Linear Quadratic Regulator Algorithm Research Articles

A Hybrid Data-Driven and Model-Based Approach for Leak Reduction in Water Distribution Systems Using LQR and Genetic Algorithms

This paper presents a pressure management technique for the reduction of leaks considering as a case study a branched water distribution system. The proposed technique is based on the detection and location of the leak using a genetic algorithm (GA) and pressure control using a Linear Quadratic Regulator (LQR). The validation of the proposed method uses measured pressure and flow data from a laboratory-scale water distribution system and its dynamic model.

Advanced seismic control strategies for smart base isolation buildings utilizing active tendon and MR dampers

This paper investigates the seismic behaviour of a five-storey shear building that incorporates a base isolation system. Initially, the study considers passive base isolation and employs a multi-objective archived-based whale optimization algorithm called MAWOA to optimize the parameters of base isolation. Subsequently, a novel model is proposed, which incorporates an interval type-2 Takagi-Sugeno fuzzy logic controller (IT2TSFLC) utilizing clustering techniques. The building includes Magneto-rheological (MR) dampers installed at the base isolation level and two active tendons positioned on the first and second storeys of the structure. The semi-active control force of the base isolation with MR dampers is determined by the fuzzy system, while the active control force for the active tendons is computed using the linear quadratic regulator (LQR) algorithm, enabling control force provision during seismic events. The primary objective of this model is to enhance the seismic control of the building. Therefore, it is classified as a proposed model. The structural system is subjected to seismic analyses, considering three different structural configurations: uncontrolled, equipped with passive base isolation, and equipped with semi-active base isolation combining MR dampers and active tendons. The findings of the research demonstrate that by considering the optimization of parameters of the passive base isolation based on the white noise scenario and using these parameters as design parameters, during seismic analysis of the structure in some earthquakes, increased structural responses were observed when compared to uncontrolled structure, highlighting a potential risk. Nevertheless, the proposed system effectively addresses this drawback of passive control systems by markedly reducing structural responses, as compared to both passive base isolation and uncontrolled structure. These results suggest that the proposed system is an effective solution for mitigating seismic risks in structural seismic control.

Wavelet LQR based gain scheduling for power regulation and vibration control of floating horizontal axis wind turbine with double-pitched rotor

This paper introduces a wavelet-based linear quadratic regulator (LQR) control strategy for double-pitched rotor systems of an offshore horizontal axis wind turbines. A comprehensive aero-servo-elastic model incorporating bending-torsion coupling is developed to assess the performance of the proposed controller under combined turbulent wind and wave loading. The weight matrices of the classical LQR algorithm are optimized using a nonlinear optimization scheme. Additionally, frequency-dependent gain scheduling is proposed using wavelet transform where the analytic Morse wavelet serves as the basis function. The resulting LQR algorithm operates in the time-frequency domain and solves scale-dependent Algebraic Riccati equations to determine optimal gains. Numerical simulations demonstrate the superior performance of the proposed gain scheduling compared to the classical LQR approach. The effectiveness of the algorithm is evaluated across various flow conditions and wind-wave misalignment, with benchmark results used for performance comparison.

GA tuned LQR controller for active vibration control of a rotor bearing system using piezoelectric actuators

This paper proposes a vibration identification method based on a Genetic Algorithm (GA) to improve the reliability of rotating machinery by effectively controlling rotor vibrations. The classical active control approach, known as the Linear Quadratic Regulator (LQR) control algorithm, is influential in this regard but heavily depends on specific parameters. However, using a predetermined set of parameters may not suffice to address the diverse vibration control needs of different rotating systems. To address this issue, an active vibration control system employing flexible piezoelectric patches attached to the external surface of the rotating shaft, functioning as actuators, is designed. These patches are individually supplied with actuation voltages. Through a numerical example, the effectiveness of the proposed system is validated. The numerical results demonstrate a significant reduction of the amplitude of the unbalance response, with a reduction of 79% at the first critical speed during a steady-state condition and 75% during run-up. The numerical findings underscore the effectiveness of the proposed control strategy (LQR-GA), highlighting its notable dynamic impact compared to the conventional LQR algorithm with fixed parameters.

Using LQR controller for vertical position control on EAST

Vertical position control is essential for stabilizing plasma with elongated configurations. The EAST tokamak is equipped with a set of in-vessel control (IC) coils dedicated to this purpose. Currently, a PD controller with fixed parameters is used for the vertical position control of EAST plasma. However, the response of the plasma in the vertical position changes with changes in plasma configuration, which can result in different control parameter requirements. It is essential to develop a model-based fast-tuning control algorithm for ensuring stability in the vertical position under different configurations. In this study, a model-based vertical position controller tuning method based on a linear quadratic regulator algorithm (LQR) is proposed. Compared with contemporary PD controllers, the proposed model-based LQR controller can enable adjusting controller parameters based on the response of the system, achieving stable control under different vertical position responses. In the EAST experiment, the model-based LQR controller achieved stable control under a shot with a continuously increasing growth rate and reached a maximum controllable vertical displacement growth rate of 968 s−1. The robustness of the system was also demonstrated in a free drift experiment. The new vertical displacement control method can be adapted to different system states and plasma configurations and improve the controllability and safety of future devices.

Distributed Intelligent Vehicle Path Tracking and Stability Cooperative Control

To enhance the path tracking capability and driving stability of intelligent vehicles, a controller is designed that synergizes active front wheel steering (AFS) and direct yaw moment (DYC), specifically tailored for distributed-drive electric vehicles. To address the challenge of determining the weight matrix in the linear quadratic regulator (LQR) algorithm during the path tracking design for intelligent vehicles on conventional roads, a genetic algorithm (GA)-optimized LQR path tracking controller is introduced. The 2-degree-of-freedom vehicle dynamics error model and the desired path information are established. The genetic algorithm optimization strategy, utilizing the vehicle’s lateral error, heading error, and output front wheel steering angle as the objective functions, is employed to optimally determine the weight matrices Q and R. Subsequently, the optimal front wheel steering angle control (AFS) output of the vehicle is calculated. Under extreme operating conditions, to enhance vehicle dynamics stability, while ensuring effective path tracking, the active yaw moment is crafted using the sliding mode control with a hyperbolic tangent convergence law function. The control weights of the sliding mode surface related to the center-of-mass lateral declination are adjusted based on the theory of the center-of-mass lateral declination phase diagram, and the vehicle’s target yaw moment is calculated. Validation is conducted through Matlab/Simulink and Carsim co-simulation. The results demonstrate that the genetic algorithm-optimized LQR path tracking controller enhances vehicle tracking accuracy and exhibits improved robustness under conventional road conditions. In extreme working conditions, the designed path tracking and stability cooperative controller (AFS+DYC) is implemented to enhance the vehicle’s path tracking effect, while ensuring its driving stability.

Path-Tracking Control of Soft-Target Vehicle Test System Based on Compensation Weight Coefficient Matrix and Adaptive Preview Time

<div>In order to enhance the path-tracking accuracy and adaptability of the electric flatbed vehicle (EFV) in the soft-target vehicle test system, an improved controller is designed based on the linear quadratic regulator (LQR) algorithm. First, the LQR feedback controller is designed based on the EFV dynamics tracking error model, and the genetic algorithm is utilized to obtain the optimal weight coefficient matrix for different speeds. Second, a weight coefficient matrix compensation strategy is proposed to address the changes in the relationship between the vehicle–road position and attitude caused by external disturbances and the state of EFV. An offline parameter table is created to reduce the computational load on the microcontroller of EFV and enhance real-time path-tracking performance. Furthermore, an adaptive preview time control strategy is added to reduce the overshooting caused by control delay. This strategy is based on road curvature and traveling speed. Finally, the simulation experiment and field experiment are carried out. The results show that the improved LQR controller exhibits high tracking accuracy during the emergency double lane changes experiment and can maintain accuracy and stability at different speeds.</div>

Comparative Analysis of Optimal Control Strategies: LQR, PID, and Sliding Mode Control for DC Motor Position Performance

This study applies these control methods to the DC motor system to examine the robustness and performance of four optimal control methods. Optimal controllers aim to control the system to minimize a selected performance index. These control methods offer advantages such as improving energy efficiency, reducing costs, and enhancing system security. The Linear Quadratic Regulator (LQR) based controller is the primary optimal control method. Two well-known traditional control techniques include the Proportional-Integral-Derivative (PID) and Integral Sliding Mode Controller (ISMC). However, they do not usually contain optimal properties. In this study, the optimal control algorithms, defined by obtaining controller parameters through the Riccati equation, are applied to achieve accurate position-tracking control in a DC motor system using Matlab/Simulink. The integral term-based algorithms seem to be robust and eliminate steady-state errors. The optimal PID controller could not provide the minimum performance index, unlike the other controllers in the study. LQR and optimal ISMC algorithms could allow the performance index to be a minimum. An illustrative comparison of the performances of all optimal control algorithms has been presented through graphical representation, along with corresponding interpretations.

A deterministic robust control with parameter optimization for uncertain two-wheel driven mobile robot

The uncertainty in mobile robot greatly affects control accuracy. This makes it difficult to apply to more rigorous high-precision engineering fields. Therefore, the fuzzy set theory is introduced to describe the uncertainty. Based on that, the fuzzy mobile robot system is established. The virtual speed controller using backstepping method is designed. Then, a robust control method is proposed to guarantee the uniform boundedness and uniform ultimate boundedness of the controlled system. Furthermore, the balance optimization problem of the performance and cost of the controlled system is explored. By minimizing the performance index containing fuzzy numbers, the optimal control parameter is obtained. Compared with the linear quadratic regulator algorithm, which is the representative optimal robust controller, the proposed control method and optimization strategy based on fuzzy set theory are verified to be effective. The control accuracy is further improved.

Path following fault-tolerant control of distributed drive autonomous unmanned vehicle via adaptive terminal sliding mode

The distributed drive autonomous unmanned vehicle (DDAUV) with unknown fault input of steering system will seriously deviate from the desired path and affect driving safety. This paper proposes a fault estimation and fault-tolerant control (FTC) algorithm, which can improve the comprehensive performance of lateral stability and path following through the torque redundancy characteristics of steering motor and in-wheel motors (IWMs). Firstly, Bayesian algorithm is applied for fault estimation with the prior estimation based on model and posterior observation by sensors. Once steering system fault occurs, the path following model will be reconstructed, and the linear quadratic regulator (LQR) algorithm can dynamically adjust desired front wheel steering angle for path following compensation. Besides, the torque vectoring control of IWMs is applied to further compensate considering the saturation of steering motor. Adaptive terminal sliding mode (ATSM) algorithm is employed to calculate desired additional yaw-moment where the weight matrix of ATSM is adjusted dynamically based on cooperative game theory. Furthermore, an oriented torque distribution method is designed to generate required additional yaw-moment. Finally, the CarSim-MATLAB/Simulink co-simulation and HIL experiment are carried out to test the effectiveness. The results indicate that the proposed FTC algorithm can ensure the lateral stability and improve the path following accuracy with steering system fault.

Spherical robot: A novel robot for exploration in harsh unknown environments

AbstractThe authors propose a complete software and hardware framework for a novel spherical robot to cope with exploration in harsh and unknown environments. The proposed robot is driven by a heavy pendulum covered by a fully enclosed spherical shell, which is strongly protected, amphibious, anti‐overturn and has a long‐battery‐life. Algorithms for location and perception, planning and motion control are comprehensively designed. On the one hand, the authors fully consider the kinematic model of a spherical robot, propose a positioning algorithm that fuses data from inertial measurement units, motor encoder and Global Navigation Satellite System, improve global path planning algorithm based on Hybrid A* and design an instruction planning controller based on model predictive control (MPC). On the other hand, the dynamic model is built, linear MPC and robust servo linear quadratic regulator algorithm is improved, and a speed controller and a direction controller are designed. In addition, based on the pose and motion characteristics of a spherical robot, a visual obstacle perception algorithm and an electronic image stabilisation algorithm are designed. Finally, the authors build physical systems to verify the effectiveness of the above algorithms through experiments.

Research on L1 Adaptive Control of Autonomous Underwater Vehicles with X-Rudder

This study focuses on addressing the the coupling problem of the vertical and horizontal plane of an autonomous underwater vehicle (AUV) with an X-rudder. To guarantee the steering performance of the AUV, a depth and course control algorithm based on an L1 adaptive control algorithm (L1AC) is proposed. Firstly, the linear quadratic regulator (LQR) is designed on the basis of an AUV vertical and horizontal linear model, and the system has optimal control quality for both of the nominal vertical and horizontal models. Secondly, the nonlinear state predictor, disturbance estimator, and adaptive controller are designed separately, which is used for the compensation of the uncertainty and disturbance of the AUV dynamic. Finally, the rudder angle allocation algorithm is designed to realize the rudder angle command of the cross rudder to the X-rudder. The simulation and experiment results show that the adaptive control algorithm proposed in this paper can effectively control AUV to complete high-performance course and depth control. Based on the experiments, the prospects and shortcomings of the L1AC, LQR and MRAC algorithm in AUV control are compared and analyzed.

Wide-Area Measurement-Based Two-Level Control Design to Tolerate Permanent Communication Failures

The operation of modern power systems must meet stability requirements to guarantee the supply of electrical energy. One of these requirements is to ensure that the low-frequency oscillation modes have high damping ratios to avoid angular instability and future power system blackouts. Advances in phasor measurement units (PMUs) have contributed to the development and improvement of wide-area damping controllers (WADCs) capable of increasing the damping rates of the oscillation modes of the system, especially the inter-area modes. Nevertheless, the operation of WADCs is vulnerable to communication failures and cyber-attacks, and if not properly designed the WADC can affect the stability of the entire system. This research proposes a procedure for designing a WADC robust to permanent communication failures using a linear quadratic regulator (LQR) and genetic algorithms. Case studies conducted on an IEEE 68-bus test power system show the effectiveness of the WADC designed by the proposed procedure even when communication failures are occurring in the system. The use of genetic algorithms improves the convergence and results of the LQR-based method.

Research on Path Planning and Tracking Control of Autonomous Vehicles Based on Improved RRT* and PSO-LQR

Path planning and tracking control are essential parts of autonomous vehicle research. Regarding path planning, the Rapid Exploration Random Tree Star (RRT*) algorithm has attracted much attention due to its completeness. However, the algorithm still suffers from slow convergence and high randomness. Regarding path tracking, the Linear Quadratic Regulator (LQR) algorithm is widely used in various control applications due to its efficient stability and ease of implementation. However, the relatively empirical selection of its weight matrix can affect the control effect. This study suggests a path planning and tracking control framework for autonomous vehicles based on an upgraded RRT* and Particle Swarm Optimization Linear Quadratic Regulator (PSO-LQR) to address the abovementioned issues. Firstly, according to the driving characteristics of autonomous vehicles, a variable sampling area is used to limit the generation of random sampling points, significantly reducing the number of iterations. At the same time, an improved Artificial Potential Field (APF) method was introduced into the RRT* algorithm, which improved the convergence speed of the algorithm. Utilizing path pruning based on the maximum steering angle constraint of the vehicle and the cubic B-spline algorithm to achieve path optimization, a continuous curvature path that conforms to the precise tracking of the vehicle was obtained. In addition, optimizing the weight matrix of LQR using POS improved path-tracking accuracy. Finally, this article’s improved RRT* algorithm was simulated and compared with the RRT*, target bias RRT*, and P-RRT*. At the same time, on the Simulink–Carsim joint simulation platform, the PSO-LQR is used to track the planned path at different vehicle speeds. The results show that the improved RRT* algorithm optimizes the path search speed by 34.40% and the iteration number by 33.97%, respectively, and the generated paths are curvature continuous. The tracking accuracy of the PSO-LQR was improved by about 59% compared to LQR, and its stability was higher. The position error and heading error were controlled within 0.06 m and 0.05 rad, respectively, verifying the effectiveness and feasibility of the proposed path planning and tracking control framework.

LQR and LQG control of the helicopter during landing on the ship deck

PurposeThe purpose of this study is to test the performance of the designed automatic control system based on the Linear Quadratic Regulator (LQR) and Linear Quadratic Gaussian (LQG) algorithms during landing of the helicopter on the ship deck. This paper is a further development of the series based on Topczewski et al. (2020).Design/methodology/approachThe system consists of two automatic control algorithms based on LQR and the LQG. It is integrated with the ship motion prediction system based on autoregressive algorithm with parameters calculated using Burg’s method. It is assumed that the source of necessary navigation data is integrated Inertial Navigation System with Global Positioning System. Landing of the helicopter on the ship deck is performed in automatic way, based on the preselected procedure. Performance of the control system is analyzed when all necessary navigation data is available for the system and in case when one of the parameters is unavailable during performing the procedure.FindingsIn this paper, description of the designed control system developed for performing the approach and landing of the helicopter using selected procedure is presented. Helicopter dynamic model is validated using the manufacturer data and by test pilots, overview is presented. Necessary information about ship motion model is also included. Tests showing mission performance while using LQR and LQG algorithms applied to the control system are presented and analyzed, taking into account both situations when full navigation data is available/unavailable for the control system.Practical implicationsResults of the system performance analyses can be used for selection of the proper control methodology for prospective helicopters autopilots. Furthermore, the system can be used to analyze the mission safety when information about one of the navigation parameters is identified by the navigation system as unavailable or incorrect and therefore unavailable during landing on the ship deck.Originality/valueIn this paper, control system dedicated for the automatic landing of the helicopter on the ship deck, based on two different control algorithms is presented. Influence of lack of information about one of the navigation parameters on the mission performance is analyzed.

GA-LQR for vehicle semi-active suspension with BiLSTM inverse model of magnetic rheological damper

This paper proposes a magnetic rheological (MR) semi-active control method based on bidirectional long short-term memory (BiLSTM) neural network, linear quadratic regulator (LQR) control algorithm, and genetic algorithm (GA). The LQR algorithm with GA optimizing the weight coefficients generates the expected damping force. Due to the nonlinear hysteresis characteristics of the magnetic rheological damper (MRD) and the fact that its input and output have certain time dependence, an inverse model of MRD is established by BiLSTM. The control current is predicted by BiLSTM and then the current is input to the MRD to obtain the damping force that is infinitely close to the expected damping force. The damping force is then applied to the suspension system to form a complete closed-loop feedback control, which realizes the damping effect and generates a real-time control. The simulation results show that the MRD inverse model can accurately predict the required control current, and the GA-optimized LQR control algorithm has a good suppression effect on the vertical vehicle acceleration, dynamic tire load, and suspension dynamic stroke.

A Tube Model Predictive Control Method for Autonomous Lateral Vehicle Control Based on Sliding Mode Control.

This paper aims to enhance the lateral path tracking control of autonomous vehicles (AV) in the presence of external disturbances. While AV technology has made significant strides, real-world driving scenarios often pose challenges such as slippery or uneven roads, which can adversely affect the lateral path tracking control and reduce driving safety and efficiency. Conventional control algorithms struggle to address this issue due to their inability to account for unmodeled uncertainties and external disturbances. To tackle this problem, this paper proposes a novel algorithm that combines robust sliding mode control (SMC) and tube model predictive control (MPC). The proposed algorithm leverages the strengths of both MPC and SMC. Specifically, MPC is used to derive the control law for the nominal system to track the desired trajectory. The error system is then employed to minimize the difference between the actual state and the nominal state. Finally, the sliding surface and reaching law of SMC are utilized to derive an auxiliary tube SMC control law, which helps the actual system keep up with the nominal system and achieve robustness. Experimental results demonstrate that the proposed method outperforms conventional tube MPC, linear quadratic regulator (LQR) algorithms, and MPC in terms of robustness and tracking accuracy, especially in the presence of unmodeled uncertainties and external disturbances.

UKF-Based Observer Design for the Electric Brake Booster in Situations of Disturbance

The motor-driven electric brake booster (E-Booster) can replace the traditional vacuum booster to realize the braking power assistance and active braking. Independent of extra sensors, this paper proposes a full-state observer for E-Booster based on Unscented Kalman Filter (UKF) in the presence of a driver’s input force disturbance. The electro-hydraulic system is first modeled, which includes a nonlinear hydraulic model and the reaction disk’s rubber model. The pre-compression is designed to produce linear power assistance based on the properties of rubber material. With the existence of the disturbance, the linear quadratic regulator (LQR) algorithm is used to track the pre-compression of the reaction disk so that E-Booster is developed into a closed-loop system to achieve power assistance. The proposed UKF observer can online estimate the states considering the controller input and disturbance input. To reduce the process error, the hydraulic p-V characteristic is fitted using the recursive least squares (RLS) method before observation. Furthermore, the simulation test and vehicle tests are performed to validate the observation effect. In the closed-loop test, UKF decreases residual error by 16% when compared to the typical Extended Kalman Filter (EKF). The simulation results remain consistent with the experimental results, demonstrating the effectiveness of the proposed method.

Research on steering coordination control strategy for distributed drive electric vehicles

The key problems of the steering system and vehicle handling stability of distributed drive electric vehicles are studied in the paper. According to the performance of the distributed drive electric vehicle, a seven-degree-of-freedom is established to match the parameters with the model of CarSim software. Based on the maneuverability improvement control algorithm of the active front wheel system [Active Front Steering (AFS)]/differential power steering system coupling redundancy between differential drive assist steering (DDAS), a AFS/DDAS system coordination control strategy is formulated to reduce the influence of undesirable cross-pendulum moments on vehicle stability. Through the requirements for vehicle stability, a distributed control strategy for the steering stratification of electric vehicles is developed. In the upper layer, the direct transverse moment controller is designed by the linear quadratic regulator algorithm, and the stability control area is divided into a stable region, a transition region, and an unstable region according to the center-of-mass deviation angle. Then the weights of the three subsystems are determined by judging the control area of the vehicle. The lower controller distributes the additional torque from the final calculation of the upper controller to the driving wheels through an allocation algorithm. Finally, using the CarSim/Simulink simulation platform and the dSPACE hardware-in-the-loop real-time simulation platform, the effectiveness and real-time performance of the steering coordination control strategy are verified by simulation experiments under typical working conditions, such as double shift line, step, and sinusoid.

Improvement of Linear and Nonlinear Control for PMSM Using Computational Intelligence and Reinforcement Learning

Starting from the nonlinear operating equations of the permanent magnet synchronous motor (PMSM) and from the global strategy of the field-oriented control (FOC), this article compares the linear and nonlinear control of a PMSM. It presents the linear quadratic regulator (LQR) algorithm as a linear control algorithm, in addition to that obtained through feedback linearization (FL). Naturally, the nonlinear approach through the Lyapunov and Hamiltonian functions leads to results that are superior to those of the linear algorithms. With the particle swarm optimization (PSO), simulated annealing (SA), genetic algorithm (GA), and gray wolf Optimization (GWO) computational intelligence (CI) algorithms, the performance of the PMSM–control system (CS) was optimized by obtaining parameter vectors from the control algorithms by optimizing specific performance indices. Superior performance of the PMSM–CS was also obtained by using reinforcement learning (RL) algorithms, which provided correction command signals (CCSs) after the training stages. Starting from the PMSM–CS performance that was obtained for a benchmark, there were four types of linear and nonlinear control algorithms for the control of a PMSM, together with the means of improving the PMSM–CS performance by using CI algorithms and RL–twin delayed deep deterministic policy gradient (TD3) agent algorithms. The article also presents experimental results that confirm the superiority of PMSM–CS–CI over classical PI-type controllers.