ENHANCEMENT OF STABILITY ON AUTONOMOUS WAYPOINT MISSION OF QUADROTOR USING LQR INTEGRATOR CONTROL

The ability of the quadrotor in the waypoint trajectory tracking becomes an essential requirement in the completion of various missions nowadays. However, the magnitude of steady-state errors and multiple overshoots due to environmental disturbances leads to motion instability. These conditions make the quadrotor experience a shift and even change direction from the reference path. As a result, to minimize steady-state error and multiple overshoots, this study employs a Linear Quadratic Regulator control method with the addition of an Integrator. Comparisons between LQR without Integrator and LQR with Integrator were performed. They were implemented on a quadrotor controller to track square and zig-zag waypoint patterns. From experimental results, LQR without Integrator produce of 2 meters steady-state error and -1.04 meters undershoot average with an accuracy of 64.84 % for square pattern, along 3.19 meters steady-state error, and -1.12 meters undershoot average with an accuracy of 46.73 % for a zig-zag way. The LQR method with integrator produce of 1.06 meters steady-state error with accuracy 94.96 % without multiple-overshoot for square pattern, the 1.06 meters steady-state error, and -0.18 meters undershoot average with an accuracy of 86.49 % for the zig-zag way. The results show that the LQR control method with Integrator can minimize and improve steady-state error and multiple overshoots in quadrotor flight. The condition makes the quadrotor able to flying path waypoints with the correct system specification. ABSTRAK: Kemampuan quadrotor dalam pengesanan lintasan waypoint menjadi syarat penting dalam menyelesaikan pelbagai misi pada masa kini. Walau bagaimanapun, besarnya ralat keadaan mantap dan banyak kelebihan kerana gangguan persekitaran menyebabkan ketidakstabilan pergerakan. Keadaan ini menjadikan quadrotor mengalami pergeseran dan bahkan mengubah arah dari jalur rujukan. Oleh itu, kajian ini menggunakan kaedah kawalan Linear Quadratic Regulator dengan penambahan integrator dalam meminimumkan ralat keadaan mantap dan banyak kelebihan. Perbandingan antara LQR tanpa Integrator dan LQR dengan Integrator dilakukan. Mereka dilaksanakan pada pengawal quadrotor untuk mengesan corak titik jalan persegi dan zig-zag. Dari hasil eksperimen, LQR tanpa Integrator menghasilkan ralat keadaan mantap 2 meter dan -1.04 meter rata-rata undur tembak dengan ketepatan 64.84% untuk corak persegi, sepanjang ralat keadaan tetap 3.19 meter, dan -1.12 meter rata-rata undur bawah dengan ketepatan 46.73 % untuk cara zig-zag. Kaedah LQR dengan integrator menghasilkan ralat keadaan mantap 1.06 meter dengan ketepatan 94.96% tanpa tembakan berlebihan untuk corak segi empat sama, ralat keadaan mantap 1.06 meter, dan rata-rata undur tembak -0.18 meter dengan ketepatan 86.49% untuk zig-zag cara. Hasilnya menunjukkan bahawa kaedah kawalan LQR dengan Integrator dapat meminimumkan dan memperbaiki ralat keadaan mantap dan banyak overhoot dalam penerbangan quadrotor. Keadaan tersebut menjadikan quadrotor dapat terbang ke titik jalan dengan spesifikasi sistem yang betul.

Control Analysis with Modified LQR Method of Anti-Tank Missile with Vectorization of the Rocket Engine Thrust

This article approaches the issue of the optimal control of a hypothetical anti-tank guided missile (ATGM) with an innovative rocket engine thrust vectorization system. This is a highly non-linear dynamic system; therefore, the linearization of such a mathematical model requires numerous simplifications. For this reason, the application of a classic linear-quadratic regulator (LQR) for controlling such a flying object introduces significant errors, and such a model would diverge significantly from the actual object. This research paper proposes a modified linear-quadratic regulator, which analyzes state and control matrices in flight. The state matrix is replaced by a Jacobian determinant. The ATGM autopilot, through the LQR method, determines the signals that control the control surface deflection angles and the thrust vector via calculated Jacobians. This article supplements and develops the topics addressed in the authors’ previous work. Its added value includes the introduction of control in the flight direction channel and the decimation of the integration step, aimed at speeding up the computational processes of the second control loop, which is the LQR based on a linearized model.

Integral State Feedback Control Using Linear Quadratic Gaussian in DC-drive System

The electric motor is one of the technological developments which can support the production process. DC motor has some advantages compared to AC motor especially on the easier way to control its speed or position as well as its widely adjustable range. The main issue in the DC motor is controlling the angular speed with uncertainty and disturbance. The alternative solution of a control method with simple, easy to design, and implementable in a multi-input multi-output system is integral state feedback such as linear quadratic Gaussian (LQG). It is a combination between linear quadratic regulator and Kalman filter. One of the advantages of this method is the usage of fewer sensors compared with the original linear quadratic regulator method which uses sensors as many as the state in the system model. The design, simulation, and experimental study of the application of LQG as state feedback control in a DC-drive system have been done. Both performance and energy were analyzed and compared with conventional proportional integral derivative (PID). The gain of LQG was determined by trial whereas the PID gain is determined from MATLAB autotuning without fine-tuning. The load test and tracking test were carried out in the experiment. Both simulation and hardware tests showed the same result which LQG is superior in integral absolute error (IAE) by up to 74.37 % in loading test compared to PID. On the other side, LQG needs more energy, it consumes higher energy by 6.34 % in the load test.

Modeling of Discrete Networked Control Systems in State Space for Electrical Power System with Time Delays: نمذجة نظم التحكم الشبكية المتقطعة في فضاء الحالة لنظام قدرة كهربائية مع وجود التأخيرات الزمنية

Electrical power systems distributed over wide geographical areas are exposed to a set of factors that affect their stability. The most important factors are the time delays between their subsystems. In this paper, a flexible modeling method was concluded consisting of a set of generalized rules and conditions that apply to any network controlled system to ensure its stability with time delays between the elements of the controlled network. In addition, a linear quadratic regulator (LQR) controller was implemented. The aim of the LQR controller is to reduce the negative impact of the time delay on the stability of the electrical power system. The study was applied to a networked electrical power system consisting of three-generation stations distributed in three separate geographical areas. Computer simulations using MATLAB showed a remarkable improvement in the stability of the discrete networked system through the speed of damping the vibrations in the system, and the system ability to be stable at certain limits of the time delay.

Leaderless Maneuver Guidance and Event-Triggered Formation Control for Distributed Multi-Space-Robot Systems

In this paper, the distributed displacement-based formation and leaderless maneuver guidance control problems of multi-space-robot systems are investigated by introducing event-triggered control update mechanisms. A distributed formation and leaderless maneuver guidance control framework is first constructed, which includes two parallel controllers, namely, an improved linear quadratic regulator and a distributed consensus-based formation controller. By applying this control framework, the desired formation configuration of multi-space-robot systems can be achieved and the center of leaderless formation can converge to the target point globally. Second, a pull-based event triggering mechanism is introduced to the distributed formation controller, which makes the control update independent of the events of neighboring robots, avoids unnecessary control updates, and saves the extremely limited energy of space robots. Furthermore, the potential Zeno behaviors have been excluded by proving a positive lower bound for the inter-event times. Finally, numerical simulation verifies the effectiveness of the theoretical results.

Optimized LQR-PID Controller Using Squirrel Search Algorithm for Trajectory Tracking of a 6-DoF Parallel Manipulator

In 6 Degree of Freedom (DOF) parallel manipulator, trajectory tracking is one of the main challenges. To obtain the desired trajectory, the DC motor needs to generate optimal torque. So to obtain optimal torque, an optimized Linear Quadratic Regulator-Proportional–Integral–Derivative (LQR-PID) controller is presented in this paper. For optimizing the Q, R and gain parameters of LQR-PID controller, Squirrel Search Algorithm (SSA) is presented. In this algorithm, minimal cost function of LQR-PID controller is considered as objective function. The SSA based LQR-PID controller leads the motor to generate optimal torque that helps to attain the desired trajectory of 6-DOF parallel manipulator. Results of the work depicts that the SSA based LQR-PID controller achieves the best mean velocity, sum square error (SSE), integral square error (ISE) and integral absolute error (IAE).

LQR and Fuzzy Logic Control for the Three-Area Power System

The three-area power system is widely considered a suitable example to test load frequency control of the distributed generation system. In this article, for such a system, for the power stabilization task, we introduce two controllers: Linear Quadratic Regulator (LQR), which is model-based, and Fuzzy Logic Controller (FLC), which is data-based. The purpose is to compare the two approaches from the point of view of (i) ease of implementation and tuning, and (ii) robustness to changes in the model. The model, together with controls strategies, has been implemented in the MATLAB software. Then, it has been tested for different simulation scenarios, taking into account the disturbances and faulty tie-lines between areas. Various quality measures allow to compare the performance of each control strategy. The comparison in terms of parameter change and load disturbances prompt us to propose suitable metrics and advice notes on the application of each controller.

Design of Static Output Feedback and Structured Controllers for Active Suspension with Quarter-Car Model

This paper presents a method to design active suspension controllers for a 7-Degree-of-Freedom (DOF) full-car (FC) model from controllers designed with a 2-DOF quarter-car (QC) one. A linear quadratic regulator (LQR) with 7-DOF FC model has been widely used for active suspension control. However, it is too hard to implement the LQR in real vehicles because it requires so many state variables to be precisely measured and has so many elements to be implemented in the gain matrix of the LQR. To cope with the problem, a 2-DOF QC model describing vertical motions of sprung and unsprung masses is adopted for controller design. LQR designed with the QC model has a simpler structure and much smaller number of gain elements than that designed with the FC one. In this paper, several controllers for the FC model are derived from LQR designed with the QC model. These controllers can give equivalent or better performance than that designed with the FC model in terms of ride comfort. In order to use available sensor signals instead of using full-state feedback for active suspension control, LQ static output feedback (SOF) and linear quadratic Gaussian (LQG) controllers are designed with the QC model. From these controllers, observer-based controllers for the FC model are also derived. To verify the performance of the controllers for the FC model derived from LQR and LQ SOF ones designed with the QC model, frequency domain analysis is undertaken. From the analysis, it is confirmed that the controllers for the FC model derived from LQ and LQ SOF ones designed with the QC model can give equivalent performance to those designed with the FC one in terms of ride comfort.

Seismic control of damaged structure by pole assignment and intermittent wavelet-based identification

Calculation of the control forces by control algorithms, such as the pole assignment, proportional-integral-derivative, and linear quadratic regulator, is usually based on initial dynamic characteristics of the intact and undamaged structure, which is considered to be in the ideal conditions. However, because of the effect of natural loads and damage due to aging, these features can change during the structure’s life span, eventually leading to incorrect control forces. In this research, to overcome this problem and to get closer to the actual dynamic characteristics and on the other hand, in order to elude the adverse effects of real-time identification, such as elapsed time of detection, induced to the controller, the intermitted wavelet-based identification technique besides the pole assignment control is introduced. Performance of the proposed controller on three- and five-story with different cases of stiffness and two failure scenarios, under far and near-field earthquakes, are examined and compared by non-updated wavelet-based pole assignment, proportional-integral-derivative and linear quadratic regulator controllers. Results show that damaged structure response controlled by the suggested adapted pole assignment method is significantly reduced compared to ones controlled by other control methods.