Linear Quadratic Regulator Controller Research Articles

Lqr-Fuzzy Logic Control of a Quarter Vehicle Model

In this study, a new control rule was developed using two different control methods, and the results were discussed by applying the developed controller to the quarter vehicle model. A new hybrid controller was designed by considering the advantages of Fuzzy Logic control method and Linear Quadratic Regulator (LQR) control method. Control gain coefficients used in LQR controller were determined by fuzzy logic control method. The developed new controller has been applied to the quarter vehicle model. In the results, control with only Fuzzy Logic controller and developed LQR-Fuzzy Logic controller were compared. It was understood from the results that the developed control method was satisfactory.

Utilizing Linear Quadratic Regulator and Model Predictive Control for Optimizing the Suspension of a Quarter Car Vehicle in Response to Road Excitation

Utilizing Linear Quadratic Regulator and Model Predictive Control for Optimizing the Suspension of a Quarter Car Vehicle in Response to Road Excitation

Reinforcement Learning of a Six-DOF Industrial Manipulator for Pick-and-Place Application Using Efficient Control in Warehouse Management

This study investigates the integration of reinforcement learning (RL) with optimal control to enhance precision and energy efficiency in industrial robotic manipulation. A novel framework is proposed, combining Deep Deterministic Policy Gradient (DDPG) with a Linear Quadratic Regulator (LQR) controller, specifically applied to the ABB IRB120, a six-degree-of-freedom (6-DOF) industrial manipulator, for pick-and-place tasks in warehouse automation. The methodology employs an actor–critic RL architecture with a 27-dimensional state input and a 6-dimensional joint action output. The RL agent was trained using MATLAB’s Reinforcement Learning Toolbox and integrated with ABB’s RobotStudio simulation environment via TCP/IP communication. LQR controllers were incorporated to optimize joint-space trajectory tracking, minimizing energy consumption while ensuring precise control. The novelty of this research lies in its synergistic combination of RL and LQR control, addressing energy efficiency and precision simultaneously—an area that has seen limited exploration in industrial robotics. Experimental validation across 100 diverse scenarios confirmed the framework’s effectiveness, achieving a mean positioning accuracy of 2.14 mm (a 28% improvement over traditional methods), a 92.5% success rate in pick-and-place tasks, and a 22.7% reduction in energy consumption. The system demonstrated stable convergence after 458 episodes and maintained a mean joint angle error of 4.30°, validating its robustness and efficiency. These findings highlight the potential of RL for broader industrial applications. The demonstrated accuracy and success rate suggest its applicability to complex tasks such as electronic component assembly, multi-step manufacturing, delicate material handling, precision coordination, and quality inspection tasks like automated visual inspection, surface defect detection, and dimensional verification. Successful implementation in such contexts requires addressing challenges including task complexity, computational efficiency, and adaptability to process variability, alongside ensuring safety, reliability, and seamless system integration. This research builds upon existing advancements in warehouse automation, inverse kinematics, and energy-efficient robotics, contributing to the development of adaptive and sustainable control strategies for industrial manipulators in automated environments.

Comparative Analysis of the Performance of Linear Quadratic Regulator and State Feedback Control on DC-DC Shunt Boost Converter

In recent years, DC-DC converters, particularly shunt boost types, have become essential components in power systems, especially for applications requiring efficient voltage and current regulation. Proper control of these converters is crucial for ensuring optimal performance. This study analyzes two commonly used control methods: Linear Quadratic Regulator (LQR) and State Feedback Control for shunt boost DC-DC converters. LQR is known for its ability to minimize a cost function and optimize system performance, while State Feedback Control offers a simpler yet effective approach to system state control. Through MATLAB/Simulink-based simulations, this study evaluates the performance of both methods in terms of transient response, stability, and energy efficiency. The results show that LQR offers faster and more stable responses compared to State Feedback Control. However, the complexity of LQR in implementation makes it less practical than State Feedback Control, which is easier to apply in real-time applications

A Novel Approach to High Stability Engine Control for Aero-Propulsion Systems in Supersonic Conditions

In a supersonic state, the aero-engine operates under harsh circumstances of elevated temperature, high pressure, and rapid rotor speed. This work provides an innovative high-stability control technique for engines with fixed-geometry inlets, addressing stability control issues at the aero-propulsion system level. The discussion begins with the importance of an integrated model for the intake and the aero-engine, introducing two stability indices (surge margin and buzz margin) to characterize inlet stability. A novel predictive model for engine air mass flow is developed to address the indeterminate issue of engine air mass flow. The integration of input parameters in the predictive model is refined using the least squares support vector regression (LSSVR) algorithm, and historical input data is used to enhance predictive performance, as validated by numerical simulation results. A data-driven adaptive augmented linear quadratic regulator (d-ALQR) control technique is suggested to adaptively modify the control parameters of the augmented linear quadratic regulator. A highly stable control strategy is finally proposed, integrating the predictive model with the d-ALQR controller. The simulation results conducted during maneuvering flight operations demonstrate that the developed high-stability controller can maintain the inlet in an efficient and safe condition, ensuring optimal compatibility between the engine and the inlet.

Hybrid feedforward-feedback LQR controller based on model prediction for open channel water level control

ABSTRACT Linear quadratic regulator (LQR), as one of the most popular optimal feedback controllers, has been used in open-channel automatic control. However, existing hybrid feedforward-feedback controllers are simple combinations lacking consistency and neglect the potential of model prediction in the feedforward part. This paper presents a novel hybrid linear quadratic regulator (HLQR) controller with a feedforward-feedback structure. Rather than achieving feedforward control by compensation of discharge or volume, HLQR incorporates a water level prediction of the canal model into the conventional LQR, allowing consistent optimal control and flexible adjustment of weight coefficients in both feedforward and feedback parts. The designed hybrid controller can provide a simple effective way for canal control. It has been numerically tested in a test canal compared with the discharge compensation linear quadratic regulator (DCLQR). Results show that the proposed HLQR can reduce the water level fluctuations and shorten the transition time. The maximum absolute error of the water level can be reduced by 56.65%, the gate movement is decreased by 69.69%, and the transition time is cut down from 21.5 to 7.5 h. With outstanding control performance, the proposed HLQR controller can promote water distribution practically and flexibly, showing great potential in hydraulic control.

Study on lateral stability of distributed drive electric tractor semi-trailers under low adhesion road conditions

To improve the lateral stability of tractor-semitrailer under low adhesion road surface, a direct yaw torque control strategy considering longitudinal speed control was proposed based on distributed electric drive technology. A hierarchical control strategy was designed, with the upper layer using a linear quadratic regulator (LQR) controller to calculate the yaw moment. To distribute the longitudinal force and additional yaw moment, the torque distribution method was adopted based on quadratic programming in the lower controller. The co-simulation was conducted by Trucksim and Matlab/Simulink under the conditions of single lane change (SLC) of 110 km/h and double lane change (DLC) of 70 km/h. The results indicate that in comparison with the PID controller and the uncontrolled vehicle, the LQR controller improves the lateral stability of the vehicle on the low-adhesion road.

Rotationary feedback control of the cylinder wake flow using a linear dynamic model

This study presents an active feedback control of the Kármán vortex shedding flow past a circular cylinder at low Reynolds numbers. The cylinder's rotational motion functions as the control actuator, while the transverse velocities of points along the wake axis serve as the feedback signals. First, using the autoregressive with exogenous input method, a linear reduced-order model (ROM) for the unstable flow is developed to capture the input–output behavior between the cylinder's rotational displacement and the feedback signals. This model is then utilized for controller design using the proportional and linear quadratic regulator (LQR) control methods, respectively, with their effectiveness analyzed and validated through high-fidelity numerical simulations. The results show that both methods can effectively suppress the unstable vortex shedding flow, while proportional control exhibits strong sensitivity to monitoring point locations and time delays. The ROM-based model can accurately predict the stability characteristics of the control system, providing valuable guidance for selecting optimal feedback signals. Moreover, we show that by appropriately adjusting the phase angle between the control input and feedback signals via time delays, the performance of proportional control can be significantly enhanced. Lastly, based on the ROM, an output-feedback suboptimal control law is designed using the LQR method. This suboptimal feedback control transforms unstable fluid modes into stable ones, resulting in complete suppression of the unsteady vortex shedding. It is further revealed that the inherent mechanism of suboptimal flow control is to construct an optimal phase shift through the linear superposition of multiple feedback signals. Overall, model-based analysis results agree well with those obtained from direct numerical simulations, confirming the validity of the proposed ROM-based feedback control procedure.

The direct yaw-moment control based on adaptive fuzzy LQR for distributed drive electric vehicles

This paper introduced a hierarchical control strategy for direct yaw moment (DYC) to enhance the handling and stability of distributed drive electric vehicles (DDEVs) at medium to high speeds. The upper controller entailed a speed-following PI controller and an adaptive fuzzy linear quadratic regulator (AFLQR) controller, with the control objectives centered on reducing the absolute value of the sideslip angle and tracking the desired yaw rate. The proposed approach utilizes a fuzzy logic-based AFLQR controller, which could dynamically adjust the weighting parameters for sideslip angle and yaw rate in response to the vehicle speed and sideslip angle, offering better adaptability to varying driving conditions. At the lower control level, a tire-dynamic-load-based torque distribution method was applied. The control strategy’s efficacy was demonstrated through co-simulation involving CarSim and Simulink. This evaluation compared AFLQR control against non-yaw control, conventional LQR control and sliding mode control (SMC), focusing on handling and stability during sinusoidal steering wheel input test and double lane change maneuver. Results highlight that AFLQR reduces the sideslip angle by 7.88% and the yaw rate error by 84.29% compared to LQR, enhancing vehicle handling and stability. Lastly, a hardware-in-the-loop (HIL) experiment verified the control strategy’s validity.

Simulation and evaluation of lateral/directional dynamics in an aircraft autopilot control system

The objective of the research was to design and simulate the lateral/directional dynamics control of an aircraft’s autopilot system to automate the landing approach execution, complying with the requirements of the Instrument Landing System (CAT III C). The design methodology involved integrating a Linear Quadratic Regulator (LQR) with Affine Parameterization techniques to create a robust control system. The prototype was developed using Matlab and simulated in Simulink. Through various simulations, adjustments were made to the Q and R matrices of the LQR controller based on Bryson’s rule, allowing the system to adapt to the nonlinearities and dynamic constraints of the aircraft model. These adjustments included modifying the lateral attitude control parameters to achieve the desired damping factors and time constants, ensuring flight quality standards according to MIL-8785C. Validation under real conditions through a flight simulator confirmed the control system’s effectiveness under various operational conditions. The controllers are able to maintain the aircraft’s alignment with the runway centerline, even in the presence of external disturbances, thus demonstrating the system’s robustness and reliability. The methodologies and results provide a solid foundation for future improvements and comparative analyses of autopilot systems within CAT III C requirements.

Vehicle Attitude Control of Magnetorheological Semi-Active Suspension Based on Multi-Objective Intelligent Optimization Algorithm

A multi-objective intelligent optimization algorithm-based attitude control strategy for magnetorheological semi-active suspension is proposed to address the vehicle attitude imbalance generated during steering and braking. Firstly, the mechanical properties of the magnetorheological damper (MRD) are tested, and the parameters in the hyperbolic tangent model of the magnetorheological damper are identified through experiments. Secondly, a simulation model of the whole vehicle multi-degree-of-freedom vehicle dynamics including magnetorheological damper is established, and the whole-vehicle Linear Quadratic Regulator (LQR) controller is designed. Then, the optimization design model of the joint vehicle controller and vehicle dynamics is established to design the optimization fitness function oriented to the body attitude control performance, and the attitude optimal controller is calculated with the help of multi-objective intelligent optimization algorithm. Simulation results show that the proposed control method is able to improve the body roll angle, body pitch angle, and suspension dynamic deflection well on the basis of ensuring no deterioration in other performance indexes, ensuring good attitude control capability of the vehicle and verifying the feasibility of the control strategy.

Intelligent Driving Vehicle Trajectory Tracking Control Based on an Improved Fractional‐Order Super‐Twisting Sliding Mode Control Strategy

ABSTRACTAiming at resolving trajectory tracking control challenges during high‐speed lane changes in intelligent driving vehicles, an innovative fractional‐order sliding mode control approach is introduced in the present study. The control strategy comprises upper and lower‐level controls. First, the upper‐level control designs the vehicle trajectory tracking controller, integrating a non‐singular terminal sliding mode (NTSM) surface with a fractional‐order fast super‐twisted sliding mode control (FOF‐STSMC) algorithm. The NTSM surface properties ensure rapid convergence of the system tracking error to zero within a finite time, while the fractional‐order control extends the control system's regulation range and enhances algorithm flexibility. Additionally, the integration with the super‐twisting algorithm effectively mitigates oscillation issues in the control input, achieving a smooth input. Second, the lower‐level control aims to enhance vehicle driving stability. Utilizing the reference yaw rate, and sideslip angle and accounting for tire force saturation, a fractional‐order sliding mode control (FOSMC) algorithm is developed to compute the external yaw moment. Through dynamic load allocation, considering the vertical load for each tire, intelligent external yaw moment distribution significantly improves vehicle stability. Finally, the results of the Carsim–Simulink co‐simulation demonstrate that, compared to the STSMC strategy, the FOSMC strategy with front‐wheel‐only steering, and the linear quadratic regulator (LQR) control strategy, the proposed control strategy in this paper reduces the tracking error by 77%, 61%, and 58%, respectively, achieving more precise and stable trajectory tracking under high‐speed conditions.

Compact Analysis of the Necessity of Padé Approximation for Delayed Continuous-time Models in LQR, H-Infinity and Root Locus Control Strategies

This paper presents a comprehensive analysis of the need for the Padé approximation for continuous-time models with delays, focusing on its critical role in addressing the control challenges posed by time delays. Time delays, often referred to as dead times, transport delays or time lags, are inherent in a wide range of industrial and engineering processes. These delays introduce phase shifts that degrade control performance by reducing control bandwidth and threatening the stability of closed-loop systems. Accurate modelling and compensation of these delays is essential to maintain system stability and ensure effective control. This paper highlights the difficulties that arise when using advanced control techniques such as root locus (RL), linear quadratic regulator (LQR) and H-infinity (H_∞) control in systems with delays. Representing delays in exponential form leads to an infinite number of state problems, complicating the design and analysis of controllers in such systems. To address these challenges, the Padé approximation is proposed as an effective method for approximating time delays with rational polynomials of appropriate order. This approach allows for more accurate simulation, system analysis and controller design, thereby mitigating the problems caused by delays. The paper also provides a detailed comparative analysis between the Padé approximation and Taylor polynomials, demonstrating the superiority of the former in achieving accurate delay modelling and control performance. The results show that the use of Padé approximation not only improves the accuracy of system models, but also improves the robustness and stability of control strategies such as RL, LQR, and H_∞. These results highlight the importance of the Padé approximation as a valuable tool in the design of delay-affected control systems, offering significant advantages for both theoretical and practical applications.

Adaptive Neural Delay Feedback Control of a Typical Robot on a Slope

ABSTRACTIn this article, an adaptive neural delay feedback control strategy is proposed for the motion control of a two‐wheel self‐balancing robot (TWSBR) on a slope with an input delay. Based on the Lagrange equation, the dynamic model of the robot is derived. Given a target trajectory vector, the corresponding error system is obtained. An input delay and uncertainties are considered. First, the system with an input delay is transformed into a delay‐free one. Second, a quadratic performance optimization criterion is defined, and a linear quadratic regulator (LQR) controller is designed to minimize the error between the system's state vector and the target vector. Thirdly, an integral sliding mode controller is added to the LQR controller to enhance the system's robustness. To reduce the “chattering” phenomenon, an adaptive neural delay feedback control scheme is developed based on the adaptive learning of the uncertainties' upper bound by a radial basis function neural network (RBFNN). It is demonstrated that a relaxation process exists at the beginning of the upslope motion. As the input delay increases, the swing range of the center of gravity of the pendulum expands. The angle can converge to the steady state more quickly, but the relaxation time is still 0.031 s which has nothing to do with the input delay. An example of the back‐and‐forth motion of a TWSBR on a slope can verify an excellent agreement between theoretical analysis and numerical results.

Optimal DMD Koopman Data-Driven Control of a Worm Robot.

Bio-inspired robots are devices that mimic an animal's motions and structures in nature. Worm robots are robots that are inspired by the movements of the worm in nature. This robot has different applications such as medicine and rescue plans. However, control of the worm robot is a challenging task due to the high-nonlinearity dynamic model and external noises that are applied to that robot. This research uses an optimal data-driven controller to control the worm robot. First, data are obtained from the nonlinear model of the worm robot. Then, the Koopman theory is used to generate a linear dynamic model of the Worm robot. The dynamic mode decomposition (DMD) method is used to generate the Koopman operator. Finally, a linear quadratic regulator (LQR) control method is applied for the control of the worm robot. The simulation results verify the performance of the proposed control method.

A Linear Quadratic Regulation Controller Based on Radial Basis Function Network Approximation

This paper proposes a linear quadratic regulation (LQR) tracking control method based on a radial basis function (RBF) that successfully compensates for the shortcomings of the LQR method. The LQR method depends on the linearity of a model. Specifically, an RBF neural network is used to approximate and compensate for the nonlinear part of a controlled object in the PID type-I, type-II and type-III control loops to improve the performance of the system. Through the simulation of different industrial systems, such as underdamped, overdamped and critically damped systems, the method significantly improves the dynamic response performance indices, such as the rise time and settling time, of the system.

Optimal shift control for new dual-clutch full-powershift transmission of heavy-duty tractor based on genetic algorithm–particle swarm optimization

The calculation of a linear quadratic regulator (LQR) control weighting matrix determines whether it can achieve optimal control. In order to solve the problem of complex calculation and low efficiency of this matrix, this paper proposed genetic algorithm–particle swarm optimizatio algorithm (GAPSO) combining genetic algorithm and particle swarm algorithm to solve the weighting matrix of LQR clutch oil pressure control strategy, so as to control the design efficiency and precision of the strategy. Subsequently, the shifting quality of a tractor was improved. A dynamic model of the shifting process was established using a comprehensive indicator that combined jerk and sliding friction work as a quadratic function. An LQR-weighted matrix calculated using GAPSO enabled optimal control strategy designing for clutch hydraulic pressure. Furthermore, the shift process from the 11th to 12th gear was analyzed via simulations during plowing operations. The simulation results show that the genetic operation of crossover and variation is introduced into PSO, and the optimization ability of PSO is improved effectively. Compared with the clutch oil pressure control strategy calculated by GAPSO with LQR weighted matrix and LQR clutch oil pressure control strategy calculated by PSO with LQR weighted matrix, the clutch heat load is slightly increased, the smoothness of shifting is greatly improved, and the shifting quality of tractors is improved. Overall, this study provides valuable insights for designing and computationally analyzing optimal clutch LQR control.

Semi-active vibration control via a magnetorheological damper and active disturbance rejection control

This work provides an alternative for the semi-active vibration control problem via state feedback plus an active disturbance rejection control (K-ADRC) for a multistory building structure equipped with one magnetorheological damper (MRD) located between the ground and the first story. This control law introduces a disturbance observer (DOB) to estimate the total disturbance in real time, produced by the earthquake perturbation, unmodeled dynamics, and parametric uncertainties, and then cancel their effect using a part of the control signal. Moreover, using a diffeomorphism, the K-ADRC provides a proportional derivative (PD) controller designed to improve internal stability. A prominent feature of the active disturbance rejection control (ADRC) algorithm is that the value of the DOB gain is selected according to the system bandwidth. The stability of the system is verified via Lyapunov analysis. Moreover, the building structure model and the MRD are accomplished by incorporating a nonlinearity state that represents the hysteresis effect to perform real behavior in addition to assuming that acceleration is the only available measurement of building structures. Thus, integral filters are provided based on the appropriate cut-off frequency to estimate displacement and velocity, avoiding bias, offset, and phase shifts. Experimental results from a reduced-scale two-story building prototype demonstrate that the proposed K-ADRC is promising for real applications, and it has better performance than the state feedback (K) and the linear quadratic regulator (LQR) control techniques.

Real‐Time Implementation of Unknown Input Observer‐Based State and Unknown Disturbance Estimation for Series Active Filters

ABSTRACTSeries active filter (SAF) is generally utilized in compensating harmonic voltage source‐type loads. In this paper, a combined action of controller and observer is proposed for SAF. Full state feedback (SFB) and linear quadratic regulator (LQR) controllers are posited in order to estimate states, and fault. SFB utilizes the pole placement method, whereas LQR utilizes the tuning of matrices by Bryson's rule. Luenberger observer (LO), proportional–integral observer (PIO), and unknown input observer (UIO) were also designed. The efficacy of this scheme is illustrated through the simulations, in the presence of faults. The state dynamics of SFB‐ and LQR‐based control of SAF with LO, PIO, and UIO in different faulty cases are compared. It can be clearly seen through simulations that the state dynamic response of LQR‐based control of SAF is faster when compared to SFB‐based control of SAF in both cases. Further, LO and PIO established a steady‐state error between the actual state and its estimate, with reference to desired input, in the presence of a fault. UIO perfectly tracked the desired input, even in the presence of various unknown fault, when compared to LO and PIO. Furthermore, UIO also estimates the unknown faults better when compared to PIO. Finally, in a dynamic operating scenario, the effectiveness of the suggested control strategy has been assessed and verified using MATLAB/SIMULINK and the output of a real‐time simulator (OPAL‐RT OP4510).

A Fractional-Order Model Predictive Control Strategy with Takagi–Sugeno Fuzzy Optimization for Vehicle Active Suspension System

Aiming at the problem of system controller performance failure caused by improperly setting the value of each weighting coefficient of the model predictive control (MPC), a fractional-order MPC strategy with Takagi–Sugeno fuzzy optimization (T–SFO MPC) is proposed for a vehicle active suspension system. Firstly, the fractional-order model predictive control framework for active suspension systems is designed based on a 1/4 vehicle model. Then, we analyze the influence of different weighting coefficients on the suspension performance and introduce the Takagi–Sugeno fuzzy optimization theory to adaptively adjust the weighting coefficients of the fractional-order MPC controller. Finally, the system responses of the T–SFO MPC, traditional MPC, linear quadratic regulator (LQR), and passive suspension control are numerically analyzed under various road conditions. Simulation results show that suspension response with the T–SFO MPC is significantly improved compared with passive suspension control, traditional MPC control, and LQR control, and the weight coefficients of the T–SFO MPC can be adaptively adjusted according to the dynamic changes of suspension response. Compared with passive suspension, the root mean square (RMS) value of the vertical acceleration of the T–SFO MPC under various roads decreased by a maximum of 37.97%, and the RMS value of suspension dynamic deflection and tire dynamic load decreased by a maximum of 32.94% and 37.8%, respectively. These results validate that the proposed control method can achieve coordinated optimization of vehicle comfort and handling stability.