Linear Quadratic Method Research Articles

Quadrotor Trajectory Tracking using Combined Stochastic Model-Free Position and DDPG-based Attitude Control

This article presents a cascade controller for the quadrotor to track the desired trajectory effectively. Unlike previous approaches, this method avoids simplification and linearization assumptions, making it applicable in a wider range of scenarios. A novel linear quadratic tracking method is utilized, which takes into account both process noise and measurement noise while maintaining a model-free nature. Furthermore, the stability analysis of this stochastic method is thoroughly investigated. In terms of attitude control, a model-free approach is adopted. The Deep Deterministic Policy Gradient (DDPG) algorithm is implemented, leveraging an actor-critic network to handle the nonlinearities associated with attitude control. This model-free approach eliminates the need for an accurate model of the quadrotor's dynamics. Simulations are conducted to evaluate the performance of the proposed controller, and the results demonstrate its ability to effectively control the quadrotor, ensuring accurate trajectory tracking and stability.

Optimal control of a doubly fed induction generator of a wind turbine in cooperation with weak and rigid grids

In this article a control method for a rotor side converter (RSC) of a doubly fed induction generator of a wind turbine is developed. The doubly-fed induction generator (DFIG) system of a wind energy power plant that improves grid symmetrization was applied. The issue of optimal control was treated as an extended linear quadratic regulator (ELQR) having an extra set of exogenous inputs, which are source voltages of the electric grid. No additional knowledge of equations modelling the exogenous inputs was assumed. The proposed method is much more efficient than the currently available linear quadratic control methods. The control objective for a weak grid was to maintain the given value of the voltage module on load terminals and the given value of active power transferred from the stator’s winding. First harmonic components of relevant waveforms were used for this purpose. This task also required the DFIG system to provide reactive power to the grid. In the case of a rigid grid, this reactive power would be too high. Therefore, in this case, it was assumed that the system would supply only part of the required active and reactive power, based on its capabilities. It was required that the voltage and current ratings of the system, mainly the DFIG, were not exceeded. Therefore, the parameters of the network in these difficult failure cases were corrected only partially. The behaviour of the grid in the conditions of failure, as well as the return to the steady state after failure disappearance, were studied.

Optimization design of unmanned mining truck path tracking controller based on road adhesion coefficient estimation

Abstract In response to the issues of inaccurate tracking precision caused by continuous turning and variable road adhesion coefficients on complex roads in mining areas for unmanned mining trucks, this paper adopts unscented Kalman filter (UKF) to estimate the road adhesion coefficient. Based on this, an adaptive preview feedforward linear quadratic regulator (LQR) control algorithm is designed using genetic algorithm, feedforward control, and linear quadratic optimal path tracking control methods. Firstly, a nine degree of freedom vehicle dynamics model and a two degree of freedom vehicle lateral dynamics model are established, and the Dugoff model to calculate tire forces is introduced; secondly, utilizing UKF to estimate the road adhesion coefficient, and leveraging active disturbance rejection control for rapid tracking of road curvature, an optimized design of the LQR controller is carried out. Then, the effectiveness of the designed controller was verified through Trucksim/Simulink joint simulation testing. Finally, the hardware in the loop test results showed that the designed controller had good tracking accuracy and strong adaptability in complex road and special working conditions in mining areas.

An autopilot-based method for unmanned aerial vehicles trajectories control and adjustment

In today's world, the rapid development of aviation technologies, particularly unmanned aerial vehicles (UAVs), presents new challenges and opportunities. UAVs are utilized across various industries, including scientific research, military, robotics, surveying, logistics, and postal delivery. However, to ensure efficient and safe operation, UAVs require a reliable autopilot system that delivers precise navigation control and flight stability. This paper introduces a method for controlling and adjusting UAV trajectories, which enhances accuracy in environments and tasks corresponding to the first or second level of autonomy. It outperforms the linear-quadratic method and the unmodified predictive control method by 43% and 74%, respectively. The findings of this study can be applied to the development and modernization of new UAV, as well as the advancement of new UAV motion control systems, thereby enhancing their quality and efficiency.

A cubic spline projection method for computing stationary densities for random maps

We apply the cubic spline projection method to compute a stationary density of the Foias operator for a random map to improve the convergence rate of the linear spline and quadratic spline projection methods. We analyze the convergence of the numerical scheme as well as provide numerical experiments that support our claims.

Genetic algorithm-enhanced linear quadratic control for balancing bicopter system with non-zero set point

Bicopter is an unmanned aerial vehicle (UAV) with the advantage of saving energy consumption. However, the unique two rotors design presents a challenge in designing a controller that achieves good stability, fast settling time, and the ability to overcome oscillations simultaneously. This article proposes a new control method for bicopter that uses a genetic algorithm optimization approach in the linear quadratic (LQ-GA) control method. The GA is used to search for the best weighting matrix parameters, Q and R, in the Linear Quadratic (LQ) control scheme. The proposed control method was tested on a balancing bicopter test platform with an input in the form of difference in pulse width modulation (PWM) signals for both rotors and an output in the form of roll angle. The control system was evaluated based on the stability of the transient response and the generated control signal. The results of the tests showed that the proposed LQ-GA control method has better stability, faster settling time, and smaller overshoot than the existing PI and standard LQ control methods. Therefore, the proposed LQ-GA control method is the most suitable for use in a balancing bicopter system with a non-zero setpoint.

Determination of FFB Raw Material Needs for CPO Production by Forecasting Method at PT. Socfindo Kebun Mata Pao

This research was conducted at PT. Socfindo Kebun Mata Pao is one of the industrial companies engaged in palm oil processing. The main raw material used in processing Crude Palm Oil (CPO) is Fresh Fruit Bunches (FFB), where the FFB used must be based on good characteristics to get quality CPO. PT. Socfindo Kebun Mata Pao needs to pay attention to the adequacy of raw materials or the shortage of FFB raw materials. If the FFB inventory exceeds the production needed, it will certainly cause additional storage costs and a decrease in the quality of CPO. Meanwhile, if the FFB supply is too small, it will increase procurement costs and interfere with the smooth running of products, resulting in inefficient production activities. Therefore, companies need to forecast the need for FFB raw materials to minimize the occurrence of excess or shortage of FFB. The methods used in forecasting the needs of FFB raw materials are the Linear Regression method and the Quadratic method. This study aims to obtain forecasting results with the best accuracy between the Linear Regression and Quadratic methods to predict the need for FFB raw materials in the 2022 period so that companies can manage FFB raw material inventory by production needs. The data collection method was used from the observations and study document results. The forecasting results from calculating the error rate in the Linear Regression method obtained a Standard Error of Estimate (SEE) of 317.16 and a Mean Absolute Percentage Error (MAPE) of 0.58%. In comparison, the error rate in the Quadratic method obtained a Standard Error of Estimate (SEE) of 323.55 and a Mean Absolute Percentage Error (MAPE) of 4.75%. The smallest error rate is obtained in the Linear Regression method from the calculation of the error rate in both methods

An Objective Holographic Feedback Linearization Based on a Sliding Mode Control for a Buck Converter with a Constant Power Load

As a typical load, the constant power load (CPL) has negative impedance characteristics. The stability of the buck converter system with a mixed load of CPL and resistive load is affected by the size of the CPL. When the resistive load is larger than the CPL, the buck converter with the output voltage as an output function is a non-minimum phase nonlinear system, because its linear approximation has a right-half-plane pole. The non-minimum phase characteristic limits the application of many control techniques, but the objective holographic feedback linearization control (OHFLC) method is a good control strategy that can bypass the non-minimum phase system and make the system stable. However, the traditional OHFLC method, in designing the controller, generally uses a linear optimal quadratic design method to obtain a linear feedback control law. It requires a state quantity component with a one-order relative degree to the system. But it is not easy to find such a suitable state quantity with a one-order relative degree to the system. In this paper, an improved OHFLC method is proposed for Buck converters with a mixed loads of CPL and resistive loads, using the sliding mode control (SMC) theory to design the controller, so that the output state quantity components with different relative degrees to the system can be used in the holographic feedback linearization method. Finally, the simulation and experimental results also demonstrate that this method has the same, or even better, dynamic response performance and robustness than the traditional OHFLC method.

Control of Quarter-Car Active Suspension System Based on Optimized Fuzzy Linear Quadratic Regulator Control Method

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

Robust Observer-Based Visual Servo Control for Quadrotors Tracking Unknown Moving Targets

This article addresses the image-based control problem of a quadrotor for tracking an unknown moving target under external disturbances. Based on the continuous observer design, a constructive image-based visual servoing (IBVS) geometric tracking control strategy is proposed and utilized. First, a higher order sliding mode observer is designed based on image dynamics for continuous estimation of unmeasurable linear velocities and time-varying disturbances. Furthermore, exploiting the linear quadratic regulator optimal design method, an outer loop IBVS controller is proposed such that the position of the quadrotor converges to the desired tracking pattern. Next, an inner loop geometric controller is designed using Lie algebra functions to regulate the attitudes. Based on the Lyapunov stability theory, it is rigorously proven that the proposed IBVS geometric controller achieves asymptotic stability. Finally, the effectiveness and robustness of the proposed approach against uncertain targets, time-varying disturbances, and large initial inclination angles are demonstrated through numerical simulations and experiments.

Density and Attendance Frequency of Seagrass In Coastal Waters of Porto Village, Saparua Island, Central Maluku

Seagrass acts as a food source in supporting the productivity of the living creatures that lives sorrounds, rearing areas, and sediment filtering systems. The Village of Porto is one of the coastal villages that has a fairly extensive seagrass ecosystem. Seagrass, locally known as "lalamong" is located quite far from residential areas, but information about the condition of the seagrass is still lacking. So, this study aims to inventory the species of seagrass found there, analyze the density and attendance frequency and assess environmental parameters for seagrass growth. The research was conducted from January to March 2019. Seagrass data was collected using the linear quadratic transect method at the five stations and each station consisted of three transects. The results showed that seagrass beds in the research area consists of eight species of seagrass, namely Enhalus acoroides, Thalassia hemprichi, Halophila ovalis, Cymodocea rotundata, Cymodocea serrulata, Halodule uninervis, Halodule pinifolia and Syringodium isoetifolium. C. serrulata is the species with the highest density number, but the highest attendance frequency is represented by E. acoroides. S. isoetifolium is the species with the lowest density and attendance frequency. Station three has the highest seagrass density but has a low on attendance frequency. Water quality parameters (temperature and salinity) are suitable for seagrass in the coastal waters of Porto village.

Distributional Robustness in Minimax Linear Quadratic Control with Wasserstein Distance

To address the issue of inaccurate distributions in discrete-time stochastic systems, a minimax linear quadratic control method using the Wasserstein metric is proposed. Our method aims to construct a control policy that is robust against errors in an empirical distribution of underlying uncertainty by adopting an adversary that selects the worst-case distribution at each time. The opponent receives a Wasserstein penalty proportional to the amount of deviation from the empirical distribution. As a tractable solution, a closed-form expression of the optimal policy pair is derived using a Riccati equation. We identify nontrivial stabilizability and observability conditions under which the Riccati recursion converges to the unique positive semidefinite solution of an algebraic Riccati equation. Our method is shown to possess several salient features, including closed-loop stability, a guaranteed-cost property, and a probabilistic out-of-sample performance guarantee.

Improving the method of linear-quadratic control over a physical model of vessel with azimuthal thrusters

The object of this research is the algorithms for controlling large-scale models of sea-based vehicles (SBVs). The subject of the research is a linear-quadratic method for controlling a model of the propulsion complex with azimuthal thrusters (ATs) in the aft part. The problem is the solution between the interdependent throws of surge, sway, and yaw speeds predicted by the linear controller. Input signals are the rotational speeds and the angles of ATs propeller thrusts with respect to the diametrical plane of SBVs. During the simulation, step responses of a closed system for overload and rotation speed are compared. Simulation of speed jumps showed an adequate response, in contrast to the speed of rotation of ATs, which showed a greater impact on the system than the orientation of ATs. When modeling the rate of yaw, the behavior of the ATs angle did not correspond to its limitations inherent in the device rotating at the appropriate speed. It is concluded that this is the result of linearization of the actuators, and the proposed solution is to implement the strengthening of the task to better adapt to the rotating behavior of ATs. Despite these problems, the simulation showed the potential of the model and controller for use in similar situations. Several modifications are also offered to significantly improve the model and simulations. One of the main changes that could be made is the implementation of a predictive gain during the linearization of the ATs control system. The practical significance of the results obtained is the fact that the quadratic optimization model is an effective and reliable technique in the process of designing SBVs of various configurations of steering devices for optimal control

Trading Portfolio Strategy Optimization via Mean-Variance Model Considering Multiple Energy Derivatives

Energy retailers that sell energy at fixed prices are at risk of bankruptcy due to instantaneous fluctuations in wholesale electricity prices. Energy derivatives, e.g., electricity options, can be purchased by energy retailers then sold to customers as one potential risk-mitigation tool. A class of energy retailers that trade energy derivatives, including the electricity option, the carbon option and the green certificate, is considered in this paper. In terms of energy retailers, a strategy that can maximize the value of the purchased energy derivatives over a period of time and minimize the risk due to the stochastic price fluctuations is developed. Firstly, the dynamic prices of the electricity option as well as the carbon option are described by stochastic differential equations, and the dynamic prices of the green certificate are described by ordinary differential equations. Historical price data are used to obtain the parameters of both stochastic and ordinary differential equations by maximum likelihood estimation. Next, an investment portfolio is established as a mean-variance portfolio selection problem where the retailer maintains the satisfactory asset value and minimizes the risk simultaneously. Then, the problem is transformed into a stochastic optimal control problem which can be solved analytically by using the linear-quadratic method. Finally, the numerical simulations illustrate the feasibility of the proposed method.

Radiotherapy effective clonogens model graphical optimization approaching linear quadratic method for head and neck tumors

Fowler model for NEffective tumor clonogens number in Biological Effective Dose (BED) algorithms constrained to head and neck cancer is simulated. RT biological models provide with a dose delivery radioprotection optimal minimization of photon-dose deposition while keeping the most efficacious dose to maximize Tumor Control Probability in head and neck tumors. Results comprise the Effective Clonogens model for head and neck cancer parameters 3D Graphical Optimization simulations. 3D imaging results for NEffective (Effective Tumor Population Clonogenes Number) determination after passing on the standard radiotherapy treatment time are shown. RT applications for TPO in head and neck cancer with Fractionation-dose are explained.

Pengendalian Sudut Pitch dan Roll Pesawat Flying Wing

The development of the aviation world in recent years has increased, one of which is the field of unmanned aerial vehicles. This development is in line with the increasing use of UAVs in various fields, including for military missions, natural disaster monitoring missions, and aerial photography missions. Many types of aircraft that can be used to complete these missions, one type of aircraft that is widely used is the flying wing type aircraft. This type of aircraft is triangular in shape and does not have a tail. This aircraft controller uses elevons on the right and left sides of its wings, and its form is relatively small, so this aircraft is susceptible to environmental disturbances and causes flight mission failures. To overcome this problem, a control system is needed that is able to make the aircraft maintain flight stability. In this study, the Linear Quadratic Regulator control method was applied to overcome this. The LQR control method is used to control the pitch and roll angles of the aircraft. Based on the test results, the interference given can be handled well by the aircraft. It was proven that when given a disturbance, the aircraft experienced an overshoot of 4.24º at the pitch angle and 4.26º at the roll angle, but could quickly return to the setpoint within 1.2 seconds at the pitch angle, and 1.3 seconds at the roll angle. Thus the aircraft is able to maintain flight stability.

Optimal Sliding Mode Preview Repetitive Control for Three-Phase Z-Source Inverters

Aiming at high output voltage and obvious current fluctuation of the off grids inverters with unbalanced and nonlinear loads, a compound control strategy of sliding mode controller and optimal preview controller based on Z-source inverter (ZSI) is proposed. ZSI can boost the pressure and improve the system energy conversion rate through by combining the state with the linear quadratic design method of optimal control. The preview controller is introduced in the feedforward compensation link. With the help of difference operator, an extended state error system covering the target value signal and lag link feedback is designed. The optimal preview repetitive control (PRC) is transformed into a linear quadratic regulation matter of the discrete systems. Furthermore, a preview repetitive controller is obtained by using the Lyapunov method, linear matrix inequality, and the design method of optimal controller, which can realize sliding mode control, state feedback, repetitive control, and preview compensation. Finally, a 10 kV A prototype is built to verify the effectiveness of the proposed strategy.

A Novel Design of Disturbance Compensator in Active Disturbance Rejection Control

This article aims to describe a novel design method of disturbance compensator in ADRC (Active Disturbance Rejection Control) based on Lyapunov stability theory. Error-based state equation is used to simplify the ADRC structure. The state feedback controller is designed using LQ (Linear Quadratic) method based on a linearized model. The generalized ESO (Extended State Observer) estimates the nonlinear part, model uncertainty, and external disturbance regarded as "total disturbance." Based on the estimate of the disturbance, disturbance compensator is designed using Lyapunov stability theory. In conventional ADRC, after estimating the disturbance compensator rejects the disturbance. But in this paper, it was not simply rejected. Instead the estimate of the disturbance is used in compensator design to make the Lyapunov candidate decrease more quickly. Our method allowed improved the convergence rate of ADRC. A numerical example and IWP (Inertia Wheel Pendulum) stabilization simulation confirmed the new method for effectiveness evaluation.

Keanekaragaman Flora Mangrove pada Tingkat Pohon di Cagar Alam Pulau Dua Banten

Abstract. One of the countries that has the largest mangrove forest is Indonesia, the area of mangrove forests in Indonesia reaches 3.1 million ha. Mangroves can live in tropical and subtropical climates, mangroves have so many benefits, one of which is to prevent disasters such as tsunamis and protect beaches from erosion. This research was conducted in the Pulau Dua Nature Reserve in the Banten area. This study uses a linear quadratic transect method by determining the location of the study as many as 2 station points. Data analysis was carried out quantitatively using vegetation analysis. Based on the results of the research conducted, it shows that the value of the mangrove flora diversity index is classified as low, namely H'<1. The species of mangrove flora were found such as Avicennia germinans, Avicennia marina, Avicennia officinalis, Bruguiera parviflora, and Rhizophora apiculata. The condition of the mangrove forest in the Pulau Dua Banten Nature Reserve is still relatively natural, because it is still very well preserved and the diversity of flora and fauna is still high.Keywords: mangrove, nature reserve, dua banten island

Development and Evaluation of Control Architectures for a Mechanically Deployed Entry Vehicle

The NASA-funded Pterodactyl Project seeks to advance the current state of the art for atmospheric entry vehicles by developing novel guidance and control technologies for deployable entry vehicles (DEVs). This paper details the efforts of the Pterodactyl team to develop, implement, and evaluate different control hardware effectors on an asymmetric, mechanically deployed DEV. Multiple control effector designs are developed for a baseline vehicle including propulsive control systems (reaction control systems) and nonpropulsive control systems (aerodynamic control surfaces and internal moving masses). For each control system, state-feedback integral controllers based on linear quadratic regulator optimal control methods are designed to track the guidance commands of either the bank angle or the angle of attack and sideslip angle. Using a lunar return reference mission, a comparative analysis of the performance and maneuverability of the DEV using the different control system configurations is conducted. The aerodynamic control surface design is demonstrated to be the most suitable architecture, primarily due to its ability to achieve acceleration rates that supersede the other designs. Considering performance, maneuverability, and guidance tracking during entry, the aerodynamic control surface design is recommended for this DEV and chosen reference mission.