Linear Quadratic Regulator Research Articles

LQR controller design for portable power supply based on flyback converter

Abstract The stability of the power repair equipment guarantees the reliability of the repair of electrical equipment. The following problems exist in the power supply of the emergency equipment: the load equipment randomly cuts in the power supply network; load equipment requires fast dynamic performance of the power supply. This challenges the stability of the portable power supply with the Flyback converter as the core. In this paper, an optimal feedback control strategy based on linear quadratic regulator (LQR) theory is proposed to improve the dynamic and steady-state performance of the Flyback converter. First, the state-averaged space model of the Flyback is derived and established. Second, an output voltage feedback integral controller is introduced to eliminate the steady-state error of the output voltage. Next, according to the LQR optimal control theory, the control model of the Flyback converter has been established, and the parameter design of the controller has been carried out by obtaining the optimal feedback gain matrix of the system. Finally, the simulation models are implemented with an output power of 120 W and a switching frequency of 50 kHz. The simulation results prove that the LQR controller provides superior performance than the traditional PI controller.

Control of a solid fuel rocket using Artificial Intelligence

Abstract This work is about the application of a trajectory control system for a solid-fueled sounding rocket using Neural Networks. The first part consisted of searching for a mathematical model that described the rocket’s behavior in space as accurately as possible. After this, the LQR (Linear Quadratic Regulator) methodology was used to find the control gains ’k’ for subsequent use. Trajectories are proposed for servo motor tracking, to be able to follow a proposed path in the x-z plane.

A modified model predictive current control of SRMs for torque ripple suppression

In this paper, the model predictive current control (MPCC) is proposed to reduce the torque ripple of a switched reluctance motor by realizing precise current tracking. The Linear Quadratic Regulator (LQR) is employed to establish the cost functions of MPCC, which can select optimal control variables. Besides, the Kalman filter is employed to estimate the system state to reduce the influence of disturbance. In addition, the PI controller is replaced by automatic disturbance rejection control (ADRC) to further improve the robustness of the system. Finally, experimental results are shown to verify the effectiveness regarding distinguished tracking performance, dynamic response, and robustness of the proposed MPCC. It can be found that the improved MPCC proposed in this paper can achieve lower torque ripple, distinguished current tracking performance, and dynamic response performance.

Understanding Childhood Victimization Experiences and Mental Health Outcomes in a Sample of Prison Inmates in Northern Chile

In this paper, the weak points have been investigated, the proposal to solve them, the application of the solution and the comparison of the results in the mode of simulation and experimental testing have been discussed. For this purpose, a four-wheel mobile robot has been considered for simulation and implementation, and a linear quadratic regulator controller and a nonlinear model predictive controller have been used to control it. But the combination of these classic and modern controllers with machine learning can greatly help to make these controllers work more accurately; As a result, in order to increase the accuracy of the performance of these controllers, by training neural networks of multilayer perceptrons, the controllers have been made intelligent. Controllers with cost function have coefficients as weighting to the matrix of system state variables and control input, which are greatly affected by changing these two weighting matrices of problem solving and optimization. For this reason, it is necessary to extract these two matrices for each separate path in order to improve the performance of the controller by trial and error. But by applying the proposed network which is trained with a new algorithm, not only the performance accuracy has increased, but the network extracts these two matrices without the need to spend human energy. Also, in order to reduce the existing time delays, especially in the implementation of the nonlinear controller on the robot in the experimental mode, by training other neural networks to optimally extract the benefit of the forecast horizon, reducing the calculations and increasing the speed of the solution has been achieved. In the hardware part, by examining and using operators such as the pixy camera and the U2D2 interface, which are faster than the usual method, the solution time has been reduced.

Data-driven acoustic control of a spherical bubble using a Koopman linear quadratic regulator.

Koopman operator theory has gained interest as a framework for transforming nonlinear dynamics on the state space into linear dynamics on abstract function spaces, which preserves the underlying nonlinear dynamics of the system. These spaces can be approximated through data-driven methodologies, which enables the application of classical linear control strategies to nonlinear systems. Here, a Koopman linear quadratic regulator (KLQR) was used to acoustically control the nonlinear dynamics of a single spherical bubble, as described by the well-known Rayleigh-Plesset equation, with several objectives: (1) simple harmonic oscillation at amplitudes large enough to incite nonlinearities, (2) stabilization of the bubble at a nonequilibrium radius, and (3) periodic and quasiperiodic oscillation with multiple frequency components of arbitrary amplitude. The results demonstrate that the KLQR controller can effectively drive a spherical bubble to radially oscillate according to prescribed trajectories using both broadband and single-frequency acoustic driving. This approach has several advantages over previous efforts to acoustically control bubbles, including the ability to track arbitrary trajectories, robustness, and the use of linear control methods, which do not depend on initial guesses.

Reducción del Sobrepico de un Elevador de tijeras Mediante Observador de Estado, LQR y LQG

Scissor lifts are crucial in various industries, known for their robust design and ability to lift heavy loads to significant heights. Their interlinked scissor mechanism allows controlled elevation and descent of the work platform. Precision and safety in their operation are essential to prevent accidents and ensure efficiency. A critical issue is the "overshoot," where the lift exceeds the desired height before stabilizing, causing instability and safety risks. This phenomenon is related to the system's dynamics and control, which typically employ hydraulic or electric systems to regulate the extension and retraction of the scissors. Precision in these systems is vital to stop the platform at the correct height smoothly and accurately. This paper presents a solution based on MATLAB/Simulink to improve the overshoot in scissor lifts using advanced control techniques. Different control strategies are implemented and evaluated, including the use of a State Observer, LQR (Linear Quadratic Regulator), and LQG (Linear Quadratic Gaussian Controller). The State Observer is used to estimate the system's internal variables, allowing for more precise feedback. The LQR is employed to design a controller that minimizes a cost function, optimizing the balance between control effort and state error. Finally, the LQG incorporates a Kalman filter to handle system uncertainty and noise, providing robust and efficient control. This demonstrates a significant improvement in the precision and stability of the scissor lift, reducing overshoot and enhancing operational safety. This research contributes to the development of more advanced and safer control systems for industrial applications, optimizing the performance and reliability of scissor lifts.

Quadrotor height control system using LQR and recurrent artificial neural networks

The quadorotor is a type of unmanned flying vehicle known as Unmanned Aerial Vehicle (UAV). In recent years, quadrotors have attracted much attention from researchers around the world due to their excellent maneuverability. A good control system in this quadrotor system is needed for ease of use of this quadrotor. One control system that is often used is the Linear Quadratic Regulator (LQR) control system. This control system has challenges for dynamic system disturbances in quadrotor control. Researchers proposed a recurrent artificial neural network (RNN) system to address these challenges.RRN is used to change the value of the feedback component in the LQR control system. The nature of the feedback component in LQR, which is static, is changed based on the system error value based on changes in the error value entered into the RNN. The result of this RNN is a change in the value of the LQR feedback component based on the input of the system. The results of this research show that LQR control with RNN produces a faster system response of 0.075 seconds and a faster settling time of 0.221 seconds. Compensation for the system response speed produces a higher overshot value.

LQR control strategy for virtual synchronous generator adapted to stiff grid

Virtual synchronous generators (VSG) exhibit good small-signal stability in low short-circuit ratio (SCR) grids. However, the small-signal stability of the grid decreases as its SCRs increase, and there is even a risk of sub-synchronous resonance (SSR). The VSG sequence impedance model considering the frequency coupling effect is developed. The reasons for SSR caused by VSG integration into a stiff grids are analyzed using the sequence impedance analysis method and the Nyquist criterion. To enhance the grid-connected stability of VSG under stiff grids conditions, a linear quadratic regulator (LQR) control strategy with full-state feedback was proposed. The control strategy of LQR can effectively improve the phase margin of VSG output impedance in the low-frequency region, and it also exhibits strong robustness to variations in grid short-circuit ratios. It can also significantly improve the stability margin of the grid-tied system consisting of VSG and stiff grid, and effectively suppress the occurrence of SSR. Finally, the effectiveness and reliability of LQR control strategy are verified by OPAL-RT experimental platform.

Design and comparison of particle swarm optimization tuned Kalman filter based linear quadratic Gaussian controller and linear quadratic regulator for surface to air missile guidance system

AbstractThe study of missile guidance systems is a well‐known nonlinear control engineering area of research. To enhance the control performance of a missle guidance system, several technologies have been proposed in existing works. To resolve the weighting matrix selection issue of a linear quadratic Gaussian (LQG) controller for the surface‐to‐air missile guidance control system, this study utilizes the particle swarm optimization (PSO) technique. Selecting the best state (Q) and input (R) weighting matrices is a significant difficulty in the design of the LQG controller for real‐time applications since it affects the controller's performance and optimality. The weighting matrices are often chosen by a trial‐and‐error method that not only complicates the design but also does not yield optimal outcomes. Therefore, in this paper, a PSO method is developed and used in the design of the linear quadratic regulator (LQR) and LQG controllers for the surface‐to‐air missile control system to choose the elements of the Q and R matrices in the best possible way. Finally, a comparative analysis between the designed controllers was presented. The results shows that a good performance was achieved by using the proposed PSO‐tuned design process. The LQG and LQR are designed by manually adjusting the weighting matrices and utilizing an intelligent procedure, PSO algorithm which achieved optimal results. Further results indicate that the designed controllers, the PSO tuned LQR and LQG achieved a better performance over the manually adjusted LQR and LQG controllers.

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

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

Optimal hybrid resonant current controller for microgrids connected to an unbalanced IEEE test distribution network

Microgrids (MGs) based on renewable energies have emerged as a proficient strategy for tackling power quality issues in conventional distribution networks. Nonetheless, MG systems require a suitable control scheme to supply energy optimally towards the electrical grid. This paper presents an innovative framework for designing hybrid Proportional-Resonant (PR) controllers with Linear Quadratic Regulators (LQR), PR+LQR, which merge relevant properties of PR and LQR controllers. This method simultaneously determines the MG control parameters and the current unbalanced factor generated at the distribution network. We select the traditional IEEE 13-bus test feeder network and place two MGs at strategic locations to validate our approach. Moreover, we use the Grey Wolf Optimizer (GWO) to find control parameters through a reliable fitness function that leads to high-performance microgrids. Finally, we conceive several tests to assess the efficacy of GWO for tuning the hybrid controller and compare the resulting data across distinct realistic operation conditions representing power quality events. So, we choose four case studies considering different renewable energy penetration indexes and power factors and evaluate the effects of the MGs over the distribution grid. We also compare the proposed hybrid PR+LQR controller against closely-related alternatives from the literature and validate its robustness and stability through the disk margin approach and the Nyquist criterion. Our numerical simulations prove that hybrid controllers driven by GWO are highly reliable strategies, yielding an average unbalanced current reduction of 30.03%.

Active suspension control using novel HB3C optimized LQR controller for vibration suppression and ride comfort enhancement

This article addresses the optimization of a Vehicle Active Suspension System (VASS) through the application of a Linear Quadratic Regulator (LQR) controller. The primary objective is to enhance ride comfort and ensure vehicle stability by addressing the divergent needs of vibration control. The research identifies key issues in existing optimization algorithms, namely, the exploration stage inefficiency in Big Bang Big Crunch Optimization (B3C) and the slow convergence rate in Coyote Optimization (CO). To overcome these challenges, a novel hybrid algorithm, Hybrid Coyote optimization based Big Bang Big Crunch (HB3C), is proposed. The research objective is to optimize the LQR weighting matrices using the HB3C algorithm, aiming for improved ride comfort and vehicle safety. The problem statement involves the inadequacies of existing algorithms in addressing the exploration and convergence issues. The motivation lies in enhancing the efficiency of VASS through optimal control, leading to better ride comfort and safety. The methodology involves integrating CO within a loop with B3C to compute the optimum reduction rate for the algorithm. Since, B3C algorithm’s success is highly dependent on selecting the ideal reduction rate. This hybrid approach is then applied to optimize the existing LQR weighting matrices. The results are evaluated in terms of time domain and frequency domain response analysis, with a focus on ride comfort based on ISO 2631-1 standards. The study demonstrates a maximum reduction of approximately 74% achieved by the optimized HB3C-LQR controllers.

A sensitivity-based estimation method for investigating control co-design relevance

Abstract. Control co-design is a promising approach for wind turbine design due to the importance of the controller in power production, stability, load alleviation, and the resulting coupled effects on the sizing of the turbine components. However, the high computational effort required to solve optimization problems with added control design variables is a major obstacle to quantifying the benefit of this approach. In this work, we propose a methodology to identify if a design problem can benefit from control co-design. The estimation method, based on post-optimum sensitivity analysis, quantifies how the optimal objective value varies with a change in control tuning. The performance of the method is evaluated on a tower design optimization problem, where fatigue load constraints are a major driver, and using a linear quadratic regulator targeting fatigue load alleviation. We use the gradient-based multi-disciplinary optimization framework Cp-max. Fatigue damage is evaluated with time-domain simulations corresponding to the certification standards. The estimation method applied to the optimal tower mass and optimal cost of energy show good agreement with the results of the control co-design optimization while using only a fraction of the computational effort. Our results additionally show that there may be little benefit to using control co-design in the presence of an active frequency constraint. However, for a soft–soft tower configuration where the resonance can be avoided with active control, using control co-design results in a taller tower with reduced mass.

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

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

Modeling and virtual simulation of the boost chopper by DCM using the optimal PIDF control

This work introduces an improved method for modeling and simulating the Boost Converter utilizing Duty Cycle Modulation (DCM) regulated by an optimum PIDF (Proportional-Integral-Derivative with Filter) regulator. We optimized the characteristic parameters of the PIDF regulator for a second-order system generated from its transfer function by using a mix of theoretical study and simulation using the Matlab/LQR tool. The conventional PID parameters in the time domain were converted into their corresponding LQR (Linear Quadratic Regulator) counterparts, allowing for the solution of the Riccati problem and the creation of an optimum state trajectory model. The results of analog virtual simulations done in a Multisim environment indicate that the system has improved dependability. It maintains a high level of accuracy in a stable condition, with no static error and a reaction time of 1.5 ms, without any overshooting. The effectiveness of the optimum PIDF control in regulating the DCM Boost Converter is highlighted by the system's strong ability to handle changes in load during transient states within a time frame of 300 ms. This study represents a substantial enhancement compared to conventional PID-based approaches, providing valuable knowledge about the possible uses in power electronics and control systems.

Learning-based data-driven optimal deployment control of tethered space robot

To avoid complex constraints of the traditional nonlinear method for tethered space robot (TSR) deployment, a data-driven optimal control framework with an improve deep learning based Koopman operator is proposed in this work. In consideration of nonlinearity of tethered space robot dynamics, its finite dimensional global linear representation called lifted linear system is derived with the Koopman operator theory. A deep learning scheme is adopted to find the embedding functions associate with Koopman operator. And an auxiliary neural network is developed to encode the nonlinear control term of finite dimensional lifted system. Then a controllability constraint is considered for learning a controllable lifted linear system. Besides two loss functions that relate to reconstruction and prediction ability of lifted linear system are designed for training the deep neural network. With the learned lifted linear dynamics, Linear Quadratic Regulator (LQR) is applied to derive the optimal control policy for the tethered space robot deployment. Finally, simulation results verify the effectiveness of proposed framework and show that it could deploy tethered space robot more quickly with less swing of in-plane angle.

Autonomous vehicle tracking control for a curved trajectory

Recently, research about trajectory tracking of autonomous vehicles has significantly contributed to the development of autonomous vehicle technology, particularly with novel control methods. However, tracking a curved trajectory is still a challenge for autonomous vehicles. This research proposes a state feedback linearization with observer feedback to overcome some difficulties arising from such a path. This approach suits a complex nonlinear system such as an autonomous vehicle. This method also has been compared with the linear-quadratic regulator (LQR) method. So, the goal of this research is to improve the control system performance of autonomous vehicles that are stable enough to navigate a curved path. Moreover, the study shows that the developed control law can track the curved path and solve existing problems. However, improvements are still necessary for the vehicle's performance and robustness.

OPTIMAL CONTROL DESIGN FOR FREQUENCY REGULATION IN ELECTRIC POWER SYSTEM WITH LOW INERTIA

Electricity is a very important element in this era because almost all aspects of modern life depend on electricity. Therefore, electricity plays a very important role in improving people's quality of life and maintaining an efficient and productive life. An efficient and reliable electrical system is essential to ensure adequate electricity availability and maintain system reliability. Therefore, planning, designing and operating electrical systems must be carried out carefully to ensure stability, reliability and efficiency. However, a decrease in frequency in the electrical system sometimes occurs when there is a sudden change in load. This can affect system stability. Therefore, Load Frequency Control (LFC) and Linear Quadratic Regulator (LQR) analysis is needed to maintain the stability of the electrical system frequency. The combination of these two techniques, namely LFC with LQR modeling, provides a better solution for maintaining frequency stability and optimizing electrical system performance. LFC analysis regulates power generation settings automatically to compensate for fluctuations in load demand and maintain a stable frequency, while LQR is a control technique used to minimize system errors and optimize system performance. Therefore, LFC with LQR results in system performance increasing very significantly with a faster response, undershoot that can be reduced to 0.001 and a better settling time of 300s in area-1 and 450s in area-2 and rise time reaching 270s in area-1 and 405s in area-2 as well as the use of LQR can maintain the system frequency at its nominal limit and the presence of New Renewable Energy (EBT) has an effect in the form of a greater undershoot level than without EBT.

An optimal regulation of grid-connected doubly-fed induction generator angular speed and the DC-link voltage

In this work, a linear quadratic regulator controller is utilized to optimize the gains of the machine-side converter and grid-side converter controllers. The DC-link voltage and the rotational speed of the doubly-fed induction generator are optimally regulated by these controls. Additionally, the small-signal stability of the proposed system has been evaluated using the linearized model of the system. The small-signal stability analysis of the designed system has been accomplished through the application of the eigenvalues and participation factors technique. The suggested controller has been tested in a variety of operating conditions under small disturbances. MATLAB/SIMULINK simulation simulations have been used to evaluate the efficacy of the suggested optimal control system. Additionally, the generator-angular speed and DC-link voltage dynamic performances demonstrate the efficacy of the proposed controller. Finally, the robustness of the proposed controller has also been tested and validated using OPAL-RT technology under large perturbations at stator terminal voltage.

Reduction of data amount in data-driven design of linear quadratic regulators

Reduction of data amount in data-driven design of linear quadratic regulators