LQR Algorithm Research Articles

Intelligent vehicle lateral control strategy research based on feedforward + predictive LQR algorithm with GA optimisation and PID compensation

Targeting the lateral motion control problem in the intelligent vehicle autopilot structural system, this paper proposes a feedforward + predictive LQR algorithm for lateral motion control based on Genetic Algorithm (GA) parameter optimisation and PID steering angle compensation. Firstly, based on the vehicle dynamics tracking error model, the intelligent vehicle LQR lateral motion controller as well as the feedforward controller are designed, and upon which the predictive controller is added to eliminate the system lag.Subsequently, exploiting the advantage that the PID algorithm is not model-based, a PID steering angle compensation controller that can directly control and correct the lateral error is designed. Second, a LQR controller based on path tracking deviation is designed by using the parameter rectification method of genetic algorithm (GA), which optimizes the control parameters of the lateral motion controller and improves the adaptivity of the control accuracy. Finally, Based on the Carsim-Simulink co-simulation platform, the simulation validation and analysis of double lane change (DLC) test and circular condition test (CCT) are carried out, and the results indicate that compared with the other two LQR controllers, the optimised controllers improved more than 50% in lateral error and heading error control, and the vehicle sideslip angle and vehicle yaw rate are in the range of −0.05° to 0.05° and − 0.15 rad/s to 0.10 rad/s, and it showed improved performance in tracking accuracy and satisfied vehicle stability constrains.

Adaptive suspension state estimation based on IMMAKF on variable vehicle speed, road roughness grade and sprung mass condition

Vehicle speed, road roughness grade and sprung mass are the three main factors to influence suspension control and state estimation. Aiming at the problem that fixed state observer cannot guarantee the estimation accuracy of suspension with driving scenario changes, a suspension state observer based on interactive multiple model adaptive Kalman filter (IMMAKF) is established. Firstly, an adaptive control suspension is proposed based on LQR algorithm and multi-objective optimization algorithm, which can automatically adjust the controller parameters according to the vehicle speed, road roughness grade and sprung acceleration parameters, so as to keep the optimal control effect of the suspension. Secondly, the theoretical model of IMMAKF is derived, and two kinds of IMMAKF suspension state observers and controllers are established. Finally, a simulation condition with the vehicle speed, road roughness grade and sprung mass changing simultaneously is established. The simulation results shows that: compared with ordinary IMMKF, AKF and KF observers, the estimation accuracy of IMMAKF5 is improved. Except for state observation, IMMAKF can be used to identify the road roughness grade and estimate the suspension sprung mass.

Anti-Swing Control for Quadrotor-Slung Load Transportation System with Underactuated State Constraints

Quadrotors play a crucial role in the national economy. The control technology for quadrotor-slung load transportation systems has become a research hotspot. However, the underactuated load’s swing poses significant challenges to the stability of the system. In this paper, we propose a Lyapunov-based control strategy, to ensure the stability of the quadrotor-slung load transportation system while satisfying the constraints of the load’s swing angles. Firstly, a position controller without swing angle constraints is proposed, to ensure the stability of the system. Then, a barrier Lyapunov function based on the load’s swing angle constraints is constructed, and an anti-swing controller is designed to guarantee the states’ asymptotic stability. Finally, a PD controller is designed, to drive the actual angles to the virtual ones, which are extracted from the position controller. The effectiveness of the control method is verified by comparing it to the results of the LQR algorithm. The proposed control method not only guarantees the payload’s swing angle constraints but also reduces energy consumption.

Study on automatic lane change trajectory control of intelligent vehicle on expressway

Aiming at the dangerous working condition of the front car driving at low speed, a safety distance model using the vehicle braking process is proposed to determine the best time for intelligent vehicles to change lanes. Based on the fitting method of quintic polynomial, an automatic lane change fitting trajectory is constructed, and the LQR algorithm is used to achieve accurate tracking. Through the joint simulation and experiment of CarSim, PreScan, and MATLAB/Simulink, it is shown that the established lane change trajectory control model can determine the best time for intelligent vehicles to change lanes, plan safe and comfortable lane change trajectory, and achieve good tracking effect.

Multihazard life-cycle cost optimization of active mass dampers in tall buildings

This article proposes an optimization-based-methodology for designing multiple active mass dampers (AMDs) in tall buildings in multihazard environments. A realistic cost of the AMD system is formulated as the objective-function, and the multihazard Life-Cycle-Cost (LCC) that represents the long-term hazard-related losses, is selected as the main performance-constraint. This allows joining winds and earthquakes in a single decision parameter. Additional constraints limit the dampers forces and strokes. To ensure stability of the actively controlled building, the LQR algorithm is nested within the formal optimization problem. In addition, for the first time in the context of AMDs, their masses are considered as design variables, emerging directly as an optimization output. As the LQR control law is not aimed at optimizing costs and LCC, the lower triangular matrices related to the LQR weighting matrices are used as additional design variables. Thus, their values converge throughout the optimization to optimize the formulated cost function while satisfying the constraints. As this strategy produces large-scale problems, an efficient gradient-based algorithm is developed, using the adjoint sensitivity analysis method. The framework is applied to several examples for a benchmark-building, providing consistent results. One example demonstrates that AMDs can offer similar performance to its passive TMDs counterpart, requiring a mass 40% lower.

Second-Order Differential Dynamic Programming for Whole-Body MPC of Legged Robots

This paper presents the first use-case of full second-order Differential Dynamic Programming (DDP) with a whole-body model for model predictive control on legged robot hardware. Recent advances in the literature show that DDP can be simplified by exploiting the dynamics structure in the algorithm, allowing the use of reverse-mode derivative accumulation to efficiently compute dynamics sensitives. These advances allow DDP to be run at similar compute times as the iterative LQR (iLQR) algorithm, its first-order counterpart. Beyond a hardware implementation of these past theoretical developments, this paper provides a characterization of DDP vs. iLQR following push disturbances. One challenge is that DDP often requires regularization to ensure the algorithm improves its control law from iteration to iteration, and an expensive matrix reconditioning is often necessary. We explore a novel methodology to carry out this matrix reconditioning, which considers the local geometry of the cost landscape. The resulting controller is shown to achieve lower costs and withstand larger disturbances as compared to traditional regularization schemes.

Improved Linear Quadratic Regulator Lateral Path Tracking Approach Based on a Real-Time Updated Algorithm with Fuzzy Control and Cosine Similarity for Autonomous Vehicles

Path tracking plays a crucial role in autonomous driving. In order to ensure the real-time performance of the controller and at the same time improve the stability and adaptability of the path tracking controller, a lateral path control strategy based on the improved LQR algorithm is proposed in this paper. To begin with, a discrete LQR controller with feedforward and feedback components is designed based on the error model of vehicle lateral dynamics constructed by the natural coordinate system. Then, a fuzzy control method is applied to adjust the weight coefficients of the LQR in real time according to the state of the vehicle. Furthermore, an update mechanism based on cosine similarity is designed to reduce the computational effort of the controller. The improved LQR controller is tested on a joint Simulink–Carsim simulation platform for a two-lane shift maneuver. The results show that the control algorithm improves tracking accuracy, steering stability and computational efficiency.

Trajectory Planning and Tracking for Carrier Aircraft-Tractor System Based on Autonomous and Cooperative Movement

The solution of how to plan out the cooperative moving trajectory autonomously and control the motion of carrier-based aircraft timely and accurately is the key to helping improve the overall deck operation efficiency. The main problem discussed in this article is coordinated trajectory planning strategy for multicarrier aircraft and cooperative control between tractor and carrier aircraft. First, the kinematic model and three-degree-of-freedom dynamics model of the towbarless traction system are established. Then, a coevolution mechanism for aircraft systems is proposed to ensure coordinated trajectory planning among multiple aircraft and a trajectory adapted to the tractor-aircraft system is generated based on the hybrid RRT∗ algorithm. Next, a double-layer closed-loop controller is designed for the trajectory tracking of the tractor-aircraft system on the deck under the constraints of incomplete constraints and various physical conditions. It includes an outer model predictive controller which effectively controls the cooperative motion between the carrier aircraft and tractor and an inner torque control strategy based on adaptive fuzzy PID control which strictly ensures the stability of the system. Simulation results demonstrate that the controller is more rapid, more accurate, and more robust in tracking line trajectory with initial deviation, sine curve with large curvature, and complex trajectories on decks compared with backstepping control and LQR algorithm.

Analysis of the Lqr Algorithm in the Field of Testing the Dynamics of Quadcopter Movement

The subject of this article is to present the issues related to the LQR control algorithm used in the linear model describing the dynamics of the flying object in terms of tracking its flight trajectory. The use of the LQR regulator is also a method of calculating the optimal K-feedback reinforcement, with this type of reinforcement used to control the system in the form of a control signal can be determined by tuning the Q and R weight matrix elements in the LQR method. Based on the above, the main research goal of the article is to develop an algorithm for the control system implemented on the quadrotor using the LQR method to obtain the best K-feedback gain in flight state with unstable motion. To this end, a mathematical model describing the essence of linear-quadratic control using the LQR controller is presented in this paper. It should be noted that due to the fact that only four states can be controlled at the same time in a quadrotor, hence the flight trajectories are determined on the basis of four states, while the three-dimensional position, position of the tested object in the coordinate system and rotation along the axis are described as deviation movement. In addition, the work also designed on the basis of the created linear model of a linear quadrotor LQR control approach for this model due to the fact that the performance of the linear model and non-linear model around a specified nominal point is almost identical. The control system based on the LQR algorithm was developed in the Matlab/Simulink environment, and the results obtained in the form of graphs for the quantities characterizing the dynamics of the tested object were used to assess the effectiveness of the LQR method used. In the final part of the work, practical conclusions have been formulated based on the research (analysis, models, simulations) and analysis of the results obtained.

Semi-active control of ambulance stretcher system based on parallel mechanism with MR dampers and perturbation analysis

The recumbent patients on ambulance stretcher experience multi-dimensional excitations due to road roughness. In order to isolate the multi-dimensional vibrations validly, a novel ambulance stretcher system based on 4-PUU parallel mechanism with Magneto-Rheological dampers is proposed. Firstly, the kinematic and dynamic equation are deduced by geometric relation and Lagrange equation respectively. Subsequently, the vibration isolation performance is investigated in time and frequency domain. The robustness of LQR algorithm is addressed with parameters perturbation by deducing Lyapunov equation. Further, selecting RMS values as the index of vibration isolation performance, the index which includes geometric parameters perturbation, mass and spring uncertainties is discussed. Simulations demonstrate the stretcher system can effectively isolate multi-dimensional vibrations in sensitive frequency range for supine patients with perturbation and uncertainties. The RMS values show different characteristics because of altering Jacobin matrix of the stretcher.

A State Feedback Controller Based on GCC Algorithm against Wind‐Induced Motion for High‐Rise Buildings with Parametric Uncertainties

High‐rise buildings with an active mass damper/driver (AMD) system generally use a simplified mathematical model. The result leads to parametric uncertainties including the stiffness and mass variations exist, and the accuracy of its controller is seriously affected. In view of the above uncertainties, based on a Lyapunov stability theory and linear matrix inequality (LMI) approach, a state feedback controller based on the guaranteed cost control (GCC) algorithm is proposed in this paper. A ten‐storey frame with an AMD system is taken as a numerical example, and its control effect and AMD parameters are viewed as the control indexes. The performance of the proposed robust controller is compared with a conventional controller based on the classical LQR algorithm. The analysis results show that the new controller effectively suppresses the dynamic responses of high‐rise buildings with parametric uncertainties and keeps the AMD parameters stable. Finally, a four‐storey steel experimental frame with an AMD system is used to verify the correctness of the conclusions.

Active control of micro Reddy beam integrated with functionally graded nanocomposite sensor and actuator based on linear quadratic regulator method

In this paper, optimal active vibration control of a micro sandwich beam is studied. Face sheets are made from piezoelectric materials and reinforced by functionally graded distributions of carbon nanotubes. Also bottom and top face sheets operate as distributed sensor and actuator, respectively. Based on modified strain gradient theory and Hamilton's principle, the governing equations of motion for presented smart micro Reddy beam are derived and optimal active vibration control is applied using state-space form of equations of motion and linear quadratic regulator algorithm. The results show that considering MSGT, the amplitude of the center point deflection and settling time decrease. Also CNTs distributions effect on stability and active vibration control of the smart structure and LQR algorithm is essentially an automated way of finding an appropriate state-feedback controller. This study is a theoretical background for more research and further experimental investigation, in the field of micro smart structures.

Inverse discounted-based LQR algorithm for learning human movement behaviors

Recently, there has been an increasing interest towards understanding human movement behaviors. In this regard, one of the approaches is to retrieve the unknown underlying objective function that the human has to optimize while achieving a certain movement behavior. Existing research of behavioral understanding merely depends on predefined optimality criteria, where the minimum time, minimum variance or/and minimum effort are mainly adopted. These criteria are assumed to be constant, where the human is assumed to have the same preferences during the movement duration. However, in this paper, the optimality criteria underlying the kinematic characteristics of a certain human behavior are assumed to be exponentially discounted to account for the change in the human preferences that could happen while achieving this behavior. A new Inverse Discounted-based Linear Quadratic Regulator (ID-LQR) algorithm is developed in the light of Inverse Optimal Control (IOC) framework to find out the discounted cost function that could reproduce the measured human behavior perfectly. Meanwhile, an Incremental version of the ID-LQR algorithm is proposed to continuously refine the so far learned cost function in the case of sequentially presented demonstrations. The saccadic eye gaze movement is studied as an example to quantify both the proposed ID-LQR and Inverse ID-LQR approaches. Simulation results are encouraging and show that the saccadic trajectories generated by ID-LQR approach match the experimental data in many aspects, including position and velocity profiles of saccades. Moreover, when it is assessed by a subsequent set of scenarios, the incremental ID-LQR algorithm confirms its capability to generalize the so far retrieved cost function for the unseen saccadic demonstrations.

Application of LQR Algorithm with Pole Placement in TEA Control for Space Station

在进行空间站力矩平衡姿态（TEA）控制设计时，需要将姿态动力学、动量管理与干扰抑制滤波器相结合形成系统模型，以抑制外部干扰对姿态的影响.带有区域配置的改进LQR算法用于线性化的系统模型，能够使得系统闭环极点落入期望的扇形区域，区域分别由给定整数定义张角、正数定义稳定阈，建立的代数Riccati方程组可采用两步法进行迭代求解，自动生成所需要的状态权矩阵，并得到系统的反馈增益，完成闭环极点的区域配置.该算法用于对空间站姿态控制及动量管理的控制系统，结果表明系统稳态及动态特性能够达到预期目标.

Seismic control of irregular multistory buildings using active tendons considering soil–structure interaction effect

Much research has been conducted in recent decades on structural control to improve the performance of different towers and high-rise buildings against severe earthquakes and strong winds. Most studies on building vibration control have been considered just two-dimensionally using shear frame models. In reality, most of the buildings might have irregular plans and thus experience torsion when subjected to earthquakes. Such torsion would further increase the structural response. On the other hand, some buildings are located on soft soil that would trigger the soil-structure interaction (SSI) effects required to be considered for design purposes. The main dynamic behavior parameters like natural frequencies, damping ratios and mode shapes would depend on construction site conditions and thus the SSI effects must be taken into account for buildings on soft soil. In this paper, a mathematical model is developed for calculating the seismic response of an irregular multi-story building equipped with active tendons. The SSI effect is then introduced by changing structure mass, stiffness and damping matrices. The model is employed to obtain the seismic response of 10-story buildings using active tendon with LQR algorithm. The building is modeled as a structure composed of members connected by rigid floor diaphragms with three degrees of freedom at each story; i.e. lateral displacements in two perpendicular directions and a rotation with respect to a vertical axis. Results showed that active tendons have low effects on the reduction of structural response when the building has been located on soft soils.

Dual PD Control of Flexible Smart Structure Based on LQR Algorithm

The flexible smart structure is broadly applied in various fields. In order to reduce the vibration of smart structures, a dual loop PD control strategy is proposed based on the Lagrangian dynamics mathematical modeling of the flexible system and a revision of the traditional LQR algorithm, the simulation and physical experiments show that the proposed approach is efficient in controlling and damping out the vibration and disturbance in flexible smart structure system.

Study on the Optimization of the Double-Layer Hybrid Vibration Isolation System Based on the LQR Algorithm

The LQR algorithm has been widely used in the hybrid vibration isolation system. However, it cannot make the hybrid vibration isolation system global optimal with the coupling of structure and controller. Hence, the multi-object optimal design of the double-layer hybrid vibration isolation system based on the LQR algorithm was made by the NCGA method. The results showed that the vibration of the mechanical equipment did not get worse with the reduction of the force transmission ratio, and it made an approach to the optimal design of the hybrid vibration isolation system.

Integrated optimization of structure and control systems for interconnected building structures subjected to earthquake

The integrated optimization of structure and control systems is investigated for n interconnected building structures subjected to earthquake. The vibration control model is established for the interconnected building structures, and optimal stiffness and damping parameters of assigned passive controllers are calculated based on LQR algorithm and an equivalent control effect strategy in the frequency domain. The integrated optimization model of structure and control, including design variables, the objective function and constraint function, is built. The design variables are size parameters of structural elements, the parameters of the weighted matrix, and the number and locations of passive controllers. The maximal displacement of the controlled system in the time domain and the energy index in the frequency domain are introduced as the optimized objective functions. A genetic algorithm is adopted to solve this kind of optimization problem with discrete and continuous design variables. The results of a numerical example show that the proposed method is reasonable and effective.

A Randomized Approach for Robust Control of Uncertain UAVs

The objective of this paper is the development of a randomized LQR algorithm for UAVs subject to uncertainty. A controller gain is synthesized using a Lyapunov approach dealing with a formation of two mini-UAV systems in the classical Leader/Wingman configuration. Our contribution is to demonstrate that the proposed sequential algorithm provides a randomized controller which stabilizes the uncertain system. This probabilistic technique is then validated with an extensive a posteriori analysis. We show that the UAV reaches the desired altitude without an additional PID channel, and therefore tuning of the controller gains is avoided.

LQR CONTROL OF THE NODAL DISPLACEMENTS IN A SPATIAL TRUSS WITH ACTIVE PIEZOELECTRIC MEMBERS

The ability to damp vibrations is important in many structures, in which trusses are one of the main elements. The increase of the damping of the truss vibrations is possible by passive means or by the use of an active vibration control system integrated with the structure of the truss. The control system can affect the truss structure by specially designed actuators, which generate active forces in appropriate nodes of the truss. Piezoelectrics can be used to build such actuators. The design of the control system encompasses the structure of the actuating active truss member, the spacing of active members inside the truss structure, the design of the control algorithm and the spacing of measurement sensors generating feedback signals. In this article, the application of the LQR algorithm to the node displacement control in a spatial truss has been presented. The spacing of active members in the truss structure on the basis of the force distribution in the truss members has been suggested.