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Shauqee, Mohamad Norherman, Parvathy Rajendran, and Nurulasikin Mohd Suhadis. "Proportional Double Derivative Linear Quadratic Regulator Controller Using Improvised Grey Wolf Optimization Technique to Control Quadcopter." Applied Sciences 11, no. 6 (2021): 2699. http://dx.doi.org/10.3390/app11062699.
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A hybrid proportional double derivative and linear quadratic regulator (PD2-LQR) controller is designed for altitude (z) and attitude (roll, pitch, and yaw) control of a quadrotor vehicle. The derivation of a mathematical model of the quadrotor is formulated based on the Newton–Euler approach. An appropriate controller’s parameter must be obtained to obtain a superior control performance. Therefore, we exploit the advantages of the nature-inspired optimization algorithm called Grey Wolf Optimizer (GWO) to search for those optimal values. Hence, an improved version of GWO called IGWO is proposed and used instead of the original one. A comparative study with the conventional controllers, namely proportional derivative (PD), proportional integral derivative (PID), linear quadratic regulator (LQR), proportional linear quadratic regulator (P-LQR), proportional derivative and linear quadratic regulator (PD-LQR), PD2-LQR, and original GWO-based PD2-LQR, was undertaken to show the effectiveness of the proposed approach. An investigation of 20 different quadcopter models using the proposed hybrid controller is presented. Simulation results prove that the IGWO-based PD2-LQR controller can better track the desired reference input with shorter rise time and settling time, lower percentage overshoot, and minimal steady-state error and root mean square error (RMSE).
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Majumdar, Jharna, Sudip C Gupta, and B. Prassanna Prasath. "Linear and Non-Linear Control Design of Skid Steer Mobile Robot on an Embedded." IAES International Journal of Robotics and Automation (IJRA) 7, no. 3 (2018): 185. http://dx.doi.org/10.11591/ijra.v7i3.pp185-196.
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A detailed approach for a linear Proportional-Integral-Derivative (PID) controller and a non-linear controller - Linear Quadratic Regulator (LQR) is discussed in this paper. By analyzing several mathematical designs for the Skid Steer Mobile Robot (SSMR), the controllers are implemented in an embedded microcontroller - Mbed LPC1768. To verify the controllers, MATLAB-Simulink is used for the simulation of both the controllers involving motors - Maxon RE40. This paper compares between PID and LQR controller along with the performance comparison between Homogenous and Non-Homogenous LQR controllers.
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Vo, Minh-Tai, Van-Dong-Hai Nguyen, Hoai-Nghia Duong, and Vinh-Hao Nguyen. "Combining Passivity-Based Control and Linear Quadratic Regulator to Control a Rotary Inverted Pendulum." Journal of Robotics and Control (JRC) 4, no. 4 (2023): 479–90. http://dx.doi.org/10.18196/jrc.v4i4.18498.
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In this manuscript, new combination methodology is proposed, which named combining Passivity-Based Control and Linear Quadratic Regulator (for short, CPBC-LQR), to support the stabilization process as the system is far from equilibrium point. More precisely, Linear Quadratic Regulator (for short, LQR) is used together with Passivity-Based Control (for short, PBC) controller. Though passivity-based control and linear quadratic regulator are two control methods, it is possible to integrate them together. The combination of passivity-based control and linear quadratic regulator is analyzed, designed and implemented on so-called rotary inverted pendulum system (for short, RIP). In this work, CPBC-LQR is validated and discussed on both MATLAB/Simulink environment and real-time experimental setup. The numerical simulation and experimental results reveal the ability of CPBC-LQR control scheme in stabilization problem and achieve a good and stable performance. Effectiveness and feasibility of proposed controller are confirmed via comparative simulation and experiments.
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Mohammad, A. Thanoon, R. Awad Sohaib, and Kh. Abdullah Ismael. "LQR controller design for stabilization of non-linear DIP system based on ABC algorithm." Eastern-European Journal of Enterprise Technologies 2, no. 2(122) (2023): 36–44. https://doi.org/10.15587/1729-4061.2023.275657.
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Inverted pendulum systems, such as double or single, rotational or translational inverted pendulums are non-linear and unstable, which have been the most dominant approaches for control systems. The double inverted pendulum is one kind of a non-linear, unstable system, multivariable, and strong coupling with a wide range of control methods. To model these types of systems, many techniques have been proposed so that motivating researchers to come up with new innovative solutions. The Linear Quadratic Regulator (LQR) controller has been a common controller used in this field. Meanwhile, the Artificial Bee Colony (ABC) technique has become an alternative solution for employing Bee Swarm Intelligence algorithms. The research solutions of the artificial bee colony algorithm in the literature can be beneficial, however, the utilization of discovered sources of food is ineffective. Thus, in this paper, we aim to provide a double inverted pendulum system for stabilization by selecting linear quadratic regulator parameters using a bio-inspired optimization methodology of artificial bee colony and weight matrices Q and R. The results show that when the artificial bee colony algorithm is applied to a linear quadratic regulator controller, it gains the capacity to autonomously tune itself in an online process. To further demonstrate the efficiency and viability of the suggested methodology, simulations have been performed and compared to conventional linear quadratic regulator controllers. The obtained results demonstrate that employing artificial intelligence (AI) together with the proposed controller outperforms the conventional linear quadratic regulator controllers by more than 50 % in transient response and improved time response and stability performance
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KARAŞAHİN, Ali Tahir. "Genetically Tuned Linear Quadratic Regulator for Trajectory Tracking of a Quadrotor." Academic Platform Journal of Engineering and Smart Systems 12, no. 1 (2024): 37–46. http://dx.doi.org/10.21541/apjess.1316025.
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In this paper, a linear quadratic regulator (LQR) controller operating according to the genetically tuned inner-outer loop structure is proposed for trajectory tracking of a quadrotor. Setting the parameters of a linear controller operating according to the inner-outer loop structure is a matter that requires profound expertise. Optimization algorithms are used to cope with the solution of this problem. First, the dynamic equations of motion of the quadrotor are obtained and modelled in state-space form. The LQR controller, which will operate according to the inner-outer loop structure in the MATLAB/Simulink environment, has been developed separately for 6 degrees of freedom (DOF) of the quadrotor. Since adjusting these parameters will take a long time, a genetic algorithm has been used at this point. The LQR controller with optimized coefficients and a proposed LQR controller-based study in the literature are evaluated according to their success in following the reference trajectory and their responses to specific control inputs. According to the results obtained, it was observed that the genetically adjusted LQR controller produced more successful outcomes.
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Thanoon, Mohammad A., Sohaib R. Awad, and Ismael Kh Abdullah. "LQR controller design for stabilization of non-linear DIP system based on ABC algorithm." Eastern-European Journal of Enterprise Technologies 2, no. 2 (122) (2023): 36–44. http://dx.doi.org/10.15587/1729-4061.2023.275657.
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Inverted pendulum systems, such as double or single, rotational or translational inverted pendulums are non-linear and unstable, which have been the most dominant approaches for control systems. The double inverted pendulum is one kind of a non-linear, unstable system, multivariable, and strong coupling with a wide range of control methods. To model these types of systems, many techniques have been proposed so that motivating researchers to come up with new innovative solutions. The Linear Quadratic Regulator (LQR) controller has been a common controller used in this field. Meanwhile, the Artificial Bee Colony (ABC) technique has become an alternative solution for employing Bee Swarm Intelligence algorithms. The research solutions of the artificial bee colony algorithm in the literature can be beneficial, however, the utilization of discovered sources of food is ineffective. Thus, in this paper, we aim to provide a double inverted pendulum system for stabilization by selecting linear quadratic regulator parameters using a bio-inspired optimization methodology of artificial bee colony and weight matrices Q and R. The results show that when the artificial bee colony algorithm is applied to a linear quadratic regulator controller, it gains the capacity to autonomously tune itself in an online process. To further demonstrate the efficiency and viability of the suggested methodology, simulations have been performed and compared to conventional linear quadratic regulator controllers. The obtained results demonstrate that employing artificial intelligence (AI) together with the proposed controller outperforms the conventional linear quadratic regulator controllers by more than 50 % in transient response and improved time response and stability performance
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Enejor, Emmanuel U., Folashade M. Dahunsi, Kayode F. Akingbade, and Ibigbami O. Nelson. "Low Earth Orbit Satellite Attitude Stabilization Using Linear Quadratic Regulator." European Journal of Electrical Engineering and Computer Science 7, no. 3 (2023): 17–29. http://dx.doi.org/10.24018/ejece.2023.7.3.505.
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This study compares the result of the PID controller to the LQR controller when used in the on-orbit stabilization of a satellite in the low earth orbit. The results from the PID controller show that the controller is too weak when used alone as the controller could not stabilize the system after 500 s which is not even allowable in practical application. For the LQR controller, a performance metric was set which is: i. the settling time is to be ≤ 10 seconds, ii. Maximum power consumption ≤ 1.5 Watts and iii. Zero (0) steady-state error / final value. The LQR controller meets system performance by achieving a settling time of roll (peak amplitude=0.26 s, settling time=10.0 s), Pitch (peak amplitude=0.395 s, settling time=5.52 s), Yaw (peak amplitude=0.350 s, settling time=5.52 s) and Total power consumption are 1.26 watt with a maximum torque of 3.22 mNm. Because power consumption and precision are critical in satellite applications, particularly military surveillance satellites. As a result, for an aerospace engineer to achieve their space mission, for instance, space mission like low earth orbit surveillance satellites, flexible solar panels, a high accuracy pointing accuracy, it will be impossible to adopt a PID controller except the engineer is ready for the complexity of design filters and compensators. An LQR design in this study can take care of all this complexity with minimum power consumption.
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Nekoui, Mohammad Ali, and Hassan Heidari Jame Bozorgi. "Weighting Matrix Selection Method for LQR Design Based on a Multi-Objective Evolutionary Algorithm." Advanced Materials Research 383-390 (November 2011): 1047–54. http://dx.doi.org/10.4028/www.scientific.net/amr.383-390.1047.
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This paper introduces an application of Multi-Objective Evolution Algorithm (MOEA) to design Q and R weighting matrices in Linear Quadratic regulators (LQR). Considering the difficulty of designing weighting matrices for a linear quadratic regulator, a multi-objective evolutionary algorithm based approach is proposed. The LQR weighting matrices, state feedback control rate and consequently the optimal controller are obtained by means of establishing the multi-objective optimization model of LQR weighting matrices and applying MOEA to it, which makes control system meet multiple performance indexes simultaneously. Controller of double inverted pendulum system is designed using the proposed approach. Simulation results show that it has shorter adjusting time and smaller amplitude value deviating from steady-state than a Non-dominated Sorting Genetic Algorithm LQR ( NSGA- LQR )weighting matrices design approach.
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Camino, J. F., and I. F. Santos. "A periodic linear–quadratic controller for suppressing rotor-blade vibration." Journal of Vibration and Control 25, no. 17 (2019): 2351–64. http://dx.doi.org/10.1177/1077546319853358.
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This paper presents an active control strategy, based on a time-varying linear–quadratic optimal control problem, to attenuate the tip vibration of a two-dimensional coupled rotor-blade system whose dynamics is periodic. First, a periodic full-state feedback controller based on the linear–quadratic regulator (LQR) problem is designed. If all the states are not available for feedback, then an optimal periodic time-varying estimator, using the Kalman–Bucy filter, is computed. Both the Kalman filter gain and the LQR gain are obtained as the solution of a periodic Riccati differential equation (PRDE). Together, these gains provide the observer-based linear–quadratic–Gaussian (LQG) controller. An algorithm to solve the PRDE is also presented. Both controller designs ensure closed-loop stability and performance for the linear time-varying rotor-blade equation of motion. Numerical simulations show that the LQR and the LQG controllers are able to significantly attenuate the rotor-blade tip vibration.
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Helmy, M., A. T. Hafez, and M. Ashry. "CubeSat attitude control via linear quadratic regulator (LQR)." Journal of Physics: Conference Series 2616, no. 1 (2023): 012022. http://dx.doi.org/10.1088/1742-6596/2616/1/012022.
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Abstract The interest in space-related activities has grown recently on a global scale. The determination and control of attitude are necessary all space duties. As it affects the satellites mission accuracy, many researches are related to it. Attitude control systems (ACS) design and modelling are represented in this paper. The mathematical models for CubeSat and reaction wheels that act as actuator and the proposed optimal control system are introduced. The proposed controller is applied to control and stabilize the CubeSat through a set of reaction wheels. The simulation results show the superior results of the proposed controller compared with traditional control systems in the presence of external disturbances and white noise. The withdraws of each control system are presented through the simulation results. The main contribution in this paper is solving the attitude control problem for a CubeSat using LQR approach in the presences of disturbances and noise.
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Trong-Thang, Nguyen. "The linear quadratic regular algorithm-based control system of the direct current motor." International Journal of Power Electronics and Drive System (IJPEDS) 10, no. 2 (2019): 768–76. https://doi.org/10.11591/ijpeds.v10.i2.pp768-776.
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This research aims to propose an optimal controller for controlling the speed of the Direct Current (DC) motor. Based This research aims to propose an optimal controller for controlling the speed of the Direct Current (DC) motor. Based on the mathematical equations of DC Motor, the author builds the equations of the state space model and builds the linear quadratic regulator (LQR) controller to minimize the error between the set speed and the response speed of DC motor. The results of the proposed controller are compared with the traditional controllers as the PID, the feed-forward controller. The simulation results show that the quality of the control system in the case of LQR controller is much higher than the traditional controllers. The response speed always follows the set speed with the short conversion time, there isn't overshoot. The response speed is almost unaffected when the torque impact on the shaft is changed.on the mathematical equations of DC Motor, the author builds the equations of the state space model and builds the linear quadratic regulator (LQR) controller to minimize the error between the set speed and the response speed of DC motor. The results of the proposed controller are compared with the traditional controllers as the PID, the feed-forward controller. The simulation results show that the quality of the control system in the case of LQR controller is much higher than the traditional controllers. The response speed always follows the set speed with the short conversion time, there isn't overshoot. The response speed is almost unaffected when the torque impact on the shaft is changed.
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Tayebi, Javad, Amir Ali Nikkhah, and Jafar Roshanian. "LQR/LQG attitude stabilization of an agile microsatellite with CMG." Aircraft Engineering and Aerospace Technology 89, no. 2 (2017): 290–96. http://dx.doi.org/10.1108/aeat-07-2014-0102.
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Purpose The purpose of the paper is to design a new attitude stabilization system for a microsatellite based on single gimbal control moment gyro (SGCMG) in which the gimbal rates are selected as controller parameters. Design/methodology/approach In the stability mode, linear quadratic regulator (LQR) and linear quadratic Gaussian (LQG) control strategies are presented with the gimbal rates as a controller parameters. Instead of developing a control torque to solve the attitude problem, the attitude controller is developed in terms of the control moment gyroscope gimbal angular velocities. Attitude control torques are generated by means of a four SGCMG pyramid cluster. Findings Numerical simulation results are provided to show the efficiency of the proposed controllers. Simulation results show that this method could stabilize satellite from initial condition with large angles and with more accuracy in comparison with feedback quaternion and proportional-integral-derivative controllers. These results show the effect of filtering the noisy signal in the LQG controller. LQG in comparison to LQR is more realistic. Practical implications The LQR method is more appropriate for the systems that have project models reasonably exact and ideal sensors/actuators. LQG is more realistic, and it can be used when not all of the states are available or when the system presents noises. LQR/LQG controller can be used in the stabilization mode of satellite attitude control. Originality/value The originality of this paper is designing a new attitude stabilization system for an agile microsatellite using LQR and LQG controllers.
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Ingabire, Aline, and Andrey A. Sklyarov. "Control of longitudinal flight dynamics of a fixedwing UAV using LQR, LQG and nonlinear control." E3S Web of Conferences 104 (2019): 02001. http://dx.doi.org/10.1051/e3sconf/201910402001.
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This paper aim is to present a comparative study between Linear Quadratic Regulator (LQR), Linear Quadratic Gaussian (LQG) and nonlinear controllers for pitch control of a fixed-wing Unmanned Aerial Vehicle (UAV). Due to a good stability margin and strong robustness LQR has been selected. LQG was chosen because is able to overcome external disturbances. Kalman Filter controller was also introduced to the fixed-wing UAV flight control. Further, we designed an autopilot that controls the pitch angle of the fixed-wing UAV. In the end, the control laws are simulated in Matlab/Simulink. The results obtained are compared to see which method is faster, more reliable and more robust.
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Zulkarnain, Noraishikin, Hairi Zamzuri, and Saiful Amri Mazlan. "LQG Control Design for Vehicle Active Anti-Roll Bar System." Applied Mechanics and Materials 663 (October 2014): 146–51. http://dx.doi.org/10.4028/www.scientific.net/amm.663.146.
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The objective of this paper is to design a linear quadratic regulator (LQR) and linear quadratic Gaussian (LQG) controllers for an active anti-roll bar system. The use of an active anti-roll bar will be analysed from two different perspectives in vehicle ride comfort and handling performances. This paper proposed the basic vehicle dynamic modelling with four degree of freedom (DOF) on half car model and are described that show, why and how it is possible to control the handling and ride comfort of the car, with the external forces also control strategies on the front anti-roll bar. By simulation analysis, the design model is validity and the performance under control of linear quadratic regulator (LQR) and linear quadratic Gaussian (LQG) controller are achieved. Both two controllers are modeled in MATLAB/SIMULINK environment. It has to be determined which control strategy delivers better performance with respect to roll angle and the roll rate of half vehicle body. The result shows, however, that LQG produced better response compared to a LQR strategy.
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Hadid, Samira, Razika Boushaki Zamoum, and Youcef Refis. "Linear and nonlinear control design for a quadrotor." Bulletin of Electrical Engineering and Informatics 14, no. 2 (2025): 940–55. https://doi.org/10.11591/eei.v14i2.8234.
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In the current study, the quadrotor's nonlinear dynamic model is developed using the Newton-Euler approach. Following that, several nonlinear and linear control strategies for tracking the quadrotor's trajectory are applied. First, by employing distinct controllers for each output variable, direct application of the linear proportional integral derivative (PID) controller to the nonlinear system is realized. This system may also be linearized about an operational point to generate linear controllers, according to the linear quadratic regulator (LQR) demonstration. Nevertheless, in practice, the system dynamics may not always be accurately reflected by this linear approximation and may even be relatively wasteful. Nonlinear regulators, including the feedback linearization (FBL) controller, sliding mode controller (SMC), and modified sliding mode controller (MSMC), perform better in such situations. The trajectory tracking capabilities, dynamic performance, and potential disruption impact of both methods are evaluated and compared. The FBL with LQR was the best controller among them all. The SMC and the MSMC were also very good in tracking the trajectory.
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Bendor, Sampson Akem*1 Obi P. I2 Akpama E. James3 &. Okoro .O. I4. "DYNAMIC MODELING OF A LINEAR QUADRATIC REGULATOR BASED OPTIMAL DIRECT CURRENT MOTOR FOR IMPROVED PERFORMANCE." GLOBAL JOURNAL OF ENGINEERING SCIENCE AND RESEARCHES 7, no. 1 (2020): 49–57. https://doi.org/10.5281/zenodo.3631415.
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The paper herein presents the dynamic modelling of a linear quadratic regulator based optimal direct current (DC) motor controller for improved performance. This study investigates the optimal use of a controller in the control of DC motor speed. This work also carried out a comparison of time response specification of the Linear Quadratic Regulator (LQR) for a speed control of a separately excited DC motor. This paper investigates the appropriate control strategy that delivers a better performance with respect to DC motor's speed reliability. The control method to be implemented in this paper is the LQR which is a state space controller and the model of a direct current motor is presented in state space form. MATLAB/SIMULINK software program was used to simulate the steady state and transient mathematical models of the machines. The test for both controllability and observability were carried out in the rank of matrix two. When the LQR was simulated, it was observed from the plots of speed against time at open loop with unity value of 1Volt and 1Ohm, that the DC motor system with the LQR control stabilizes faster at the speed of 1rad/secand after about 1seconds<strong>.</strong>
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Huynh, Phuc-Hoang, Cong-Duy Pham, Nam-Binh Vu, et al. "A Survey of LQG over MPC and LQR Control for Rotary Inverted Pendulum." Robotica & Management 29, no. 2 (2024): 10–15. https://doi.org/10.24193/rm.2024.2.2.
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In this paper, we examine the theoretical cost function equivalence between Model Predictive Control (MPC) and Linear-Quadratic Gaussian (LQG) control, as well as Linear-Quadratic Regulator (LQR) control under specific conditions. Specifically, we linearize the Rotary Inverted Pendulum (RIP) system and construct a Kalman filter state estimator for application in both the LQG and MPC controllers with input and output constraints. We also assume measurable and computable states when designing the LQR controller. Through simulation and experimentation, we demonstrate that, despite the equivalence in cost functions, the output response of MPC is significantly better than that of both LQG and LQR. Our findings not only substantially bridge gaps in control theory but also emphasize the robustness of MPC in complex real-world applications. These insights pave the way for more effective and reliable control strategies across various engineering fields.
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Nguyen, Trong-Thang. "The linear quadratic regular algorithm-based control system of the direct current motor." International Journal of Power Electronics and Drive Systems (IJPEDS) 10, no. 2 (2019): 768. http://dx.doi.org/10.11591/ijpeds.v10.i2.pp768-776.
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<span>This research aims to propose an optimal controller for controlling the speed of the Direct Current (DC) motor. Based on the mathematical equations of DC Motor, the author builds the equations of the state space model and builds the linear quadratic regulator (LQR) controller to minimize the error between the set speed and the response speed of DC motor. The results of the proposed controller are compared with the traditional controllers as the PID, the feed-forward controller. The simulation results show that the quality of the control system in the case of LQR controller is much higher than the traditional controllers. The response speed always follows the set speed with the short conversion time, there isn't overshoot. The response speed is almost unaffected when the torque impact on the shaft is changed.</span>
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Xie, Xianyi, Lisheng Jin, Guo Baicang, and Jian Shi. "Vehicle direct yaw moment control system based on the improved linear quadratic regulator." Industrial Robot: the international journal of robotics research and application 48, no. 3 (2021): 378–87. http://dx.doi.org/10.1108/ir-08-2020-0168.
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Purpose This study aims to propose an improved linear quadratic regulator (LQR) based on the adjusting weight coefficient, which is used to improve the performance of the vehicle direct yaw moment control (DYC) system. Design/methodology/approach After analyzing the responses of the side-slip angle and the yaw rate of the vehicle when driving under different road adhesion coefficients, the genetic algorithm and fuzzy logic theory were applied to design the parameter regulator for an improved LQR. This parameter regulator works according to the changes in the road adhesion coefficient between the tires and the road. Hardware-in-the-loop (HiL) tests with double-lane changes under low and high road surface adhesion coefficients were carried out. Findings The HiL test results demonstrate the proposed controllers’ effectiveness and reasonableness and satisfy the real-time requirement. The effectiveness of the proposed controller was also proven using the vehicle-handling stability objective evaluation method. Originality/value The objective evaluation results reveal better performance using the improved LQR DYC controller than a front wheel steering vehicle, especially in reducing driver fatigue, improving vehicle-handling stability and enhancing driving safety.
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Kurnianingtyas, Rahajeng. "PERANCANGAN MOTOR DC DENGAN SISTEM KENDALI LINEAR QUADRATIC REGULATOR MENGGUNAKAN SOFTWARE MATLAB." Jurnal Kajian Teknik Elektro 9, no. 2 (2024): 128–33. https://doi.org/10.52447/jkte.v9i2.7821.
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Di dalam sebuah sistem perlu adanya perancangan sebuah sistem pengendali yang baik untuk mendapatkan nilai keluaran (output) atau hasil yang diinginkan. Motor DC adalah motor arus searah yang mengubah energi listrik menjadi energi mekanik. Motor DC sering digunakan karena kontrol kecepatan yang presisi dalam dunia industri. Di dalam sebuah sistem pengendalian motor DC dibutuhkan komponen seperti sensor dan controller. Controller merupakan sebuah pengendali yang akan memberikan sinyal keluaran berupa sinyal kontrol yang akan dikirimkan ke dalam plant atau sistem yang dikontrol. Pada sistem pengendalian tertutup terdapat adanya nilai feedback yang dibaca oleh sensor dan dikirimkan kembali ke controller sebagai nilai error. Nilai error ini yang nantinya akan mempengaruhi nilai sinyal kontrol dan akan berdampak pada nilai keluaran dari sebuah sistem atau plant. Untuk memperoleh sistem yang stabil maka respon sistem harus mencapai fase steady state. Dalam penelitian ini, sistem akan di simulasikan sedemikian rupa dengan menggunakan program Matlab dengan sistem kendali linear quadratic regulator. Pemilihan sistem kendali ini diharapkan mampu memberikan respon yang stabil. Berdasarkan penelitian yang dilakukan simulasi plant dengan sistem kendali LQR PID mempunyai nilai settling time 2.5 sekon dan rise time 2 sekon. Sedangkan plant dengan sistem kendali LQR mempunyai settling time dengan waktu 1.1 sekon dan rise time 1.05 sekon. Meskipun plant dengan sistem kendali LQR memiliki settling time dan rise time lebih cepat tetapi respon yang dihasilkan lebih stabil menggunakan sistem kendali LQR PID. Pada sistem LQR respon setelah mencapai steady state cenderung lebih tinggi daripada setpoint.Kata kunci— Motor DC, LQR, PID, Matlab
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Patarroyo-Montenegro, Juan F., Jesus D. Vasquez-Plaza, Fabio Andrade, and Lingling Fan. "An Optimal Power Control Strategy for Grid-Following Inverters in a Synchronous Frame." Applied Sciences 10, no. 19 (2020): 6730. http://dx.doi.org/10.3390/app10196730.
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This work proposes a power control strategy based on the linear quadratic regulator with optimal reference tracking (LQR-ORT) for a three-phase inverter-based generator (IBG) using an LCL filter. The use of an LQR-ORT controller increases robustness margins and reduces the quadratic value of the power error and control inputs during transient response. A model in a synchronous reference frame that integrates power sharing and voltage–current (V–I) dynamics is also proposed. This model allows for analyzing closed-loop eigenvalue location and robustness margins. The proposed controller was compared against a classical droop approach using proportional-resonant controllers for the inner loops. Mathematical analysis and hardware-in-the-loop (HIL) experiments under variations in the LCL filter components demonstrate fulfillment of robustness and performance bounds of the LQR-ORT controller. Experimental results demonstrate accuracy of the proposed model and the effectiveness of the LQR-ORT controller in improving transient response, robustness, and power decoupling.
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Adamu, Jamilu Kamilu, Mukhtar Fatihu Hamza, and Abdulbasid Ismail Isa. "Performance Comparisons Of Hybrid Fuzzy-LQR And Hybrid PID-LQR Controllers On Stabilizing Double Rotary Inverted Pendulum." Journal of Applied Materials and Technology 1, no. 2 (2020): 71–80. http://dx.doi.org/10.31258/jamt.1.2.71-80.
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Double Rotary Inverted Pendulum (DRIP) is a member of the mechanical under-actuated system which is unstable and nonlinear. The DRIP has been widely used for testing different control algorithms in both simulation and experiments. The DRIP control objectives include Stabilization control, Swing-up control and trajectory tracking control. In this research, we present the design of an intelligent controller called “hybrid Fuzzy-LQR controller” for the DRIP system. Fuzzy logic controller (FLC) is combined with a Linear Quadratic Regulator (LQR). The LQR is included to improve the performance based on full state feedback control. The FLC is used to accommodate nonlinearity based on its IF-THEN rules. The proposed controller was compared with the Hybrid PID-LQR controller. Simulation results indicate that the proposed hybrid Fuzzy-LQR controllers demonstrate a better performance compared with the hybrid PID-LQR controller especially in the presence of disturbances.
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Yildirim, Ş., M. Kalkat, İ. Uzmay, and G. Husi. "Design of a modified linear quadratic regulator for vibration control of suspension systems." International Review of Applied Sciences and Engineering 2, no. 1 (2011): 25–31. http://dx.doi.org/10.1556/irase.2.2011.1.4.
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Abstract This paper is concerned with the construction of a prototype active vehicle suspension system for a one-wheel car model by using a modified Linear Quadric Regulator (LQR). The experimental system is approximately described by a non-linear system with two degrees of freedom subject to excitation from a road profile. The active control at the suspension location is designed by using feedback constant gain controller structure. The experimental results show that the active suspension system with LQR more improves the control performance than standard PID controller. On the other hand, the results improved that the modified LQR has superior performance for controlling suspension systems in real time.
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Lei, Tianlong, Xiaochao Gu, Kanghua Zhang, Xiang Li, and Jixin Wang. "PSO-Based Variable Parameter Linear Quadratic Regulator for Articulated Vehicles Snaking Oscillation Yaw Motion Control." Actuators 11, no. 11 (2022): 337. http://dx.doi.org/10.3390/act11110337.
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In this paper, the seven degrees of freedom (DOF) nonlinear system model of articulated vehicles, including the vehicle dynamics model, tire and hydraulic steering system model, and the linearized ideal reference model, is constructed. A layered stability controller for the articulated vehicle is built. The particle swarm optimization (PSO)-based variable parameter linear quadratic regulator (LQR) for the upper-level yaw torque controller and the lower-level torque distributor based on the principle of the minimum tire utilization are established. The effectiveness of the LQR upper-level yaw torque controller for an articulated vehicle at different speeds and control references are compared and analyzed through feedforward and feedback control. We optimize the parameters in the LQR controller using PSO and verify the improvement in the controller’s performance with optimized parameters. Overall, the effect of front and rear-integrated control is best, followed by rear-based and front-based control. The PSO algorithm to optimize the LQR controller parameters for snaking oscillation control is effective.
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Nguyen, Van-Dong-Hai, Minh-Phuoc Cu, Tran-Minh-Nguyet Nguyen, et al. "PID-LQR Combined Linear Controller for Balancing Ballbot: Simulation and Experiment." Journal of Fuzzy Systems and Control 1, no. 3 (2024): 97–103. http://dx.doi.org/10.59247/jfsc.v1i3.153.
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Ballbot is a robotic structure in which the robot self-balances on a ball by rotating wheels. This robot is a popular form of service robot. Developing controllers for this system provides academic tools for reality. In this paper, after presenting the dynamic equations of the ballbot, we design a Proportional Integrated Derivative (PID)-Linear Quadratic Regulator (LQR) combined (PID-LQR) controller to balance the robot on the ball. The simulation results show the success of this method. An experimental model of a ballbot is presented. In the experiment, PID-LQR combined controller also shows its ability to self-balancing for the ballbot. With this finding, a method of controlling this model is a reference for developing this service robot.
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Teng Fong, Tang, Zamberi Jamaludin, Ahmad Yusairi Bani Hashim, and Muhamad Arfauz A. Rahman. "Design and Analysis of Linear Quadratic Regulator for a Non-Linear Positioning System." Applied Mechanics and Materials 761 (May 2015): 227–32. http://dx.doi.org/10.4028/www.scientific.net/amm.761.227.
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The control of rotary inverted pendulum is a case of classical robust controller design of non-linear system applications. In the control system design, a precise system model is a pre-requisite for an enhanced and optimum control performance. This paper describes the dynamic system model of an inverted pendulum system. The mathematical model was derived, linearized at the upright equilibrium points and validated using non-linear least square frequency domain identification approach based on measured frequency response function of the physical system. Besides that, a linear quadratic regulator (LQR) controller was designed as the balancing controller for the pendulum. An extensive analysis was performed on the effect of the weighting parameter Q on the static time of arm, balance time of pendulum, oscillation, as well as, response of arm and pendulum, in order to determine the optimum state-feedback control vector, K. Furthermore, the optimum control vector was successfully applied and validated on the physical system to stabilize the pendulum in its upright position. In the experimental validation, the LQR controller was able to keep the pendulum in its upright position even in the presence of external disturbance forces.
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Mohammed, Ibrahim K., and Abdulla I. Abdulla. "Elevation, pitch and travel axis stabilization of 3DOF helicopter with hybrid control system by GA-LQR based PID controller." International Journal of Electrical and Computer Engineering (IJECE) 10, no. 2 (2020): 1868. http://dx.doi.org/10.11591/ijece.v10i2.pp1868-1884.
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This research work presents an efficient hybrid control methodology through combining the traditional proportional-integral-derivative (PID) controller and linear quadratic regulator (LQR) optimal controlher. The proposed hybrid control approach is adopted to design three degree of freedom (3DOF) stabilizing system for helicopter. The gain parameters of the classic PID controller are determined using the elements of the LQR feedback gain matrix. The dynamic behaviour of the LQR based PID controller, is modeled and the formulated in state space form to enable utlizing state feedback controller technique. The performance of the proposed LQR based LQR controller is improved by using Genetic Algorithm optimization method which are adopted to obtain optimum values for LQR controller gain parameters. The LQR-PID hybrid controller is simulated using Matlab environment and its performance is evaluated based on rise time, settling time, overshoot and steady state error parameters to validate the proposed 3DOF helicopter balancing system. Based on GA tuning approach, the simulation results suggest that the hybrid LQR-PID controller can be effectively adopted to stabilize the 3DOF helicopter system.
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brahim, K. Mohammed, and I. Abdulla Abdulla. "Elevation, pitch and travel axis stabilization of 3DOF helicopter with hybrid control system by GA-LQR based PID controller." International Journal of Electrical and Computer Engineering (IJECE) 10, no. 2 (2020): 1868–84. https://doi.org/10.11591/ijece.v10i2.pp1868-1884.
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This research work introduces an efficient hybrid control methodology through combining the traditional proportional-integral-derivative (PID) controller and linear quadratic regulator (LQR) optimal controlher. The proposed hybrid control approach is adopted to design three degree of freedom (3DOF) stabilizing system for helicopter. The gain parameters of the classic PID controller are determined using the elements of the LQR feedback gain matrix. The dynamic behaviour of the LQR based PID controller, is modeled in state space form to enable utlizing state feedback controller technique. The performance of the proposed LQR based LQR controller is improved by using Genetic Algorithm optimization method which are adopted to obtain optimum values for LQR controller gain parameters. The LQR-PID hybrid controller is simulated using Matlab environment and its performance is evaluated based on rise time, settling time, overshoot and steady state error parameters to validate the proposed 3DOF helicopter balancing system. Based on GA tuning approach, the simulation results suggest that the hybrid LQR-PID controller can be effectively employed to stabilize the 3DOF helicopter system.
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Shah, J., M. Okasha, and W. Faris. "Gain scheduled integral linear quadratic control for quadcopter." International Journal of Engineering & Technology 7, no. 4.13 (2018): 81. http://dx.doi.org/10.14419/ijet.v7i4.13.21334.
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The findings of this paper are focused on the dynamics and control of a quadcopter using a modified version of a Linear Quadratic Regulator (LQR) control approach. The classical LQR control approach is extended to include an integral term to improve the quad copter tracking performance. The mathematical model is derived using the Newton-Euler method for the nonlinear six DOF model that includes the aerodynamics and detailed gyroscopic moments as a part of the system identification process. The linearized model is obtained and it is characterized by the heading angle (yaw angle) of the quadcopter. The adopted control approach is utilizing the LQR method to track several trajectories i.e. helical and lissajous curve with significant variation in the yaw angle. The integral term is introduced to the controller in order to minimize the steady state errors observed. The controller is modified to overcome difficulties related to the continuous changes in the operation points and to eliminate the chattering that was observed in the control technique. Numerical non-linear simulations are performed using MATLAB & Simulink to illustrate to accuracy and effectiveness of the proposed controller.
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KARABACAK, Yusuf, Ali YAŞAR, and İsmail SARİTAS. "Performance Comparison of PID and LQR Controllers for Control of Non-Linear Magnetic Levitation System." Deu Muhendislik Fakultesi Fen ve Muhendislik 25, no. 74 (2023): 339–50. http://dx.doi.org/10.21205/deufmd.2023257407.
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Magnetic Levitation System (MLS) has become a current study in the field of engineering due to its advantages such as low energy consumption and minimum friction. MLSs are nonlinear unstable systems. Due to the complexity of the structure and the difficulty of the controls, many advanced control theories can be applied on these systems and the performance of the controllers can be evaluated. In this article, Proportional-Integral-Derivative (PID) and Linear-Quadratic Regulator (LQR) controller methods are applied on MLS mathematically modeled in MATLAB environment. Controller performances were compared in the results found. The results obtained on the applicability of PID and LQR control methods for MLS were evaluated. In addition, the system performance of the controllers was compared with five parameters. These are rise time, settling time, maximum overshoot, overshoot and steady-state error. LQR controller produced great stability and homogeneous response compared to PID controller.
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Nguyen Hoai Nam. "CONTROL OF TWO-WHEELED INVERTED PENDULUM ROBOT USING ROBUST PI AND LQR CONTROLLERS." Journal of Military Science and Technology, no. 66A (May 6, 2020): 1–15. http://dx.doi.org/10.54939/1859-1043.j.mst.66a.2020.1-15.
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In this paper, a robust PI controller in combination with a linear quadratic regulator (LQR) is proposed to control a two-wheeled inverted pendulum robot (TWIPR) such that it is kept balanced while moving. The proposed TWIPR control system consists of two control loops. The inner loop has two PI controllers for two DC motors’ currents, which are separately designed based on a robust PI controller structure. The outer loop contains a LQR controller for the tilt angle, heading angle and position of the TWIPR. The proposed PI controller is compared to the existing method such as the magnitude optimum (MO) and genetic algorithm (GA) methods. The proposed control scheme is verified through simulations and practical tests, and it is also compared to the MO-LQR and GA-LQR strategies.
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Muddasar, Ali, Tahreem Zahra Syeda, Jalal Khadija, Saddiqa Ayesha, and Faisal Hayat Muhammad. "Design of Optimal Linear Quadratic Gaussian (LQG) Controller for Load Frequency Control (LFC) using Genetic Algorithm (G.A) in Power System." International Journal of Engineering Works (ISSN: 2409-2770) 5, no. 3 (2018): 40–49. https://doi.org/10.5281/zenodo.1193795.
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Nowadays power demand is increasing continuously and the biggest challenge for the power system is to provide good quality of power to the consumer under changing load conditions. When real power changes, system frequency gets affected while reactive power is dependent on variation in voltage value. For satisfactory operation the frequency of power system should be kept near constant value. Many techniques have been proposed to obtain constant value of frequency and to overcome any deviations. The Load Frequency Control (LFC) is used to restore the balance between load and generation by means of speed control. The main goal of LFC is to minimize the frequency deviations to zero. LFC incorporates an appropriate control system which is having the capability to bring the frequency of the Power system back to original set point values or very near to set point values effectively after the load change. This can be achieved by using a conventional controller like PID but the conventional controller is very slow in operation. Modern and optimal controllers are much faster and they also give better output response than conventional controllers. Linear Quadratic Regulator (LQR) is an advanced control technique in feedback control systems. It’s a control strategy based on minimizing a quadratic performance index. In despite of good results obtained from this method, the control design is not a straight forward task due to the trial and error involved in the selection of weight matrices Q and R. In this case, it may be hard to tune the controller parameters to obtain the optimal behaviour of the system. The difficulty to determine the weight matrices Q and R in LQR controller is solved using Genetic Algorithm (G.A). In this research Paper, G.A based LQG controller which is the combination of LQR and Kalman Filter is feedback in LFC using MATLAB/SIMULINK software package. Reduction in frequency deviations and settling time was successfully achieved by using LQG Controller with LFC based on G.A.
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Youns, Majed D., Abdulla I. Abdulla, and Salih M. Attya. "Optimization Control of DC Motor with Linear Quadratic Regulator and Genetic Algorithm Approach." Tikrit Journal of Engineering Sciences 21, no. 1 (2013): 35–42. http://dx.doi.org/10.25130/tjes.21.1.05.
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This paper presents LQR and GA controllers which applied to control the speed of a DCmotor and to maintain the rotation of the motor shaft with particular step response. Inthe state space, the control strategy is the states feedback and the most used techniquesare the LQR. Liner quadratic regulator (LQR) provides an optimal control law for alinear system. It’s a control strategy based on minimizing a quadratic performanceindex. In despite of the good results obtained from these method, the control design isnot a straight forward task due to the trial and error method involved in the definition ofweight matrices. In such cases, may be hard tuning the controller parameters in order toobtain the optimal behavior of the system. In this work, it proposes a states feedbacktechnique in which there are no trial and error processes involved and the control designis carried out to fulfill specifications, for minimize overshoot and minimize settling andrising times. The proposed technique is based on the use a genetic algorithms. Theobtained results show that is possible to design controllers which fulfill designspecifications.
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Mu, Chun Xin, Ming Quan Shi, Zhen Feng Han, and Qi Min Li. "Fuzzy-LQR Based Anti-Swing Control of Gantry Crane." Advanced Materials Research 1030-1032 (September 2014): 1596–601. http://dx.doi.org/10.4028/www.scientific.net/amr.1030-1032.1596.
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The paper proposed a controller combined fuzzy logic with linear quadratic regulator (LQR). This controller was able to adjust the swing angle precisely during the lifting of gantry crane. It resolved the problem that the LQR controller mostly depending on the accuracy of the mathematical model. First, the paper analyzed the design method of the LQR, then an improved method combing with fuzzy logic was put forward in detail and a further simulation experiment was carried on the MATLAB. The result shows that compared with LQR, the Fuzzy-LQR method can drive the crane to destination in a shorter time and reduced the swing angle by a third.
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Mosquera, Guillermo, Vladimir Bonilla, Sofía Vergara, Christian Rueda, and Marcelo Moya. "Design and Comparison of Controllers for a Robotic Transfemoral Prosthesis." Data and Metadata 4 (March 28, 2025): 759. https://doi.org/10.56294/dm2025759.
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This study investigates the performance of four control strategies—Proportional-Derivative (PD), Feedforward-Feedback PD (FF-FB PD), Linear Quadratic Regulator (LQR), and Feedforward-Feedback LQR (FF-FB LQR)—implemented on a robotic transfemoral prosthesis. The performance metrics, including overshoot, settling time, trajectory tracking accuracy, and torque requirements, were evaluated using simulation models. The results indicate that the FF-FB LQR controller demonstrated superior performance, achieving the lowest overshoot (4.98%) and near-zero trajectory tracking error. All controllers required approximately 8.6 Nm of torque, suggesting consistent energy requirements across strategies despite their performance differences. The LQR controller exhibited the best stability, minimizing overshoot and improving overall system response. These findings highlight the advantages of feedforward-feedback control strategies, particularly the FF-FB LQR, for controlling robotic transfemoral prostheses with enhanced stability and accuracy.
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Tu, Do Trong. "Optimizing Vehicle Ride Comfort using GA-LQR Control in In-Wheel Suspension Systems." Engineering, Technology & Applied Science Research 15, no. 2 (2025): 21306–12. https://doi.org/10.48084/etasr.9684.
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Controlled suspension systems, particularly active in-wheel suspension systems, are increasingly adopted in electric and autonomous vehicles due to their compact design and adaptability to various operating conditions. This study proposes the implementation of Linear Quadratic Regulator (LQR) controllers to improve vehicle smoothness and safety criteria. Genetic Algorithms (GA) are employed to optimize the weighting parameter values in the objective function in LQR controller, which allow them to adapt to the vehicle's condition. The simulation results demonstrate that the proposed controller model enhances system performance by up to 14% in comparison with conventional models. These findings suggest that the proposed system significantly enhances the feasibility of meeting user requirements in modern vehicle applications.
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Özgüney, Ömür Can. "Lqr-Fuzzy Logic Control of a Quarter Vehicle Model." Dokuz Eylül Üniversitesi Mühendislik Fakültesi Fen ve Mühendislik Dergisi 27, no. 79 (2025): 15–21. https://doi.org/10.21205/deufmd.2025277903.
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In this study, a new control rule was developed using two different control methods, and the results were discussed by applying the developed controller to the quarter vehicle model. A new hybrid controller was designed by considering the advantages of Fuzzy Logic control method and Linear Quadratic Regulator (LQR) control method. Control gain coefficients used in LQR controller were determined by fuzzy logic control method. The developed new controller has been applied to the quarter vehicle model. In the results, control with only Fuzzy Logic controller and developed LQR-Fuzzy Logic controller were compared. It was understood from the results that the developed control method was satisfactory.
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Damayanti, Erlyana Trie. "LQR and Fuzzy-PID Control Design on Double Inverted Pendulum." CAUCHY: Jurnal Matematika Murni dan Aplikasi 9, no. 1 (2024): 14–25. http://dx.doi.org/10.18860/ca.v9i1.22070.
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Double inverted pendulum is a non-linear and unstable system. Double inverted pendulum can be stabilized in the upright position by providing control to the system. In this research we compare two types of controllers namely Linear Quadratic Regulator (LQR) and Fuzzy-PID. The objective is to determine the control strategy that provides better performance on the position of the cart and pendulum angle. We modelled the system which is then linearized and given control. From the simulation results, it is proven that LQR and Fuzzy-PID controllers have been successfully designed to stabilize the double inverted pendulum. However, when given a disturbance in the form of noise step, the LQR controller has not been able to achieve the desired reference for up to 20 seconds. In another hand, the Fuzzy-PID controller is able to achieve the desired reference after 8 seconds. Therefore, it can be concluded that the Fuzzy-PID controller when applied to the Double Inverted pendulum system has better performance than the LQR controller.
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Nguyen, Thanh-Nhan, Ngoc-Trung-Nhan Le, Phuc-Hoa Nguyen, et al. "A Survey of LQR Control for Ball-on-Wheel System: Simulation and Experiment." Robotica & Management 29, no. 1 (2024): 9–13. http://dx.doi.org/10.24193/rm.2024.1.2.
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A ball-on-wheel system is a recently developed model in the field of automatic control. It serves as a simple model, meeting the learning and algorithmic research needs of students. With this model, there are various algorithms available for system control, such as PID controllers, fuzzy PID controllers, and sliding mode controllers, among others. In this paper, we construct a mechanical model for the system. We choose the Linear Quadratic Regulator (LQR) algorithm to design for this system. Simulation and experimental results demonstrate the effective operation of the LQR controller for the inverted pendulum on a cart system. Additionally, tuning experiments indicate that the parameters have been verified and confirmed to be consistent with the theoretical tuning principles of the LQR controller.
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Mukhatov, Azamat, Nguyen Gia Minh Thao, and Ton Duc Do. "Linear Quadratic Regulator and Fuzzy Control for Grid-Connected Photovoltaic Systems." Energies 15, no. 4 (2022): 1286. http://dx.doi.org/10.3390/en15041286.
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This work presents a control scheme to control a grid-connected single-phase photovoltaic (PV) system. The considered system has four 250 W solar panels, a non-inverting buck-boost DC-DC converter, and a DC-AC inverter with an inductor-capacitor-inductor (LCL) filter. The control system aims to track and operate at the maximum power point (MPP) of the PV panels, regulate the voltage of the DC link, and supply the grid with a unity power factor. To achieve these goals, the proposed control system consists of three parts: an MPP tracking controller module with a fuzzy-based modified incremental conductance (INC) algorithm, a DC-link voltage regulator with a hybrid fuzzy proportional-integral (PI) controller, and a current controller module using a linear quadratic regulator (LQR) for grid-connected power. Based on fuzzy control and an LQR, this work introduces a full control solution for grid-connected single-phase PV systems. The key novelty of this research is to analyze and prove that the newly proposed method is more successful in numerous aspects by comparing and evaluating previous and present control methods. The designed control system settles quickly, which is critical for output stability. In addition, as compared to the backstepping approach used in our past study, the LQR technique is more resistant to sudden changes and disturbances. Furthermore, the backstepping method produces a larger overshoot, which has a detrimental impact on efficiency. Simulation findings under various weather conditions were compared to theoretical ones to indicate that the system can deal with variations in weather parameters.
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Taherian, Shayan, Kaushik Halder, Shilp Dixit, and Saber Fallah. "Autonomous Collision Avoidance Using MPC with LQR-Based Weight Transformation." Sensors 21, no. 13 (2021): 4296. http://dx.doi.org/10.3390/s21134296.
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Model predictive control (MPC) is a multi-objective control technique that can handle system constraints. However, the performance of an MPC controller highly relies on a proper prioritization weight for each objective, which highlights the need for a precise weight tuning technique. In this paper, we propose an analytical tuning technique by matching the MPC controller performance with the performance of a linear quadratic regulator (LQR) controller. The proposed methodology derives the transformation of a LQR weighting matrix with a fixed weighting factor using a discrete algebraic Riccati equation (DARE) and designs an MPC controller using the idea of a discrete time linear quadratic tracking problem (LQT) in the presence of constraints. The proposed methodology ensures optimal performance between unconstrained MPC and LQR controllers and provides a sub-optimal solution while the constraints are active during transient operations. The resulting MPC behaves as the discrete time LQR by selecting an appropriate weighting matrix in the MPC control problem and ensures the asymptotic stability of the system. In this paper, the effectiveness of the proposed technique is investigated in the application of a novel vehicle collision avoidance system that is designed in the form of linear inequality constraints within MPC. The simulation results confirm the potency of the proposed MPC control technique in performing a safe, feasible and collision-free path while respecting the inputs, states and collision avoidance constraints.
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Patra, Subhajit, and Prabirkumar Saha. "Modeling and Control of a Complex Interacting Process." Advanced Materials Research 403-408 (November 2011): 3758–62. http://dx.doi.org/10.4028/www.scientific.net/amr.403-408.3758.
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In this paper, two efficient control algorithms are discussed viz., Linear Quadratic Regulator (LQR) and Dynamic Matrix Controller (DMC) and their applicability has been demonstrated through case study with a complex interacting process viz., a laboratory based four tank liquid storage system. The process has Two Input Two Output (TITO) structure and is available for experimental study. A mathematical model of the process has been developed using first principles. Model parameters have been estimated through the experimentation results. The performance of the controllers (LQR and DMC) has been compared to that of industrially more accepted PID controller.
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M. Radhi, Raoof, and Emad Q. Hussien. "CONTROLLR MODELLING AND DESIGN OF ROTATIONAL SPEED FOR INTERNAL COMBUSION ENGINE." University of Thi-Qar Journal for Engineering Sciences 4, no. 2 (2013): 1–13. http://dx.doi.org/10.31663/utjes.v4i2.200.
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This paper proposes a controller design of a nonlinear model of an internal combustion engine based on linear quadratic regulator (LQR) technique.The design takes into consideration the effect of external disturbances that occurs during the operation of system. The equations of motion are linearized according to the perturbation theory in order to inspect the dynamic stability of the engine motion, and the subsequent design of appropriate feedback controllers for the system, which can be obtained by solving the LQR problem.The results show that the proposed controller has good performance and stability than PID controller.The simulations have been carried out in Matlab/Simulink environment.
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Hummadi, Ruba M. K. Al-Mulla. "SIMULATION OF OPTIMAL SPEED CONTROL FOR A DC MOTOR USING LINEAR QUADRATIC REGULATOR (LQR)." Journal of Engineering 18, no. 03 (2023): 340–49. http://dx.doi.org/10.31026/j.eng.2012.03.07.
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This paper describes DC motor speed control based on optimal Linear Quadratic Regulator (LQR) technique. Controller's objective is to maintain the speed of rotation of the motor shaft with a particular step response.The controller is modeled in MATLAB environment, the simulation results show that the proposed controller gives better performance and less settling time when compared with the traditional PID controller.
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Tran, Minh-Duc, Le-Tuan-Hung Pham, Nguyen-Quang-Dong Dang, et al. "A Comparison of Control Schemes for Under-Actuated Pendubot System." Robotica & Management 28, no. 1 (2023): 53–58. http://dx.doi.org/10.24193/rm.2023.1.7.
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This paper presents a comparison of the three distinctive well-known control techniques, including Linear Quadratic Regulator (for short, LQR), Sliding Mode Control (for short, SMC), and Fuzzy Logic Control (for short, FLC). Each controller is in a different control category; LQR is an optimal controller employed in both linear and nonlinear systems, SMC is a nonlinear controller commonly applied in a nonlinear system, and the Fuzzy controller is the intelligent controller which can be archived by user’s experiment or other learning techniques. Beside the three main controllers for stabilizing at the equilibrium point, the swing-up controller is designed based on energy-based method to bring the system at the initial position close to the equilibrium points. Finally, the performance and the validity of the three methods are verified through both simulation and experimental results.
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Nura, Musa Tahir, Muhammad Mustapha, Idi Musa, Buyamin Salinda, Maijama'a Ladan, and Musa Yarima Sa'id. "Comparative analysis of observer-based LQR and LMI controllers of an inverted pendulum." Bulletin of Electrical Engineering and Informatics 9, no. 6 (2020): 2244–52. https://doi.org/10.11591/eei.v9i6.2271.
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An inverted pendulum is a multivariable, unstable, nonlinear system that is used as a yardstick in control engineering laboratories to study, verify and confirm innovative control techniques. To implement a simple control algorithm, achieve upright stabilization and precise tracking control under external disturbances constitutes a serious challenge. Observer-based linear quadratic regulator (LQR) controller and linear matrix inequality (LMI) are proposed for the upright stabilization of the system. Simulation studies are performed using step input magnitude, and the results are analyzed. Time response specifications, integral square error (ISE), integral absolute error (IAE) and mean absolute error (MAE) were employed to investigate the performances of the proposed controllers. Based on the comparative analysis, the upright stabilization of the pendulum was achieved within the shortest possible time with both controllers however, the LMI controller exhibits better performances in both stabilization and robustness. Moreover, the LMI control scheme is effective and simple.
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Muppidi, Angel, and Hari Nannam. "Experimental Evaluation of a Proposed LQR-LU Optimal Grid Controller in the Applications of Grid-Tied PV Systems." Jordan Journal of Electrical Engineering 11, no. 1 (2025): 1. http://dx.doi.org/10.5455/jjee.204-1715856762.
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This article aims to design a linear quadratic regulator (LQR)-based optimal current controller along with a Luenberger observer model in order to enhance power quality during the grid's dynamic conditions. To analyze the performance of the proposed control scheme, a three-phase photovoltaic-based gird-tied inverter is considered. A grid controller comprises a DC-link voltage controller to stabilize the capacitor voltage and a current controller to assure the output currents are well controlled according to the dynamic conditions of the grid as well as the source. In general, the capacitor-voltage and current controllers are regulated by traditional proportional Integral (PI) controllers which is associated with many demerits. In this work, a predictive LQR-based current controller with an observer algorithm and an adaptive capacitor voltage controller is proposed to improve the performance of the power grid at various dynamic conditions. The mathematical analogy is evaluated using MATLAB/SIMULINK software with different load and grid-disturbance conditions. Moreover, a laboratory prototype is designed to validate the simulation results. The outcomes prove that the proposed controller is dynamically robust to tackle any disturbance in load and grid.
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Hasmah, Mansor, Mohamad Aqil Mohamad Fadzir Tun, Surya Gunawan Teddy, and Janin Zuriati. "Design of travel angle control of quanser bench-top helicopter using mamdani-based fuzzy logic controller." Indonesian Journal of Electrical Engineering and Computer Science (IJEECS) 17, no. 2 (2020): 815–25. https://doi.org/10.11591/ijeecs.v17.i2.pp815-825.
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This research focuses on travel angle control of a laboratory scale bench-top helicopter developed by Quanser Inc. Bench top-helicopter is usually used by engineers and researchers to test their designed controllers before applying to the actual helicopter. Bench-top helicopter has the same behavior as the real helicopter, with 3 degree of freedom. The bench-top helicopter is mounted on a flat surface with two rotors that depends on the voltage supplied to change the direction of the helicopter in 3 different angles. The movement of the helicopter is based on the direction of three-different angles; travel, pitch and yaw angles. The existing Linear Quadratic Regulator-Integral controller used by Quanser Inc has some limitations in terms of tracking capability and settling time; therefore, this research is proposed. The objective of this research is to develop Mamdani-based Fuzzy Logic Controller for travel angle control of bench-top helicopter. Performance comparison has been done with the existing Linear Quadratic Regulator-Integral controller in both simulation and hardware. From the test results, it was found that the performance of Fuzzy Logic Controller is better than LQR-I controller especially for closed-loop simulation at desired angle of 30°. The percentage of overshoot of the Fuzzy Logic Controller has been improved from the existing controller which is 4.912% compared to 7.002% for LQR-I.
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Zhang, Zhidong, Gongliu Yang, Jing Fan, Tao Li, and Qingzhong Cai. "A Disturbance Sliding Mode Observer Designed for Enhancing the LQR Current-Control Scheme of a Permanent Magnet Synchronous Motor." Actuators 13, no. 8 (2024): 283. http://dx.doi.org/10.3390/act13080283.
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This paper introduces a current control method for permanent magnet synchronous motors (PMSMs) using a disturbance sliding mode observer (DSMO) in conjunction with a linear quadratic regulator (LQR). This approach enhances control performance, streamlines the tuning of controller parameters, and offers robust optimal control that is resistant to system disturbances. The LQR controller based on state feedback is advantageous for its simplicity in parameter adjustment and achieving an optimal control effect easily under specific performance indicators. It is suitable for the optimal control of strong linear systems that can be accurately modeled. However, most practical systems are difficult to model accurately, and the time-varying system parameters and existing nonlinearity limit the engineering application of LQR. In the PMSM current control loop, there is strong nonlinear disturbance manifesting as the nonlinearity of its dynamic model. Additionally, substantial noise and variations in system parameters within actual motor circuits hinder the linear quadratic regulator from attaining optimal performance. A disturbance sliding mode observer is proposed to enhance the LQR controller, enabling superior performance in nonlinear current loop control. Simulation and actual hardware experiments were conducted to verify the performance and robustness of the control scheme proposed in this paper. Compared with the widely used PI controller in engineering and sliding mode control (SMC) specialising in disturbance rejection, it offers the advantage of straightforward parameter tuning and can swiftly achieve the robust and optimal control performance that engineers prioritize.
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Rodriguez-Guevara, Daniel, Antonio Favela-Contreras, Francisco Beltran-Carbajal, Carlos Sotelo, and David Sotelo. "An MPC-LQR-LPV Controller with Quadratic Stability Conditions for a Nonlinear Half-Car Active Suspension System with Electro-Hydraulic Actuators." Machines 10, no. 2 (2022): 137. http://dx.doi.org/10.3390/machines10020137.
Full textAbstract:
The active suspension system of a vehicle manipulated using electro-hydraulic actuators is a challenging nonlinear control problem. In this research work, a novel Linear Parameter Varying (LPV) State-Space (SS) model with a fictional input is proposed to represent a nonlinear half-car active suspension system. Four different scheduling parameters are used to embed the nonlinearities of both the suspension and the electro hydraulic actuators to represent its nonlinear behavior. A recursive least squares (RLS) algorithm is used to predict the future behavior of the scheduling parameters along the prediction horizon. A Model Predictive Control-Linear Quadratic Regulator (MPC-LQR) is implemented as the control strategy and, to ensure stability, Quadratic Stability conditions are imposed as Linear Matrix Inequalities (LMI) constraints. Furthermore, the inclusion of attraction sets to overcome the conservative performance imposed by the Quadratic Stability conditions is included, as well as a terminal set were the switching between the MPC and the LQR controller is made. Simulations results for the half-car active suspension model over a typical road disturbance are tested to show the effectiveness of the proposed MPC-LQR-LPV controller with quadratic stability conditions in terms of comfort and road-holding.