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Under extreme working conditions such as high-speed driving on roads with a large road surface unevenness coefficient, turning on a road with a low road surface adhesion coefficient, and emergency acceleration and braking, a vehicle’s stability deteriorates sharply and reduces ride comfort. There is extensive existing research on vehicle active suspension control, trajectory tracking, and control methods. However, most of these studies focus on conventional operating conditions, while vehicle stability analysis under extreme operating conditions is much less studied. In order to improve the stability of the whole vehicle under extreme operating conditions, this paper investigates the stability of a vehicle under extreme operating conditions based on linear quadratic regulator (LQR) control. First, a seven degrees of freedom (7-DOF) dynamics model of the whole vehicle is established based on the use of electromagnetic active suspension, and then an LQR controller of the electromagnetic active suspension is designed. A joint simulation platform incorporating MATLAB and CarSim was built, and the CarSim model is verified by real vehicle tests. Finally, the stability of the vehicle under four different ultimate operating conditions was analyzed. The simulation results show that the root mean square (RMS) values of body droop acceleration and pitch angle acceleration are improved by 57.48% and 28.81%, respectively, under high-speed driving conditions on Class C roads. Under the double-shift condition with a low adhesion coefficient, the RMS values of body droop acceleration, pitch acceleration, and roll angle acceleration are improved by 58.25%, 55.41%, and 31.39%, respectively. These results indicate that electromagnetic active suspension can significantly improve vehicle stability and reduce driving risk under extreme working conditions when combined with an LQR controller.

This paper presents a comparative study of different linear quadratic regulator ( LQR )-based attitude controllers design for a 3-DOF helicopter system. Firstly, dynamics model of 3-DOF helicopter system is established. Then, three LQR -based attitude controllers are designed, which are robust LQR attitude controller, linear parameter varying (LPV)-based robust LQR attitude controller and weight adaptation-based LQR attitude controller are developed for the helicopter system, respectively. Finally, based on the Quanser’s 3-DOF helicopter experimental platform, the stability and tracking performance of these three attitude controllers are tested under three conditions including normal condition, actuator fault and wind disturbance. Based on the experimental results, some discussions are carried out, which are expected to provide some guidance for the design of flight control system.

With advancements in mobile robot technology, wheel-legged robots have emerged as promising next-generation mobile solutions, reducing design costs and enhancing adaptability in unstructured environments. As underactuated systems, their balance control has become a prominent research focus. Despite there being numerous control approaches, challenges remain. Balance control methods for wheel-legged robots are influenced by hardware characteristics, such as motor friction, which can induce oscillations and hinder dynamic convergence. This paper presents a friction feedforward Linear Quadratic Regulator (LQR) balance control method. Specifically, a basic LQR controller is developed based on the dynamics model of the wheel-legged robot, and a Stribeck friction model is established to characterize motor friction. A constant-speed excitation trajectory is designed to gather data for friction identification, and the Particle Swarm Optimization (PSO) algorithm is applied to determine the optimal friction parameters. The identified friction model is subsequently incorporated as feedforward compensation for the LQR controller’s torque output, resulting in the proposed friction feedforward LQR balance control algorithm. The minimum standard deviation for friction identification is approximately 0.30, and the computed friction model values closely match the actual values, indicating effective and accurate identification results. Balance experiments demonstrate that under diverse conditions—such as flat ground, single-sided bridges, and disturbance scenarios—the convergence performance of the friction feedforward LQR algorithm markedly surpasses that of the baseline LQR, effectively reducing oscillations, accelerating convergence, and improving the robot’s stability and robustness.

In order to study path tracking of AGV, the lateral dynamic model of AGV is established, and the state equation of the system is obtained. In order to make the state equation better adapt to the LQR controller, a lateral error integral is added to the controller. Then an improved state equation is obtained. The energy function is constructed and the LQR controller is designed. In order to find the optimal value of the weight Q and R in the LQR controller, Genetic Algorithm (GA) is introduced so as to realize the optimization of the LQR controller. The simulation results show that compared with the empirical method to determine the Q and R of LQR control, the LQR control method optimized by GA can effectively reduce the overshoot of the system, improve the convergence speed and stability of the system, and obtain a better path tracking effect.

This work is concerned with an original ball-on-plate laboratory process. First, a simplified process model based on state–space process description is derived. Next, a fast state–space MPC algorithm is discussed. Its main advantage is computational simplicity: the manipulated variables are found on-line using explicit formulas with parameters calculated off-line; no real-time optimization is necessary. Software and hardware implementation details of the considered MPC algorithm using the STM32 microcontroller are presented. Tuning of the fast MPC algorithm is discussed. To show the efficacy of the MPC algorithm, it is compared with the classical PID and LQR controllers.

Currently, the interest in creating autonomous driving vehicles and progressively more sophisticated active safety systems is growing enormously, being a prevailing importance factor for the end user when choosing between either one or another commercial vehicle model. While four-wheelers are ahead in the adoption of these systems, the development for two-wheelers is beginning to gain importance within the sector. This makes sense, since the vulnerability for the driver is much higher in these vehicles compared to traditional four-wheelers. The particular dynamics and stability that govern the behavior of single-track vehicles (STVs) make the task of designing active control systems, such as Anti-lock Braking System (ABS) systems or active or semi-active suspension systems, particularly challenging. The roll angle can achieve high values, which greatly affects the general behavior of the vehicle. Therefore, it is a magnitude of the utmost importance; however, its accurate measurement or estimation is far from trivial. This work is based on a previous paper, in which a roll angle estimator based on the Kalman filter was presented and tested on an instrumented bicycle. In this work, a further refinement of the method is proposed, and it is tested in more challenging situations using the multibody model of a motorcycle. Moreover, an extension of the method is also presented to improve the way noise is modeled within this Kalman filter.

A cascade technique with two control loops is designed for a DC Buck‐Boost converter that is a right half‐plane zero (RHPZ) structure called a non‐minimum phase system. This concept presents several challenging constraints for designing well‐behaved control techniques. Cascade controllers can provide various benefits compared with single loop controllers such as higher safety, higher robustness, and higher stability. This strategy assumes the system as a black‐box structure without the need for a mathematical model of the system. This benefit can decrease the computational burden and provides faster dynamics along with ease of implementation. This technique consisted of an outer Fractional‐order PID voltage controller tuned with the Antlion Optimizer (ALO) algorithm, which provides a reference current for the inner control loop of the Neural Network‐based LQR (NN‐LQR) controller. The basic principle in cascade controllers is a more rapid performance of the inner loop that has been satisfied with the NN‐LQR strategy, which optimizes and tunes the gains of the LQR controller and shows faster dynamics and higher robustness. It should be mentioned that the number of neurons is limited to 2 and 4 in each layer to decrease the computational burden with lower complexity. Also, the ALO algorithm is a modern nature‐inspired algorithm used to tune the PID gains with better results under‐constrained problems with diverse search spaces. Considering the negative impacts of various disturbances on a power converter, a Fractional‐order‐based PID (FO‐PID) control technique is a proper alternative since it shows higher robustness in load uncertainties along with better dynamical responses based on its extra degree of freedom. Moreover, to evaluate the superiority of this controller, two other controllers are designed using the PSO algorithm for PID and FO‐PID controllers. Finally, the presented cascade controller has been tested in various working conditions through simulation and experiment results. A cascade technique with two control loops for a DC/DC Buck‐Boost converter is presented here. The proposed Buck‐Boost converter is a topology working in both step‐down and step‐up modes that is a non‐minimum system in its boost mode.

A quadcopter control system is a fundamentally difficult and challenging problem because its dynamics modelling is highly nonlinear, especially after accounting for the complicated aerodynamic effects. Plus, its variables are highly interdependent and coupled in nature. There are six controllers studied and analysed in this work which are (1) Proportional-Integral-Derivative (PID), (2) Proportional-Derivative (PD), (3) Linear Quadratic Regulator (LQR), (4) Proportional-Linear Quadratic Regulator (P-LQR), (5) Proportional-Derivative-Linear Quadratic Regulator (PD-LQR) and lastly (6) the proposed controller named Proportional-Double Derivative-Linear Quadratic Regulator (PD2-LQR) controller. The altitude control and attitude stabilization of the quadcopter have been investigated using MATLAB/Simulink software. The mathematical model of the quadcopter using the Newton-Euler approach is applied to these controllers has illuminated the attitude (i.e. pitch, yaw, and roll) and altitude motions of the quadcopter. The simulation results of the proposed PD2-LQR controller have been compared with the PD, PID, LQR, P-LQR, and PD-LQR controllers. The findings elucidated that the proposed PD2-LQR controller significantly improves the performance of the control system in almost all responses. Hence, the proposed PD2-LQR controller can be applied as an alternative controller of all four motions in quadcopters.

The poor adaptability matrix of traditional LQR controller causes the problems of large payload swing and slow response for ship-mounted cranes during operation. To solve such problems, an LQR controller based on an improved grey wolf optimization algorithm (IGWO-LQR) is proposed. Firstly, the dynamics model of ship-mounted crane is constructed, the pendulum reduction problem is transformed into the LQR quadratic performance index problem, and IGWO is used to optimize the weight matrix. At the same time, the RBF neural network is applied to compensate for the non-linear wave disturbances in the system. Finally, the pendulum reduction efficiency of the controller under different parameters and conditions is verified by numerical simulation. Compared with the traditional LQR controller, the simulation results show that the control accuracy of the IGWO-LQR controller is improved by about 5%, and the response speed is improved by about 5–10 s. This method can significantly reduce the payload swing and improve work efficiency.