scholarly journals Discrete Inverse Problem Approach to Path Tracking in State Space Form

2018 ◽  
Author(s):  
Matthew Harker ◽  
Gerhard Rath
Keyword(s):  
Inverse Problem ◽  
State Space ◽  
Space Form ◽  
Path Tracking

Design and Experimental Validation of a LQG Control System for the Stabilization of a 2DOF Commercial Gimbal Using Physical Modelling Techniques

2020 ◽  
Author(s):  
Julián Andres Gómez Gómez ◽  
Camilo E. Moncada Guayazán ◽  
Sebastián Roa Prada ◽  
Hernando Gonzalez Acevedo
Keyword(s):  
Mathematical Model ◽  
Control System ◽  
State Space ◽  
Transient Response ◽  
Space Form ◽  
Angular Position ◽  
Physical Modelling ◽  
Motor Shaft ◽  
Brushless Dc ◽  
The Mathematical Model

Abstract Gimbals are mechatronic systems well known for their use in the stabilization of cameras which are under the effect of sudden movements. Gimbals help keeping cameras at previously defined fixed orientations, so that the captured images have the highest quality. This paper focuses on the design of a Linear Quadratic Gaussian, LQG, controller, based on the physical modeling of a commercial Gimbal with two degrees of freedom (2DOF), which is used for first-person applications in unmanned aerial vehicle (UAV). This approach is proposed to make a more realistic representation of the system under study, since it guarantees high accuracy in the simulation of the dynamic response, as compared to the prediction of the mathematical model of the same system. The development of the model starts by sectioning the Gimbal into a series of interconnected links. Subsequently, a fixed reference system is assigned to each link body and the corresponding homogeneous transformation matrices are established, which will allow the calculation of the orientation of each link and the displacement of their centers of mass. Once the total kinetic and potential energy of the mechanical components are obtained, Lagrange’s method is utilized to establish the mathematical model of the mechanical structure of the Gimbal. The equations of motion of the system are then expressed in state space form, with two inputs, two outputs and four states, where the inputs are the torques produced by each one of the motors, the outputs are the orientation of the first two links, and the states are the aforementioned orientations along with their time derivatives. The state space model was implemented in MATLAB’s Simulink environment to compare its prediction of the transient response with the prediction obtained with the representation of the same system using MATLAB’s SimMechanics physical modelling interface. The mathematical model of each one of the three-phase Brushless DC motors is also expressed in state space form, where the three inputs of each motor model are the voltages of the corresponding motor phases, its two outputs are the angular position and angular velocity, and its four states are the currents in two of the phases, the orientation of the motor shaft and its rate of change. This model is experimentally validated by performing a switching sequence in both the simulation model and the physical system and observing that the transient response of the angular position of the motor shaft is in accordance with the theoretical model. The control system design process starts with the interconnection of the models of the mechanical components and the models of the Brushless DC Motor, using their corresponding state space representations. The resulting model features six inputs, two outputs and eight states. The inputs are the voltages in each phase of the two motors in the Gimbal, the outputs are the angular positions of the first two links, and the states are the currents in two of the phases for each motor and the orientations of the first two links, along with their corresponding time derivatives. An optimal LQG control system is designed using MATLAB’s dlqr and Kalman functions, which calculate the gains for the control system and the gains for the states estimated by the observer. The external excitation in each of the phases is carried out by pulse width modulation. Finally, the transient response of the overall system is evaluated for different reference points. The simulation results show very good agreement with the experimental measurements.

scholarly journals Experience Rating of ARIMA Processes by the Kalman Filter

1986 ◽  
Vol 16 (1) ◽  
pp. 19-31 ◽  
Author(s):  
Jukka Rantala
Keyword(s):  
Kalman Filter ◽  
Time Delay ◽  
State Space ◽  
Theoretical Approach ◽  
Space Form ◽  
The State ◽  
Experience Rating ◽  
Filter Technique ◽  
Main Emphasis ◽  
Arima Processes

AbstractThis paper deals with experience rating of claims processes of ARIMA structures. By experience rating we mean that future premiums should be only a function of past values of the claims process. The main emphasis is on demonstrating the usefulness of the control-theoretical approach in the search for optimal rating rules. Optimality is here defined to mean as smooth a flow of premiums as possible when the variation in the accumulated profit is restricted to a certain amount. First it is shown how the underlying model in its simplest form can be transformed into the state-space form. Then the Kalman filter technique is used to find the optimal rules. Also a time delay in information is taken into account. The optimal rules are illustrated by examples.

scholarly journals Skew-Normal Shocks in the Linear State Space Form DSGE Model

2011 ◽  
Author(s):  
Grzegorz Grabek ◽  
Bohdan Klos ◽  
Grzegorz Koloch
Keyword(s):  
State Space ◽  
Space Form ◽  
Dsge Model ◽  
Linear State ◽  
Skew Normal

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.

State space regularization in the nonstationary inverse problem for diffuse optical tomography

2011 ◽  
Vol 27 (2) ◽  
pp. 025009 ◽  
Author(s):  
P Hiltunen ◽  
S Särkkä ◽  
I Nissilä ◽  
A Lajunen ◽  
J Lampinen
Keyword(s):  
Inverse Problem ◽  
State Space ◽  
Optical Tomography ◽  
Diffuse Optical Tomography

Fast Motion of Path Tracking Task with Constant Hand Speed Using Redundant Manipulator

2015 ◽  
Vol 27 (1) ◽  
pp. 74-82 ◽  
Author(s):  
Kousuke Okabe ◽  
◽  
Yasumichi Aiyama
Keyword(s):  
Motion Planning ◽  
State Space ◽  
Path Tracking ◽  
Tracking Task ◽  
Joint Torque ◽  
Redundant Manipulator ◽  
Fast Motion ◽  
Joint Velocity ◽  
Driving Torque ◽  
Joint Acceleration

<div class=""abs_img""><img src=""[disp_template_path]/JRM/abst-image/00270001/09.jpg"" width=""300"" />Limits and a motion in state space</div> We propose a motion planning method for accelerating path-tracking task with constant hand speed using redundant manipulator. Tracking-speed should be increased to satisfy the joint torque and joint velocity limits. We propose a method using the state space of redundant manipulators to analyze these limits and to operate motion planning. This state space has a position on a trajectory, redundant pose, and redundant velocity axes. These limits are projected on state space. We consider, motion planning is path-finding problem on state space at a constant hand speed. To plan a faster motion, a constant hand speed is examined by finding a path with limits in state space. We use computer simulation to test and evaluate our proposed method on 3-link planar manipulator. Results demonstrated motion faster than a motion minimizing joint acceleration norm and a motion minimizing driving torque norm. We also verified a problem when our method was applied to an actual manipulator. </span>

scholarly journals Path tracking control for inverse problem of vehicle handling dynamics

2017 ◽  
Vol 19 (6) ◽  
pp. 4591-4608 ◽  
Author(s):  
Yingjie Liu ◽  
Dawei Cui ◽  
Yu Fu
Keyword(s):  
Inverse Problem ◽  
Tracking Control ◽  
Path Tracking ◽  
Vehicle Handling
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