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.

Multi-Mode Active Suspension Control Based on a Genetic K-Means Clustering Linear Quadratic Algorithm

The traditional Linear quadratic regulator (LQR) control algorithm depends too much on expert experience during the selection of weighting coefficients. To solve this problem, we proposed a Genetic K-means clustering Linear quadratic (GKL) algorithm. Firstly, a 2-DOF 1/4 vehicle model and road input model are established. The weights of an LQR controller are optimized using a genetic algorithm. Then, a possible weighting space is constructed based on this optimal solution. Random weighting coefficients of each performance index are generated in this space. Next, LQR control for the 1/4 vehicle model is performed, and the simulation data are recorded automatically, with these random weighting values, different road classes, and driving speed. A machine learning dataset is built from these simulations. Finally, a K-means clustering algorithm is used to classify the LQR control active suspension into three performance modes: safety mode, comprehensive mode, and comfort mode. The optimal weighting matrix of each performance mode is determined to satisfy requirements for different types of drivers. The results show that the new GKL algorithm not only improves the suspension control effect but also realizes different performance modes. It can better adapt to the changes in driving conditions and drivers.

Missile Longitudinal Dynamics Control Design Using Pole Placement and LQR Methods

In high-maneuvering missile systems, with severe restrictions on actuator energy requirements, it is desirable to achieve the required performance with least actuation effort. Linear Quadratic Regulator (LQR) has been in literature for long and has proven it’s mettle as an optimal controller in many benign aerospace applications and industrial applications where the response times of the plant, in most cases, are seen to be greater than 10 seconds. It can be observed in the literature that LQR control methodology has not been explored enough in the tactical missile applications where requirement of very fast airframe response times are desired, typically of the order of milliseconds. In the present research, the applicability of LQR method for one such agile missile control has been critically explored. In the present research work, longitudinal dynamic model of an agile missile flying at high angle of attack regime has been established and an optimal LQR control solution has been proposed to bring out the required performance demanding least control actuator energy. A novel scheme has been presented to further optimise the control effort, which is essential in this class of missile systems with space and energy constraints, by iteratively computing optimal magnitude state weighing matrix Q and control cost matrix R. Pole placement design techniques, though extensively used in aerospace industry because of ease of implementation and proven results, do not address optimality of the system performance. Hence, a comparative study has been carried out to verify the results of LQR against pole placement technique based controller. The efficacy of LQR based controller over pole placement design techniques is successfully established with minimum control energy requirement in this paper. Futuristic high maneuvering, agile missile control design with severe space and energy constraints stand to benefit incorporating the controller design scheme proposed in this paper.

Designing LQR Controllers for an Active Anti-roll Bar System with a Flexible Frame Model of a Single Unit Heavy Vehicle

Rollover accidents of heavy vehicles often cause serious consequences both in terms of vehicle and environmental damage as well the loss or injury of drivers, passengers and ordinary civilians. Currently, the active anti-roll bar system is considered as the most effective solution in enhancing vehicle roll stability. In this paper, we firstly investigated the role of a flexible frame of a single unit heavy vehicle in the rollover process. This approach is an important step forward in the research of the active anti-roll bar system. Then, the LQR control method is applied in designing controllers for the active anti-roll bar control system with this frame model. The active torque of the anti-roll bar system is considered as the control signal. The simulation results in the frequency and time domains with a double lane change maneuver show that the vehicle’s roll stability is improved by over 30 % compared to a vehicle using a passive anti-roll bar system.

A didactic platform for the study of Linear Quadratic Regulator (LQR) control for Trajectory Tracking of dc motor

The main objective of this work is to show in detail the methodology to apply the Linear Quadratic Regulator (LQR) for Trajectory Tracking in an experimental way in a didactic platform which consists of a DC motor, the motor model is explained, and how the parameters were estimated experimentally and the validation thereofs. Results are shown applying the LQR control in simulation and experimentally.