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.

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.

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.

Mechatronic suspension design for full rail vehicle system

2016 ◽  
Vol 231 (4) ◽  
pp. 571-590 ◽  
Author(s):  
Mortadha Graa ◽  
Mohamed Nejlaoui ◽  
Ajmi Houidi ◽  
Zouhaier Affi ◽  
Lotfi Romdhane
Keyword(s):  
Tracking Error ◽  
Linear Quadratic Regulator ◽  
Experimental Result ◽  
Railway Vehicle ◽  
Linear Quadratic ◽  
Rail Vehicle ◽  
Vehicle System ◽  
Frequency Domains ◽  
Rail Irregularities ◽  
Vehicle Motion

In this paper, an analytical mechatronic dynamic design model of a full rail vehicle system is developed. Based on the rail vehicle motion, its degree of freedom can be reduced to only 38. This reduction is necessary for the model simplicity. The developed model is validated with experimental result and compared with other one from literature. The real characteristics of the actuators are discussed, and its controller is designed. A mechatronic model that expresses the controlled tracking error as function of the vehicle dynamics and the actuator characteristics is developed. This model is used by the linear quadratic regulator approach to identify the mechatronic rail vehicle proportional–integral–derivative controller’s gains. The mechatronic rail vehicle comfort is evaluated in terms of the passenger displacement, acceleration and frequency as a response of a rail irregularities caused by a lateral and two vertical track irregularities. The simulations of vibration analysis are obtained in time and frequency domains and compared with railway vehicle status. The robustness of the designed mechatronic rail vehicle is verified by simulations, carried out for the cases of car body mass variations. The results show the effectiveness of the proposed mechatronic rail vehicle design which improves significantly the transportation of passengers.

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 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

An Error Space Controller for a Resonating Fiber Scanner: Simulation and Implementation

2006 ◽  
Vol 128 (4) ◽  
pp. 899-913 ◽  
Author(s):  
Quinn Y. J. Smithwick ◽  
Juris Vagners ◽  
Per G. Reinhall ◽  
Eric J. Seibel
Keyword(s):  
Tracking Error ◽  
Linear Quadratic Regulator ◽  
Open Loop ◽  
Linear Quadratic ◽  
Fiber Nonlinearities ◽  
Error Space ◽  
Nonlinear Dynamics Model ◽  
Error Dynamics ◽  
Scan Pattern ◽  
Spiral Scan

A robust error-space controller for an amplitude modulated resonating fiber scanner is developed and implemented. Using a nonlinear dynamics model, the system’s open loop temporal response for a spiral scan pattern is simulated and compared to experiments to understand scan distortions, such as, toroid, swirl, and beating. A feedback linearized linear quadratic regulator based on error dynamics drives the tracking error to zero. Controller simulations determine robustness limits, and effects of fiber nonlinearities and actuator time delay. Using real-time hardware, the controller asymptotically tracks and is capable of removing the scan distortions. Image acquisition with the controlled scanner produces nearly pixel accurate images.

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.

scholarly journals Gain scheduling LQI controller design for LPV descriptor systems and motion control of two-link flexible joint robot manipulator

2018 ◽  
Vol 8 (2) ◽  
pp. 201-207 ◽  
Author(s):  
Yusuf Altun
Keyword(s):  
State Space ◽  
Motion Control ◽  
Controller Design ◽  
Linear Quadratic Regulator ◽  
Robotic Manipulator ◽  
Gain Scheduling ◽  
Descriptor Systems ◽  
Natural State ◽  
Linear Quadratic ◽  
Flexible Joint

This paper proposes a gain scheduling linear quadratic integral (LQI) servo controller design, which is derived from linear quadratic regulator (LQR) optimal control, for non-singular linear parameter varying (LPV) descriptor systems. It is assumed that state space matrices are non-singular since many mechanical systems do not have any non-singular matrices such as the natural state space forms of robotic manipulator, pendulum and suspension systems. A controller design is difficult for the systems due to rational LPV case. Therefore, the proposed gain scheduling controller is designed without the difficulty. Accordingly, the motion control design is implemented for two-link flexible joint robotic manipulator. Finally, the control system simulation is performed to prove the applicability and performance.

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