scholarly journals KONTROL SUDUT ATTITUDE MENGGUNAKAN LINEAR QUADRATIC REGULATOR (LQR) UNTUK QUADROTOR DENGAN PAYLOAD

ROTASI ◽  
2013 ◽  
Vol 15 (4) ◽  
pp. 16 ◽  
Author(s):  
Mochammad Ariyanto ◽  
Joga Dharma Setiawan ◽  
Ismoyo Haryanto
Keyword(s):  
Steady State ◽  
State Space ◽  
Linear Quadratic Regulator ◽  
Linear Quadratic ◽  
Aerial Manipulation ◽  
Step Input ◽  
Object Interaction ◽  
Integral Action ◽  
Linear State ◽  
State Error

Quadrotor telah dikembangkan oleh peneliti di dunia ini sebagai aerial object interaction/aerial manipulation. Agar quadrotor bisa terbang mengangkat beban, maka dibutuhkan sistem kontrol yang dapat mengkompensasi perubahan pusat gravitasi. Pada penelitian ini, model matematika quadrotor dengan efek beban/payload akan dikembangkan. Untuk mengkompensasi perubahan lokasi pusat gravitasi karena efek beban, Linear Quadratic Regulator (LQR) akan digunakan untuk stabilisasi sudut Euler.Model linear state space dihitung menggunakan persmaan gerak onlinear quadrotor tanpa beban, kemudian disintesis sistem kontrol   LQR. Kontrol tersebut diterapkan dalam model matematika nonlinear dengan beban/payload. Berdasarkan hasil simulasi integral action dari kontrol LQR dapat menghilangkan steady state error setelah diberikan step input, dan kondisi sudut awal sebesar 50. Variasi beban dari 0 gr sampai dengan 200 gr tidak akan memberikan steady state error

scholarly journals A Model and State-Space Controllers for an Intercooled, Regenerated (ICR) Gas Turbine Engine

1992 ◽  
Author(s):  
J. W. Watts ◽  
T. E. Dwan ◽  
R. W. Garman
Keyword(s):  
State Space ◽  
Gas Turbine ◽  
High Efficiency ◽  
Linear Quadratic Regulator ◽  
Gas Turbine Engine ◽  
Linear Quadratic ◽  
Turbine Engine ◽  
Simulation Language ◽  
Linear State ◽  
High Level

A two-and-one-half spool gas turbine engine was modeled using the Advanced Computer Simulation Language (ACSL), a high level simulation environment based on FORTRAN. A possible future high efficiency engine for powering naval ships is an intercooled, regenerated (ICR) gas turbine engine and these features were incorporated into the model. Utilizing sophisticated instructions available in ACSL linear state-space models for this engine were obtained. A high level engineering computational language, MATLAB, was employed to exercise these models to obtain optimal feedback controllers characterized by the following methods: (1) state feedback; (2) linear quadratic regulator (LQR) theory; and (3) polygonal search. The methods were compared by examining the transient curves for a fixed off-load, and on-load profile.

scholarly journals Trajectory Tracking and Stabilization of a Quadrotor Using Model Predictive Control of Laguerre Functions

2015 ◽  
Vol 2015 ◽  
pp. 1-11 ◽  
Author(s):  
Mapopa Chipofya ◽  
Deok Jin Lee ◽  
Kil To Chong
Keyword(s):  
State Space ◽  
Predictive Control ◽  
Trajectory Tracking ◽  
Linear Quadratic Regulator ◽  
Laguerre Functions ◽  
Linear Quadratic ◽  
Model Predictive Controller ◽  
Predictive Controller ◽  
Linear State ◽  
Quadrotor System

This paper presents a solution to stability and trajectory tracking of a quadrotor system using a model predictive controller designed using a type of orthonormal functions called Laguerre functions. A linear model of the quadrotor is derived and used. To check the performance of the controller we compare it with a linear quadratic regulator and a more traditional linear state space MPC. Simulations for trajectory tracking and stability are performed in MATLAB and results provided in this paper.

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

2022 ◽  
Vol 23 (1) ◽  
pp. 129-158
Author(s):  
Oktaf Agni Dhewa ◽  
Tri Kuntoro Priyambodo ◽  
Aris Nasuha ◽  
Yasir Mohd Mustofa
Keyword(s):  
Steady State ◽  
Trajectory Tracking ◽  
Control Method ◽  
Linear Quadratic Regulator ◽  
System Specification ◽  
Linear Quadratic ◽  
Environmental Disturbances ◽  
Essential Requirement ◽  
Lqr Control ◽  
State Error

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.

FULL-AND REDUCED- ORDER COMPENSATOR FOR INNOSAT ATTITUDE CONTROL

2015 ◽  
Vol 76 (12) ◽  
Author(s):  
Fadzilah Hashim ◽  
Mohd Yusoff Mashor ◽  
Siti Maryam Sharun
Keyword(s):  
State Space ◽  
Attitude Control ◽  
Space Form ◽  
Transfer Functions ◽  
Linear Quadratic Regulator ◽  
Linear Quadratic ◽  
Reduced Order ◽  
Lqr Control ◽  
Best Value ◽  
Control Scheme

This paper presents a study on the estimator based on Linear Quadratic Regulator (LQR) control scheme for Innovative Satellite (InnoSAT). By using LQR control scheme, the controller and the estimator has been derived for state space form in all three axes to stabilize the system’s performance. This study starts by converting the transfer functions of attitude control into state space form.  Then, the step continues by finding the best value of weighting matrices of LQR in order to obtain the best value of controller gain, K. After that, the best value of L is obtained for the estimator gain. The value of K and L is combined in forming full order compensator and in the same time the reduced order compensator is also formed. Lastly, the performance of full order compensator is compared to reduced order compensator. From the simulation, results indicate that both types of estimators have presented good stability and tracking performance. However, reduced order estimator has simpler equation and faster convergence to zero than the full order estimator. This property is very important in developing a satellite attitude control for real-time implementation.

scholarly journals DESIGNING DIGITAL CONTROLLERS FOR A CONTROLLED PLANT

2020 ◽  
pp. 24-33
Author(s):  
A Khaimuldin ◽  
T Mukatayev ◽  
N. Assanova ◽  
N. Khaimuldin
Keyword(s):  
Steady State ◽  
Design Procedure ◽  
Open Loop ◽  
Settling Time ◽  
System Response ◽  
Systematic Design ◽  
Digital Controllers ◽  
Controlled System ◽  
Step Input ◽  
State Error

This paper report contains an explanation of how to design a digital controller using the Laplace Transform to z-Transform conversion method. The objectives are that the controlled system should track step input with a reasonably small steady-state error and a settling time faster than the open-loop settling time. Furthermore, it should do so with the minimum overshoot that is reasonably possible. The main contribution is to establish the feasibility and ease of the systematic design procedure and future work will focus in more detail on applying the Sampling Theorem and deadbeat controller. There are several objectives that the controlled system should reach: 1. Track step input with a reasonably small steady-state error and a settling time which should be faster than the open-loop settling time. 2. Gain a small overshoot that is sufficiently possible. 3. Have a systematic design procedure. A method for finding the parameters of the deadbeat controller in the MatLab environment is presented. Based on the results obtained the simulation reveals that even when the control grows by one-step, the settling time of the system response could be less than that of the deadbeat controller. The work shows that deadbeat could be a powerful analysis tool since it is possible to grab the entire dynamic easily using several samples.

Minimizing Human Tracking Error for Robotic Rehabilitation Device

2015 ◽  
Vol 9 (4) ◽  
Author(s):  
Andrew J. Homich ◽  
Megan A. Doerzbacher ◽  
Eric L. Tschantz ◽  
Stephen J. Piazza ◽  
Everett C. Hills ◽  
...  
Keyword(s):  
State Space ◽  
Tracking Error ◽  
Linear Quadratic Regulator ◽  
Gait Training ◽  
Average Error ◽  
Linear Quadratic ◽  
Optimal State ◽  
Filter Performance ◽  
Complementary Filter ◽  
Angular Velocities

This paper explores the design of a novel robotic device for gait training and rehabilitation, a method to estimate a human's orientation within the rehabilitation device, as well as an optimal state space controller to actuate the rehabilitation device. The robotic parallel bars (RPBs) were designed to address the shortcomings of currently available assistive devices. The RPB device moves in response to a human occupant to maintain a constant distance and orientation to the human. To minimize the error in tracking the human, a complementary filter was optimized to estimate the human's orientation within the device using a magnetometer and gyroscope. Experimental measurements of complementary filter performance on a test platform show that the filter estimates orientation with an average error of 0.62 deg over a range of angular velocities from 22.5 deg/s to 180 deg/s. The RPB device response was simulated, and an optimal state space controller was implemented using a linear quadratic regulator (LQR). The controller has an average position error of 14.1 cm and an average orientation error of 14.3 deg when tracking a human, while the simulation predicted an average error of 10.5 cm and 5.6 deg. The achieved level of accuracy in following a human user is sufficiently sensitive for the RPB device to conduct more advanced, realistic gait training and rehabilitation techniques for mobility impaired patients able to safely support their body weight with their legs and arms.

Health Estimation of Gas Turbine: A Symbolic Linearization Model Approach

2017 ◽  
Author(s):  
Qingcai Yang ◽  
Yunpeng Cao ◽  
Fang Yu ◽  
Jianwei Du ◽  
Shuying Li
Keyword(s):  
Steady State ◽  
State Space ◽  
Gas Turbine ◽  
Linear Model ◽  
Piecewise Linear ◽  
State Space Model ◽  
Space Model ◽  
Linear State ◽  
Model Approach ◽  
Health Parameters

This paper is mainly concerned with the health estimation of a gas turbine using a symbolic linearization model approach. Health parameters will change with the degradation of gas turbine performance. Monitoring and evaluating these health parameters can assist in the development of predictive control techniques and maintenance schedules. Currently, various health parameter estimation methods have been studied extensively, but there have been less related studies on how to obtain statespace models. In this paper, a symbolic linearization model method is presented to overcome the shortcoming of high time consumption suffered by existing methods. In this method, each component model of the dynamic nonlinear gas turbine model is decomposed into several sub-modules, each of which contains a simple nonlinear equation. By means of symbolic computation, a linear model of the components is derived by linearizing these sub-modules, and then the generalized linear state-space model of the gas turbine is derived from the relationship among the components. In the generalized linear state-space model, the Jacobian matrices are functions of the parameters under a steady-state operating condition. Therefore, it is easy to obtain a linear model that represents the dynamics of the gas turbine under a given operating condition. To estimate the health parameters of a gas turbine, a piecewise linear model is developed using the proposed approach, and this model is verified in a simulation environment. The results show that the developed piecewise linear model can capture the behavior of a gas turbine quite closely. Then, a linearized Kalman filter is designed for estimating the health parameters under steady-state and transient conditions. The results show that the generalized linear model established using the presented method can be used to accurately estimate the health parameters of a gas turbine.

scholarly journals Controller Tuning and Robustness Testing of Attitude Control Laws for a CubeSat Mission

2021 ◽  
Author(s):  
Mohamed Jundi
Keyword(s):  
State Space ◽  
Attitude Control ◽  
Initial Conditions ◽  
Block Diagram ◽  
Linear Quadratic Regulator ◽  
Reaction Wheel ◽  
Linear Quadratic ◽  
Test Environment ◽  
Wheel Model ◽  
Space Equation

The purpose of this project was to create a test environment that can be used to test different controllers and their robustness. In this report, the equations of motion were derived using kinematics, with attitude quaternions, and spacecraft dynamics, with angular velocity and acceleration. The equations were combined and placed into the form of a linearized state-space equation. The different control methods being investigated, Linear Quadratic Regulator (LQR) for the reaction wheel model, and the Bdot with bias controller, were explained and the block diagram for each was shown. To setup the test, the tolerances for the roll, pitch, and yaw, and their rates, were taken from the mission requirement for the ESSENCE mission. The attitude tolerance being ±0.5deg and the angular rates requirement being ±0.05deg/s. Then the test setup was further explained. The test is broken up into different scripts and steps: 1. Main run function for simulation. Initializes simulation parameters. 2. Build state-space equation and calculate constant gain matrix. 3. Randomize initial conditions and pass onto simulation. 4. Post-processing and plot generation. 5. Statistics generation. This robust testing environment was used to test 5 different controllers for the reaction wheel model. Each controller was tested for 200 different simulations, in which the initial attitude, initial angular rates, and the center of mass were randomized. The first controller was successful for 198/200 simulations, where the only failure came from over-saturating the reaction wheels. The next three controllers had a perfect record and were successful for all 200 simulations each. The last controller, had only 71 successful simulations in the set, and a sample of one of the failed simulations was further investigated to see how it failed.

scholarly journals Controller Tuning and Robustness Testing of Attitude Control Laws for a CubeSat Mission

2021 ◽  
Author(s):  
Mohamed Jundi
Keyword(s):  
State Space ◽  
Attitude Control ◽  
Initial Conditions ◽  
Block Diagram ◽  
Linear Quadratic Regulator ◽  
Reaction Wheel ◽  
Linear Quadratic ◽  
Test Environment ◽  
Wheel Model ◽  
Space Equation

The purpose of this project was to create a test environment that can be used to test different controllers and their robustness. In this report, the equations of motion were derived using kinematics, with attitude quaternions, and spacecraft dynamics, with angular velocity and acceleration. The equations were combined and placed into the form of a linearized state-space equation. The different control methods being investigated, Linear Quadratic Regulator (LQR) for the reaction wheel model, and the Bdot with bias controller, were explained and the block diagram for each was shown. To setup the test, the tolerances for the roll, pitch, and yaw, and their rates, were taken from the mission requirement for the ESSENCE mission. The attitude tolerance being ±0.5deg and the angular rates requirement being ±0.05deg/s. Then the test setup was further explained. The test is broken up into different scripts and steps: 1. Main run function for simulation. Initializes simulation parameters. 2. Build state-space equation and calculate constant gain matrix. 3. Randomize initial conditions and pass onto simulation. 4. Post-processing and plot generation. 5. Statistics generation. This robust testing environment was used to test 5 different controllers for the reaction wheel model. Each controller was tested for 200 different simulations, in which the initial attitude, initial angular rates, and the center of mass were randomized. The first controller was successful for 198/200 simulations, where the only failure came from over-saturating the reaction wheels. The next three controllers had a perfect record and were successful for all 200 simulations each. The last controller, had only 71 successful simulations in the set, and a sample of one of the failed simulations was further investigated to see how it failed.

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