was designed. Finally, the co-simulation of Carsim and MATLAB/Simulink was used to verify the effectiveness of the three control algorithms. The simulation results show that DHDC and TTHDC can achieve self-stabilizing control of vehicles and enable certain control effects for the trajectory tracking of vehicles. The GHRC solves the problems of low tracking accuracy and poor stability of DHDC and TTHDC. Compared with the sliding mode controller (SMC) and linear quadratic regulator (LQR) controller, the GHRC can reduce the lateral error by 84.44% and the root mean square error (RMSE) by 83.92%, which effectively improves the accuracy and robustness of vehicle-trajectory tracking.

A new linear quadratic regulator model to mitigate frequency disturbances in the power system during cyber-attack

<span lang="EN-US">This paper proposes a new model integrating a linear quadratic regulator (LQR) controller to mitigate frequency disturbances in the power system during cyber-attack, called as linear quadratic regulator to mitigate frequency disturbances (LQRMFD). As we know, most of the existing models have a common problem with achieving significant performances in mitigating dynamic response parameters, such as frequency deviation and settling time. However, the key aspect of LQRMFD is to mitigate the above issues with remarkable performance improvements. An uncommon and stable power system model has been considered in LQRMFD first to reach such a goal. A numerical problem has been solved to derive a certain characteristic equation, where the Routh-Hurwitz array criterion is applied for determining the stability of such a power system. After that, a state-space equation is developed from the power system to activate the LQR controller. Thus, achieving diversity and eliminating the redundancy of the power system considered can be obtained in LQRMFD. To evaluate the performance of LQRMFD, a series of experiments was conducted using the MATLAB-Simulink tool. Rigorous comparisons were also made among the results of LQRMFD, self-implemented and existing models. Furthermore, a detailed analysis was reported among those models to find the performance improvement of LQRMFD in percentage.</span>

A study on PMSM drive systems fed by multi-level inverter using linear quadratic regulator control for electric vehicle applications

This paper presents research on a permanent magnet synchronous motor (PMSM) by a 5-level T-type inverter using linear quadratic regulator (LQR) control for speed control. The space vector modulation (SVM) structure for the 5-level T-type inverter to improve the control quality of the PMSM drive system is presented. This paper aims to successfully design a state feedback controller to control motor speed in a permanent magnet synchronous motor drive system. Simulink results are performed with different speed ranges and the same torque load. These results will focus on evaluating quality when the PMSM drive operates at all speeds. MATLAB/Simulink proves the results.