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This note shows an elegant relationship between the quadratic optimal control and robust stabilization for linear time-invariant (LTI) systems, where the former control can robustly stabilize the latter system, provided that the matched uncertainty is bounded. Through reviewing the relevant literature, some common mistakes in regard to this relationship are found. The correct results are obtained and proved in both frequency and time domains. The results are applicable to both single- and multi-input cases. They are significant as the simple LQR design for the nominal system can be utilized to directly solve—with no further effort—the complex robust stabilization problem for a class of linear uncertain systems. [ABSTRACT FROM AUTHOR]

This paper introduces the concept of intelligent control using Tikhonov regularization for nonlinear coupled systems. This research is driven by the increasing demand for advanced control techniques and aims to explore the impact of Tikhonov regularization on these systems. The primary objective is to determine the optimal regularization term and its integration with other control methods to enhance intelligent control for nonlinear coupled systems. Tikhonov regularization is a technique employed to adjust neural network weights and prevent overfitting. Additionally, the incorporation of ReLU activation function in the neural network simplifies thearchitecture, avoiding issues like gradient explosion, and optimizes controller performance. Furthermore, sliding surfaces are designed to improve control system stability and robustness. The proposed Tikhonov-tuned sliding neural network (TSN) controller ensures both stability and superior system performance. The methodology emphasizes the importance of determining optimal neural network weights and regularization terms to prevent overfitting, facilitating accurate predictions in inverted pendulum control system applications. To assess the functionality and stability of TSN, this paper employs simulations and experimental implementations to control both the rotary inverted pendulum and the arm-driven inverted pendulum. The results indicate that the proposed TSN methodologies are effective and feasible. [ABSTRACT FROM AUTHOR]

In the Internet of Things (IoT) era, an immense amount of sensing devices are obtained and produce various sensory data over time for a wide range of disciplines and applications. These devices will result in significant, fast, and real-time data streams based on the utilization characteristics. Utilizing analytics over such data streams to identify new information, model future insights, and make control decisions is a necessary process that makes IoT a worthy paradigm for businesses and a quality-of-life improving technology. This paper presents a study of digital agriculture and its significance in terms of the application of an IoT-based device — a two-wheeled self-balancing robot — followed by a thorough procedural explanation of the development of the device, which begins with the mathematical modeling of the system through the Euler–Lagrange method to obtain the equations of motion for the same and linearize the equation to define the control method to be used to balance the robot structure, all based on the concept of the inverted pendulum. Then paper discusses the suitable and the most efficient control method, which is the linear quadratic regulator (LQR), for these robots. Then deep learning-based LQR (DL-LQR) method is implemented in the robots performing the algorithm to balance it successfully. [ABSTRACT FROM AUTHOR]

In this paper, linear quadratic regulator (LQR) control is applied to a Cuk converter, and mathematical modeling of the converter is done using state space averaging (SSA) in continuous conduction mode (CCM). The primary focus is to design a controller for the converter and maintain output voltage within 1% of the prescribed value when there is a unit step disturbance in the input. The design done by using MATLAB improved control of the converter from that with a conventional controller when tested with disturbances. The controller did not influence the system's stability, when assessed from the Bode plot. Despite the existence of disturbances, the findings prove the efficacy of the suggested approach, and the proposed controller can track the desired output voltage in less than 14 ms. The LQR control was developed for various applications of the Cuk converter, such as in a photovoltaic system and a wind system. [ABSTRACT FROM AUTHOR]

This study investigates the problem of inertial navigation system's (INS's) vertical channel instability, which primarily results from the positive gravity feedback that takes place in the numerical integration step of the accelerometer measurements. Traditional solutions to the problem include using information from auxiliary sensors, typically barometers and global navigation satellite systems (GNSSs), integrated into INSs through feedback control loops (referred to as mechanizations) and/or Kalman filters (KFs). Most studies on this subject lack clarity regarding the methodology used for the mechanization tuning (by showing excessive empiricism) and/or disregard the benefits of using optimal control techniques for the purpose of the latter. This study, therefore, reviews the main mechanization used for vertical channel stabilization of baro‐inertial integrations and presents, as its main contribution, the performance analysis of new tuning techniques based on optimal control theory, namely, by linear quadratic regulator (LQR) and by minimization of performance indices such as the integral absolute error (IAE), integral squared error (ISE), integral of time multiplied absolute error (ITAE), and integral of time multiplied squared error (ITSE). To validate the proposed tunings, the integrated altitude and vertical velocity mean errors (MEs) and standard deviations (SDs) are used as metrics, which are compared with the corresponding MEs/SDs of the empirical tuning with highest performance/acceptance in the literature. We also evaluate the ability of the mechanizations to fulfill their ultimate goal, namely, to track the reference barometer input, by also attenuating its noise. Based on simulated and experimental results, the present study demonstrates and validates the effectiveness/robustness of the proposed optimal tunings, particularly those based on LQR and ITAE minimization. [ABSTRACT FROM AUTHOR]

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

To improve the dynamic property and the disturbance suppression ability of an electro-optical tracking system, this paper presents a disturbance-observer-based LQR tracking control method. The disturbance-observer-based robust controller is composed of three parts: one is the LQR tracking controller, one is the reference model controller and the other is a compensatory controller designed with the output of the disturbance observer. The uncertainty and disturbances are considered in the controller design. By Lyapunov stability theory and linear matrix inequality (LMI) technique, the sufficient conditions for observer gain and controller gain of the tracking reference model of the electro-optical system are given. Simulation and experimental results show that the proposed method in this paper not only improved the disturbance suppression ability of the electro-optical tracking system but also improved the dynamic property of the electro-optical tracking system, such as rise time, settling time and system overshoot. Specially, compared with other methods in this paper, the tracking accuracy and the disturbance suppression ability of the proposed method are about two to three times higher. The method presented in this paper has important reference value in the field of electro-optical system applications. But, with the development of electro-optical system applications, the tracking accuracy and disturbance suppression ability of the proposed method cannot meet the actual requirements of an electro-optical system. The next step of this paper will consider a variety of practical requirements, such as the controller saturation problem and tracking reference target with strong maneuverability, and further optimize the proposed method. [ABSTRACT FROM AUTHOR]

Vehicle suspension systems, which affect driving performance and passenger comfort, are actively researched with the development of technology and the insufficient quality of passive suspension systems. This paper establishes the suspension model of a quarter of the car and active control is realized. The suspension model was created using the Lagrange–Euler method. LQR, fuzzy logic control (FLC), and fuzzy-LQR control algorithms were developed and applied to the suspension system for active control. The purpose of these controllers is to improve car handling and passenger comfort. Undesirable vibrations occur in passive suspension systems. These vibrations should be reduced using the proposed control methods and a robust system should be developed. To enhance the performance of the fuzzy logic control (FLC) and fuzzy-LQR control methods, the optimal values of the coefficients of the points where the feet of the member functions touch are calculated using the particle swarm optimization (PSO) algorithm. Then, the designed controllers were simulated in the computer environment. The success of the control performance of the applied methods concerning the passive suspension system was compared in percentages. The results are presented and evaluated graphically and numerically. Using the integral time-weighted absolute error (ITAE) criterion, the methods were compared with each other and with the studies in the literature. As a result, it was found that the proposed control method (fuzzy-LQR) is about 84.2% more successful in body motion, 90% in car acceleration, 84.5% in suspension deflection, and 86.7% in tire deflection compared to the studies in the literature. All these results show that the car's ride comfort has been significantly improved. [ABSTRACT FROM AUTHOR]

In this paper, a hybrid particle swarm optimization genetic algorithm LQR controller is used on a quarter car model with an active suspension system. The proposed control algorithm is utilized to overcome the shortcoming that the weight matrix Q and matrix R determined by experience in the traditional LQR control method. The proposed hybrid control method makes it possible to achieve the optimal control effect. A full-order state observer is proposed to observe the state of active suspension. A quarter car active suspension model and road input model are presented at first, and the LQR controller based on the hybrid particle swarm optimization genetic algorithm is utilized in the active suspension system control. Sprung mass acceleration, suspension deflection, and tire dynamic load are selected as the control effect evaluation index. Next, simulation results are presented. According to the results, compared with the passive suspension and active suspension with a traditional LQR control, there is an obvious reduction in the sprung mass acceleration, deflection, and tire dynamic load with an optimized controller under case 1 and case 2. Simultaneously, the system state fed back by the full-order state observer can effectively reflect the true state of the active suspension system. [ABSTRACT FROM AUTHOR]

Featured Application: The methodology presented in this paper can be applied to the design and evaluation of torque vectoring systems in hybrid electric vehicles. Comparison of different controllers is helpful in making design choices in these applications. In today's automotive industry, electrification is a major trend. In-wheel electric motors are among the most promising technologies yet to be fully developed. Indeed, the presence of multiple in-wheel motors acting as independent actuators allows for the implementation of innovative active systems and control strategies. This paper analyzes different design possibilities for a torque vectoring system applied to an originally compact front-wheel drive hybrid electric vehicle with one internal combustion engine for the front axle and two added electric motors integrated in the wheels of the rear axle. A 14 degrees of freedom vehicle model is present o accurately reproduce the nonlinearities of vehicle dynamic phenomena and exploited to obtain high-fidelity numerical simulation results. Different control methods are compared, a PID, an LQR, and four different sliding mode control strategies. All controllers achieve sufficiently good results in terms of lateral dynamics compared with the basic hybrid version. The various aspects and features of the different strategies are analyzed and discussed. Chattering reduction strategies are developed to improve the performance of sliding mode controllers. For a complete overview, control systems are compared using a performance factor that weighs control accuracy and effort in different driving maneuvers, i.e., ramp and step steering maneuvers performed under quite different conditions ranging up to the limits. [ABSTRACT FROM AUTHOR]

A perturbed fractional‐order filter (FOF)‐based LQR control design with multiple performance indices is proposed in this paper. Three variants of the FOF‐based linear quadratic regulator (LQR) system have been proposed along with choices on the commensurate order of state feedback law. The multi‐objective problem formulation has been done with three performance objectives to address the different issues of design. The first performance index constitutes a weighted sum of ITAE (Integral Time of Absolute Error) and the difference between the eigenvalues of the plant and the LQR controlled plant, chosen to minimize the large oscillations as well as relative stability with respect to eigenvalues. A new lower bound of the singular values have been addressed to ensure the robust stability of the system through the formulation of a second performance objective. It is the minimization of singular values of the return ratio matrix at the plant's input. The third and the last performance index aims minimization of maximum singular values of the perturbation transfer function at the plant's output, so as to guarantee no closed‐loop right half plane zeros. The multi‐objective optimization problem is solved and the optimal solutions are obtained via Grey Wolf Optimization Algorithm. The simulation results validate the performance and effectiveness of the proposed control design. [ABSTRACT FROM AUTHOR]

Existing research on auto-berthing of ships has mainly focused on the design and implementation of controllers for automatic berthing. For the real automatic docking processes, not only do external environmental perturbations need to be taken into account but also motion paths, docking strategies and ship mechanical constraints, which are important influential factors to measure autonomous docking methods. Through a literature review of ship path planning and motion control for automatic berthing, it is found that many studies ignore the interference of the actual navigational environment, especially for ships sailing at slow speed when berthing, or do not consider the physical constraints of the steering gear and the main engine. In this paper, we propose a hybrid approach for autonomous berthing control systems based on a Linear Quadratic Regulator (LQR) and Covariance Matrix Adaptation Evolution Strategy (CMA-ES), which systematically addresses the problems involved in the berthing process, such as path planning, optimal control, adaptive berthing strategies, dynamic environmental perturbations and physically enforced structural constraints. The berthing control system based on the LQR and modified LQR-CMA-ES have been validated by simulation work. The simulation results show that the proposed method is able to achieve the automatic docking of the ship well and the system is robust and well adapted to environmental disturbances at slow speed when docking. [ABSTRACT FROM AUTHOR]

As a key type of mobile robot, the two-wheel mobile robot has been developed rapidly for varied domestic, health, and industrial applications due to human-like movement and balancing characteristics based on the inverted pendulum theory. This paper presents a developed Two-Wheel Self-Balanced Robot (TWSBR) model under road disturbance effects and simulated using MATLAB Simscape Multibody. The considered physical-mechanical structure of the proposed TWSBS is connected with a Simulink controller scheme by employing physical signal converters to describe the system dynamics efficiently. Through the Simscape environment, the TWSBR motion is visualized and effectively analyzed without the need for complicated analysis of the associated mathematical model. Besides, 3D visualization of real-time behavior for the implemented TWSBR plant model is displayed by Simulink Mechanics Explorer. Robot balancing and stability are achieved by utilizing Proportional Integral Derivative (PID) and Linear Quadratic Regulator (LQR) controllers' approaches considering specific control targets. A comparative study and evaluation of both controllers are conducted to verify the robustness and road disturbance rejection. The realized performance and robustness of developed controllers are observed by varying object-carrying loaded up on mechanical structure layers during robot motion. In particular, the objective weight is loaded on the robot layers (top, middle, and bottom) during disturbance situations. The achieved findings may have the potential to extend the deployment of using TWSBRs in the varied important application. [ABSTRACT FROM AUTHOR]

Nowadays, interceptors are often used to decrease total resistance and enhance comfort by reducing dynamic trim for high-speed planing vessels. They can be controlled manually as well as automatically by using a suitable closed-loop control system. Thus, in the present study, an automatically controllable system is presented to minimize the total resistance by reducing the dynamic trim in calm water. To reach this aim, a mathematical model which can represent the 2 degree of freedom vertical motion of a prismatic planing vessel is presented. The coefficients used in the model are calculated by using the Savitsky method. The standard dynamic trim angle and the optimum ones in terms of resistance are calculated by using the same method. For control action, a linear full state feedback control strategy (linear quadratic regulator) is applied, and instantaneous blade heights are found considering the change in forward speed. Therefore, the control-oriented model is able to change the blade height to reach the optimum trim angle in terms of the total resistance of the vessel for different forward speeds and speed profiles. The results show that the designed linear quadratic regulator control strategy is successful for reference trim tracking problems.

Controller design for airplane flight control is challenged to achieve an optimum result, particularly for safety purposes. The experiment evaluated the linear quadratic regulator (LQR) method to research the optimal gain of proportional-integral-derivative (PID) to hover accurately the bicopter model by minimizing error. The 3 degree of freedom (DOF) helicopter facility is a suitable bicopter experimental simulator to test its complex multiple input multiple output (MIMO) flight control model to respond to the challenge of multipurpose drone control strategies. The art of LQR setting is how to search for appropriate cost matrices scaling to optimize results. This study aims to accurately optimize take-off position control of the bicopter model by investigating LQR cost matrices variation in actual experiments. From the experimental results of weighted matrix variation on the bicopter simulator, the proposed LQR method has been successfully applied to achieve asymptotic stability of roll angle, although it yielded a significant overshoot. Moreover, the overshoot errors had good linearity to weighting variation. Despite that, the implementation of cost matrices is limited in the real bicopter experiment, and there are appropriate values for achieving an optimal accuracy. Moreover, the unstable step response of the controlled angle occurred because of excessive weighting.

Abstract The looper control of hot strip finishing mill is one of the most critical control items in hot strip rolling mill process. It is a highly complex nonlinear system, with strong states coupling and uncertainty that present a difficult control challenge. Loopers are placed between finishing mill stands not only to control the mass flow of the two stands but also to generate a constant specific strip tension during rolling, independent of the actual strip stock which influences the width of the strip. Some of the applicable control architectures for the finishing mill are reviewed. Two general approaches are considered: the first is based on a loop or SISO (single input single output) strategy, while the second is based on a MIMO strategy: In the loop approach, two different schemes are considered with distinct loop configuration. For both schemes, PID and fuzzy-PID are considered for comparison purposes. Since in the second scheme the most important loop is the looper control loop, it is investigated whether a nonlinear sliding mode control can significantly improve the response. In the multi-variable or MIMO approach, standard LQR (linear quadratic regulator) is investigated after linearization of the system.

In order to improve the accuracy and robustness of intelligent vehicle trajectory tracking, a longitudinal and lateral control strategy based on linear quadratic regulator (LQR) and proportional-integral-derivative (PID) algorithm was proposed. First, the two-degree-of-freedom vehicle kinematics model and trajectory tracking error model are established. Second, the trajectory tracking controller of lateral LQR control algorithm and the speed tracking controller of longitudinal double PID control algorithm are designed, and the key parameters of lateral LQR control are determined by genetic algorithm. Finally, the control algorithm is simulated by CarSim and Simulink under three working conditions: Low speed, Medium speed, and High speed. The simulation results show that the distance deviation of the lateral and longitudinal control algorithm in trajectory tracking is less than 0.05 m, and the front wheel angle and yaw angular velocity change smoothly, which ensures the accuracy and stability of trajectory tracking and improves the comfort of passengers to a certain extent.

An approach to controlling the three-link Robogymnast robotic gymnast and assessing stability is proposed and examined. In the study, a conventionally configured linear quadratic regulator is applied and compared with a fuzzy logic linear quadratic regulator hybrid approach for stabilising the Robogymnast. The Robogymnast is designed to replicate the movement of a human as they hang with both hands holding the high bar and then work to wing up into a handstand, still gripping the bar. The system, therefore has a securely attached link between the hand element and the ‘high bar’, which is mounted on ball bearings and can rotate freely. Moreover, in the study, a mathematical model for the system is linearised, investigating the means of determining the state space in the system by applying Lagrange’s equation. The fuzzy logic linear quadratic regulator controller is used to identify how far the system responses stabilise when it is implemented. This paper investigates factors affecting the control of swing-up in the underactuated three-link Robogymnast. Moreover, a system simulation using MATLAB Simulink is conducted to show the impact of factors including overshoot, rising, and settling time. The principal objective of the study lies in investigating how a linear quadratic regulator or fuzzy logic controller with a linear quadratic regulator (FLQR) can be applied to the Robogymnast, and to assess system behaviour under five scenarios, namely the original value, this value plus or minus ±25%, and plus or minus ±50%. In order to further assess the performance of the controllers used, a comparison is made between the outcomes found here and findings in the recent literature with fuzzy linear quadratic regulator controllers.

This paper synthesizes an innovative nonlinear-type self-adaptive Linear Quadratic Regulator (LQR) to enhance the robustness of under-actuated systems against bounded exogenous disturbances by using the relative-rate and state-error feedback. The control procedure is realized by augmenting the generic LQR with an online reconfiguration block that acts as a superior regulator to dynamically adjust the state-weighting-factors associated with the quadratic-performance index. The Riccati Equation uses the modified state-weighting-factors to re-compute the LQR problem and delivers the time-varying state-feedback gains. The said weighting-factors are adaptively modulated via a conventional state-error-magnitude-driven adaptation law that is retrofitted with auxiliary relative-rate-driven reconfiguration blocks. These blocks utilize error acceleration to deduce the response speed and thus re-adjust the variation rate of the weights in real time. This arrangement reinforces the controller's adaptability to flexibly manipulate the tightness of the applied control effort. The proposed scheme is analyzed by conducting real-time hardware experiments on the QNET Rotary Pendulum. The experimental outcomes validate the superior position-regulation and disturbance-rejection behavior of the proposed scheme. [ABSTRACT FROM AUTHOR]

With the aim of improving the energy utilization during the cooperative operation of multiple trains, this paper proposes an optimal distributed cooperative cruise control strategy to ensure safe and efficient tracking. A performance index function with distributed characteristics is constructed by considering the state errors among trains and energy consumption. An LQR-based optimal design technique is applied to cooperative cruise control to optimize the cooperative control gain to find the optimal solution. Additionally, the scalar coupling gains are introduced to decouple the design of the optimal cooperative control gain from the communication topology of trains. Thus, the proposed strategy is robust for arbitrary directed communication topologies and can eventually be used to achieve the distributed tracking optimization of multiple trains. The asymptotic stability of the system is proved strictly by exploiting the Hurwitz and Lyapunov stability theorem. A numerical simulation example is given to verify the feasibility and effectiveness of the proposed strategy. [ABSTRACT FROM AUTHOR]

This research presents a practical study of active disturbance rejection control law (ADRC) for the control of robotic manipulators in the presence of uncertainties. The control objective of the proposed control law is to track the trajectory accurately and rejects the disturbance caused by robotic manipulators. First, Euler Lagrange's equations are used to model the dynamic behavior of a rotary flexible joint manipulator system (RFJMS). Secondly, the ADRC is designed for the rejection of lump disturbances (modeling uncertainties, nonlinearities, and external disturbances) of the manipulator; to estimate the lump disturbances a fifth-order extended state observer is constructed. Furthermore, a state error feedback control law with disturbance compensation is designed, which needs only a few control parameters to be adjusted. Furthermore, we demonstrate the robustness and effectiveness of the proposed control law by comparing the experimental results with those of LQR and PID. Experimental results show that high precision position control as well as vibration suppression can be achieved with the proposed controller, which is superior to LQR and PID controllers. In spite of uncertainties and nonlinearity of the flexible joint, QUANSER's RFJMS exhibits excellent tracking behavior and disturbance rejection. [ABSTRACT FROM AUTHOR]

In order to improve the vibration suppression effect of the flexible beam system, active control based on soft piezoelectric macro-fiber composites (MFCs) consisting of polyimide (PI) sheet and lead zirconate titanate (PZT) is used to reduce the vibration. The vibration control system is composed of a flexible beam, a sensing piezoelectric MFC plate, and an actuated piezoelectric MFC plate. The dynamic coupling model of the flexible beam system is established according to the theory of structural mechanics and the piezoelectric stress equation. A linear quadratic optimal controller (LQR) is designed based on the optimal control theory. An optimization method, designed based on a differential evolution algorithm, is utilized for the selection of weighted matrix Q. Additionally, according to theoretical research, an experimental platform is built, and vibration active control experiments are carried out on piezoelectric flexible beams under conditions of instantaneous disturbance and continuous disturbance. The results show that the vibration of flexible beams is effectively suppressed under different disturbances. The amplitudes of the piezoelectric flexible beams are reduced by 94.4% and 65.4% under the conditions of instantaneous and continuous disturbances with LQR control. [ABSTRACT FROM AUTHOR]

The trajectory planning plays an important role in realizing the autonomous driving process. The trajectory that reflects the driving habits of human drivers and conforms with people's driving intuition enables a vehicle to operate smoother and more comfortable when passing through corners, which could improve the acceptability of autonomous vehicles in the market in the future. The research of this paper focuses on planning a human driving characterised trajectory along a road based on the test track that could reflect natural driving behaviour in corners considering the sense of natural and comfortable for the occupants. Firstly, the data collected of the test track are processed and the coordinate system transformation is completed, and the human tested trajectories in the test track is extracted and analysed. Then, the human driving characterised trajectory planning is completed based on optimal control in a lane section on the test track. The trajectory tracking control algorithm based on LQR is designed, and a CarSim/Simulink co-simulation platform is established to track the optimal trajectory generated in a lane and the lane centreline trajectory to verify the superiority of the planned trajectory. The results show that compared with the centreline trajectory, the human driving characterised trajectory planned enables the autonomous vehicle operates smoother and more comfortable, and reflects the characteristic of human drivers to a large extent. [ABSTRACT FROM AUTHOR]

Modeling and controlling highly nonlinear, multivariable, unstable, coupled and underactuated systems are challenging problems to which a unique solution does not exist. Modeling and control of Unmanned Aerial Vehicles (UAVs) with four rotors fall into that category of problems. In this paper, a nonlinear quadrotor UAV dynamical model is developed with the Newton–Euler method, and a control architecture is proposed for 3D trajectory tracking. The controller design is decoupled into two parts: an inner loop for attitude stabilization and an outer loop for trajectory tracking. A few attitude stabilization methods are discussed, implemented and compared, considering the following control approaches: Proportional–Integral–Derivative (PID), Linear–Quadratic Regulator (LQR), Model Predictive Control (MPC), Feedback Linearization (FL) and Sliding Mode Control (SMC). This paper is intended to serve as a guideline work for selecting quadcopters' control strategies, both in terms of quantitative and qualitative considerations. PID and LQR controllers are designed, exploiting the model linearized about the hovering condition, while MPC, FL and SMC directly exploit the nonlinear model, with minor simplifications. The fast dynamics ensured by the SMC-based controller together with its robustness and the limited estimated command effort of the controller make it the most promising controller for quadrotor attitude stabilization. The outer loop consists of three independent PID controllers: one for altitude control and the other two, together with a dynamics' inversion, are entitled to the computation of the reference attitude for the inner loop. The capability of the controlled closed-loop system of executing complex trajectories is demonstrated by means of simulations in MATLAB/Simulink®. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

The paper focuses on comparing applicability, tuning, and performance of different controllers implemented and tested on a finless rocket during its boost phase. The objective was to evaluate the advantages and disadvantages of each controller, such that the most appropriate one would then be developed and implemented in real-time in the finless rocket. The compared controllers were Linear Quadratic Regulator (LQR), Linear Quadratic Gaussian (LQG), and Proportional Integral Derivative (PID). To control the attitude of the rocket, emphasis is given to the Thrust Vector Control (TVC) component (sub-system) through the gimballing of the rocket engine. The launcher is commanded through the control input thrust gimbal angle δ , while the output parameter is expressed in terms of the pitch angle θ. After deriving a linearized state–space model, rocket stability is addressed before controller implementation and testing. The comparative study showed that both LQR and LQG track pitch angle changes rapidly, thus providing efficient closed-loop dynamic tracking. Tuning of the LQR controller, through the Q and R weighting matrices, illustrates how variations directly affect performance of the closed-loop system by varying the values of the feedback gain (K). The LQG controller provides a more realistic profile because, in general, not all variables are measurable and available for feedback. However, disturbances affecting the system are better handled and reduced with the PID controller, thus overcoming steady-state errors due to aerodynamic and model uncertainty. Overall controller performance is evaluated in terms of overshoot, settling and rise time, and steady-state error. [ABSTRACT FROM AUTHOR]

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In this paper, a modified block backstepping controller was formulated for double lane changing control of a two-degree-of-freedom (2DOF) autonomous vehicle. For a systematic procedure, a 5th-degree polynomial double lane change trajectory was created. Next, the state model dynamics of this underactuated 2DOF autonomous vehicle is presented, which was transformed into the block-strict feedback form. Thereafter, the block backstepping technique was implemented to achieve the control input (steering angle). For enhancing the steady state performance during the trajectory tracking, an integral action was included in the proposed controller. The stability of this controller was established through the Lyapunov theory. To investigate the effectiveness of this proposed controller, we compared it with a human driver's transfer function controller and LQR controller, in addition to the sliding mode controller. Simulation results were achieved using CarSim-Simulink. Later, this controller was implemented to track the same lane change path with a different road coefficient of friction. The supposed controller characteristic was further investigated by inspecting the motion of the vehicle when exposed to an idealized lateral step force disturbance. The simulation results indicated the power of modified block backstepping control and it has higher following accuracy, better yaw rate tracking, and stable front steering angle, at high speed and at high and low friction roads. [ABSTRACT FROM AUTHOR]

This study revealed an adaptive state feedback control method based on recursive least squares (RLS) that is introduced for a time-varying system to work with high efficiency. Firstly, a system identification block was created that gives the mathematical model of the time-varying system using the input/output data packets of the controller system. Thanks to this block, the system is constantly monitored to update the parameters of the system, which change over time. Linear quadratic regulator (LQR) is renewed according to these updated parameters, and self-adjustment of the system is provided according to the changed system parameters. The Matlab/Simulink state-space model of the variable loaded servo (VLS) system module was obtained for the simulation experiments in this study; then the system was controlled. Moreover, experiments were carried out on the servo control experimental equipment of the virtual simulation laboratories (VSIMLABS). The effectiveness of the proposed new method was observed taking the performance indexes as a reference to obtain the results of the practical application of the proposed method. Regarding the analysis of simulation and experimental results, the proposed approach minimizes the load effect and noise and the system works at high efficiency.

Unmanned aerial vehicles (UAVs) are subject to the wind and other environmental disturbances that can destabilize them. The high performance and robustness of the Linear Quadratic Regulator (LQR) controllers ensure the ability to reduce the deviations in state trajectories with minimum control effort. In this paper, the weighting matrices are adjusted automatically via a novel method implemented through state variables matrix of the quadrotor together with a preference factor. This proposed factor is determined by the designer via penalizing or rewarding a certain state of the quadrotor out of others so that the model insufficiencies against disturbances are compensated. The effectiveness of the proposed method of selecting these matrices is evaluated for the cases of LQR and LQR with a PI controller. They were evaluated with respect to the convergence of state variables to their reference values within a specific time and compliance with their desired performance characteristics. The experimental results revealed that both control strategies could stabilize the quadrotor in the desired position and attitude with better performance and robustness characteristics. The results also showed that the LQR-PI control method is a more reliable and effective approach in achieving higher tracking performances compared to the LQR only.

Double-linked rotary inverted pendulum is a developed structure of single-linked rotary inverted pendulum. Due to its high-order SIMO structure, it is a big challenge to operate this model on experiment. In this paper, we present an experimental double-linked rotary inverted pendulum that is constructed in our laboratory. A classical linear method – LQR – is used to control well this model in simulation. In experiment, we have stabilized this model for two seconds. Thence, our research contributes experimental results to confirm the ability of LQR for this kind of real model in stabilizing it in equilibrium point.

This article presents a neural algorithm based on Reinforcement Learning for optimising Linear Quadratic Regulator (LQR) creation. The proposed method allows designing such a target function that automatically leads to changes in the quality and resource matrix so that the target LQR regulator achieves the desired performance. The solution's stability and optimality are the target controller's responsibility. However, the neural mechanism allows obtaining, without expert knowledge, the appropriate Q and R matrices, which will lead to such a gain matrix that will realise the control that will lead to the desired quality. The presented algorithm was tested for the derived quadrant model of the suspension system. Its application improved user comfort by 67% compared to the passive solution and 14% compared to non-optimised LQR. [ABSTRACT FROM AUTHOR]

Hybrid aircraft configurations with combined cruise and vertical flight capabilities are increasingly being considered for unmanned aircraft and urban air mobility missions. To ensure the safety and autonomy of such missions, control challenges including fault tolerance and windy conditions must be addressed. This paper presents an observer-based optimal control approach for the active combined fault and wind disturbance rejection, with application to a quadplane unmanned aerial vehicle. The quadplane model is linearised for the longitudinal plane, vertical takeoff and landing and transition modes. Wind gusts are modelled using a Dryden turbulence model. An unknown input observer is first developed for the estimation of wind disturbance by defining an auxiliary variable that emulates body referenced accelerations. The approach is then extended to simultaneous rejection of intermittent elevator faults and wind disturbance velocities. Estimation error is mathematically proven to converge to zero, assuming a piecewise constant disturbance. A numerical simulation analysis demonstrates that for a typical quadplane flight profile at 100 m altitude, the observer-based wind gust and fault correction significantly enhances trajectory tracking accuracy compared to a linear quadratic regulator and to a H-infinity controller, which are both taken, without loss of generality, as benchmark controllers to be enhanced. This is done by adding wind and fault compensation terms to the controller with admissible control effort. The proposed observer is also shown to enhance accuracy and observer-based rejection of disturbances and faults compared to three alternative observers, based on output error integration, acceleration feedback and a sliding mode observer, respectively. The proposed approach is particularly efficient for the active rejection of actuator faults under windy conditions. [ABSTRACT FROM AUTHOR]

The control algorithm could greatly help the suspension system improve the comprehensive performance of the vehicle. Existing control methods need to obtain the intermediate states, which are difficult to obtain directly or accurately when estimated by filters or observers. Thus, this paper proposed a new practical finite state LQR control method to deal with this problem. By combining with the output state of the finite sensor of the vehicle suspension system and weakening the unknown state as the goal, an optimization model is established with the design variables as the LQR weight coefficients. Then, the direct relationship between the current control input and the finite sensor output is obtained, and the finite state LQR control is realized. Taking the quarter-car suspension model as an example, the corresponding noise is added considering sensor accuracy, and the control performance of the four control methods is studied considering the uncertainties of suspension system parameters. In addition, the acceleration of sprung mass and the dynamic travel coefficient of suspension have been separately calculated by methods of finite state LQR control, LQR control, and PID control. The results show that there is not much difference between them under shock excitation or random excitation. However, the finite state LQR control method has the best comprehensive control performance in that its dynamic tire load coefficient is better than other methods; it could take into account the suspension work stroke coefficient, dynamic tire load coefficient, and sprung mass' acceleration of the vehicle suspension system at the same time. In order to realize the optimal control effect with limited sensor arrangement, the finite state LQR control method only needs to obtain the current sensor output and the current control input, without estimating the unknown intermediate state. By this means, the proposed control method greatly simplifies the design of the control system and has great advantages on practical value. [ABSTRACT FROM AUTHOR]

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Nowadays, interceptors are often used to decrease total resistance and enhance comfort by reducing dynamic trim for high-speed planing vessels. They can be controlled manually as well as automatically by using a suitable closed-loop control system. Thus, in the present study, an automatically controllable system is presented to minimize the total resistance by reducing the dynamic trim in calm water. To reach this aim, a mathematical model which can represent the 2 degree of freedom vertical motion of a prismatic planing vessel is presented. The coefficients used in the model are calculated by using the Savitsky method. The standard dynamic trim angle and the optimum ones in terms of resistance are calculated by using the same method. For control action, a linear full state feedback control strategy (linear quadratic regulator) is applied, and instantaneous blade heights are found considering the change in forward speed. Therefore, the control-oriented model is able to change the blade height to reach the optimum trim angle in terms of the total resistance of the vessel for different forward speeds and speed profiles. The results show that the designed linear quadratic regulator control strategy is successful for reference trim tracking problems. [ABSTRACT FROM AUTHOR]