Discrete Time Linear Quadratic Tracking Controller for Omni-Directional Mobile Robots

2011 ◽  
Author(s):  
Ehsan Hashemi ◽  
Maani Ghaffari Jadidi
Keyword(s):  
Control System ◽  
Path Planning ◽  
Mobile Robots ◽  
Controller Design ◽  
Optimal Solution ◽  
Linear Quadratic Regulator ◽  
Reference Trajectory ◽  
Linear Quadratic ◽  
Tracking Controller ◽  
Quadratic Tracking

The purpose of this investigation is to suggest and examine a trajectory follower control system for linear discrete dynamic model of omni-directional mobile robots to reach a controller with optimal inputs for drivers. Introducing optimal controllers for multi input-multi output control systems in acceleration and deceleration maneuvers to track a specified path is one of essential subjects for motion study of omni-directional mobile robots. Regulated drivers’ rotational velocities and torques greatly affect the ability of these robots to perform trajectory planner tasks. Moreover, environmental influencing factors shall also be considered in such robot models for accurate path planning. Presented tracking control system in this article provides an optimal solution to minimize differences between reference trajectory and system output in the lately developed simulated model. Trajectory following system together with implemented kinematic and dynamic modeling for an optimal controller to satisfy the path planning prerequisites is mainly discussed in this paper in several sections. Main topics presented and discussed in this article are considerable improvements in simulation of the newly optimized controller by Linear Quadratic Regulator and Tracking. Utilizing the new approach on tracking controller design results in the more precise and appropriate tracking behavior of omni-directional mobile robots as the simulation and experimental results confirm this issue.

A New-Generation Motion-Control System for Twin-Hull Vessels Using a Neural Optimal Controller

2003 ◽  
Vol 40 (03) ◽  
pp. 168-180
Author(s):  
Farhad Kenevissi ◽  
Mehmet Atlar ◽  
Ehsan Mesbahi
Keyword(s):  
Control System ◽  
Optimal Solution ◽  
Linear Quadratic Regulator ◽  
Operating Conditions ◽  
Domain Model ◽  
Optimal Controller ◽  
Linear Quadratic ◽  
Motion Responses ◽  
Artificial Neural Network Ann ◽  
Operating Points

A new ride control system using a neural optimal controller (NOC) is developed and applied to improve the heave and pitch motion responses of two twin-hull vessels operating in regular head seas. A time domain model for the vessel dynamics in the presence of active fin control is used to simulate the vessel and fin motion responses. An online switching procedure is introduced to select among a number of linear quadratic regulator optimal controllers, designed for different operating conditions of the vessel, to improve the system robustness. Although the online switching offered better robustness and performance characteristics, in between switching operating points, it still remained suboptimal. Therefore, an artificial neural network (ANN) controller was developed as an alternative and initially trained to emulate the same level of control at a number of design operating points, as a NOC. The advantage of this novel application is that practical difficulties in applying an online switching procedure are no longer present and, more importantly, the ANN has been capable of nonlinear generalization to give a near optimal solution away from the trained operating conditions.

scholarly journals Autonomous Collision Avoidance Using MPC with LQR-Based Weight Transformation

Sensors ◽  
2021 ◽  
Vol 21 (13) ◽  
pp. 4296
Author(s):  
Shayan Taherian ◽  
Kaushik Halder ◽  
Shilp Dixit ◽  
Saber Fallah
Keyword(s):  
Collision Avoidance ◽  
Discrete Time ◽  
Optimal Solution ◽  
Linear Quadratic Regulator ◽  
Weighting Factor ◽  
Algebraic Riccati Equation ◽  
Control Technique ◽  
Linear Quadratic ◽  
Weighting Matrix ◽  
Quadratic Tracking

Model predictive control (MPC) is a multi-objective control technique that can handle system constraints. However, the performance of an MPC controller highly relies on a proper prioritization weight for each objective, which highlights the need for a precise weight tuning technique. In this paper, we propose an analytical tuning technique by matching the MPC controller performance with the performance of a linear quadratic regulator (LQR) controller. The proposed methodology derives the transformation of a LQR weighting matrix with a fixed weighting factor using a discrete algebraic Riccati equation (DARE) and designs an MPC controller using the idea of a discrete time linear quadratic tracking problem (LQT) in the presence of constraints. The proposed methodology ensures optimal performance between unconstrained MPC and LQR controllers and provides a sub-optimal solution while the constraints are active during transient operations. The resulting MPC behaves as the discrete time LQR by selecting an appropriate weighting matrix in the MPC control problem and ensures the asymptotic stability of the system. In this paper, the effectiveness of the proposed technique is investigated in the application of a novel vehicle collision avoidance system that is designed in the form of linear inequality constraints within MPC. The simulation results confirm the potency of the proposed MPC control technique in performing a safe, feasible and collision-free path while respecting the inputs, states and collision avoidance constraints.

Fuzzy neural network control algorithm for asymmetric building structure with active tuned mass damper

2020 ◽  
Vol 26 (21-22) ◽  
pp. 2037-2049
Author(s):  
Xiao Yan ◽  
Zhao-Dong Xu ◽  
Qing-Xuan Shi
Keyword(s):  
Neural Network ◽  
Control System ◽  
Fuzzy Neural Network ◽  
Linear Quadratic Regulator ◽  
Tuned Mass Damper ◽  
Linear Quadratic ◽  
Mass Damper ◽  
Fuzzy Neural ◽  
Neural Network Algorithm ◽  
Damper Control

Asymmetric structures experience torsional effects when subjected to seismic excitation. The resulting rotation will further aggravate the damage of the structure. A mathematical model is developed to study the translation and rotation response of the structure during seismic excitation. The motion equations of the structures which cover the translation and rotation are obtained by the theoretical derivations and calculations. Through the simulated computation, the translation and rotation response of the structure with the uncontrolled system, the tuned mass damper control system, and active tuned mass damper control system using linear quadratic regulator algorithm are compared to verify the effectiveness of the proposed active control system. In addition, the linear quadratic regulator and fuzzy neural network algorithm are used to the active tuned mass damper control system as a contrast group to study the response of the structure with different active control method. It can be concluded that the structure response has a significant reduction by using active tuned mass damper control system. Furthermore, it can be also found that fuzzy neural network algorithm can replace the linear quadratic regulator algorithm in an active control system. Because fuzzy neural network algorithm can control the process on an uncertain mathematical model, it has more potential in practical applications than the linear quadratic regulator control method.

scholarly journals Satellite Attitude Control System Design Taking into Account the Fuel Slosh and Flexible Dynamics

2014 ◽  
Vol 2014 ◽  
pp. 1-8 ◽  
Author(s):  
Alain G. de Souza ◽  
Luiz C. G. de Souza
Keyword(s):  
Control System ◽  
Attitude Control ◽  
Center Of Mass ◽  
Rigid Motion ◽  
Linear Quadratic Regulator ◽  
Comparative Investigation ◽  
Attitude Control System ◽  
Linear Quadratic ◽  
Deformable Structure ◽  
Fuel Slosh

The design of the spacecraft Attitude Control System (ACS) becomes more complex when the spacecraft has different type of components like, flexible solar panels, antennas, mechanical manipulators and tanks with fuel. The interaction between the fuel slosh motion, the panel’s flexible motion and the satellite rigid motion during translational and/or rotational manoeuvre can change the spacecraft center of mass position damaging the ACS pointing accuracy. This type of problem can be considered as a Fluid-Structure Interaction (FSI) where some movable or deformable structure interacts with an internal fluid. This paper develops a mathematical model for a rigid-flexible satellite with tank with fuel. The slosh dynamics is modelled using a common pendulum model and it is considered to be unactuated. The control inputs are defined by a transverse body fixed force and a moment about the centre of mass. A comparative investigation designing the satellite ACS by the Linear Quadratic Regulator (LQR) and Linear Quadratic Gaussian (LQG) methods is done. One has obtained a significant improvement in the satellite ACS performance and robustness of what has been done previously, since it controls the rigid-flexible satellite and the fuel slosh motion, simultaneously.

scholarly journals Design of Constructive Controller of Nonlinear System Based on Polynomial Function Growth Condition and Its Application in Deep Subsea Energy Mining and Production Control System

2021 ◽  
Vol 2021 ◽  
pp. 1-9
Author(s):  
Longchuan Guo ◽  
Chuanping Zhou ◽  
Xiaoqing Tian ◽  
Huawei Ji ◽  
Yudong Peng
Keyword(s):  
Control System ◽  
Nonlinear System ◽  
Control Problem ◽  
Growth Condition ◽  
Output Feedback ◽  
Controller Design ◽  
Polynomial Function ◽  
Growth Conditions ◽  
Simulation Software ◽  
Tracking Controller

This paper mainly studies the output feedback control problem of the stochastic nonlinear system based on loose growth conditions and applies the research results to the valve control system of underwater oil and gas pipelines, which can improve the speed and stability of the equipment system. First, the concept of randomness is introduced to study the actual tracking control problem of output feedback of stochastic nonlinear systems, remove the original harsher growth conditions, make it meet the more general polynomial function growth conditions, and propose a combination of static and dynamic output feedback practices. The design of the tracking controller makes all the states of the system meet boundedness and ensures that the tracking error of the system converges to a small neighborhood of zero. Second, the system is extended to the parameter-uncertain system, and the output feedback tracking controller with complete dynamic gain is constructed by proving the boundedness of the system state and gain. Further, the time-delay factor is introduced, and the nonlinear term of the system satisfies the more relaxed power growth condition, combined with the inverse method to cleverly construct a set of Lyapunov functions and obtain the output controller to ensure that the system is asymptotically probabilistic in the global scope. Stability. Finally, through the ocean library in the Simulation X simulation software, the controller design results are imported into the underwater electro-hydraulic actuator model to verify the effectiveness of the controller design.

scholarly journals The linear quadratic regular algorithm-based control system of the direct current motor

2019 ◽  
Vol 10 (2) ◽  
pp. 768
Author(s):  
Trong-Thang Nguyen
Keyword(s):  
Control System ◽  
Direct Current ◽  
State Space Model ◽  
Linear Quadratic Regulator ◽  
Response Speed ◽  
Dc Motor ◽  
Linear Quadratic ◽  
Lqr Controller ◽  
Mathematical Equations ◽  
Feed Forward Controller

<span>This research aims to propose an optimal controller for controlling the speed of the Direct Current (DC) motor. Based on the mathematical equations of DC Motor, the author builds the equations of the state space model and builds the linear quadratic regulator (LQR) controller to minimize the error between the set speed and the response speed of DC motor. The results of the proposed controller are compared with the traditional controllers as the PID, the feed-forward controller. The simulation results show that the quality of the control system in the case of LQR controller is much higher than the traditional controllers. The response speed always follows the set speed with the short conversion time, there isn't overshoot. The response speed is almost unaffected when the torque impact on the shaft is changed.</span>

scholarly journals A COMPARISON OF LYAPUNOV AND FUZZY APPROACHES TO TRACKING CONTROLLER DESIGN

2020 ◽  
Vol 1 (2) ◽  
pp. 54-57
Author(s):  
Tan- Sang Le ◽  
Le Hong Hieu
Keyword(s):  
Mobile Robots ◽  
Lyapunov Stability ◽  
Tracking Control ◽  
Controller Design ◽  
Final Goal ◽  
Tracking Controller

There are numerous types of locomotion of mobile robots. Therein, the most widespread type of locomotion is motion using wheels. The task of robot is transport themselves from place to place. And tracking control is always an important problem to appply robots in practice. The robot has to reach the final goal by following a referenced trajectory. The paper proposes two methods based on the lyapunov stability standard and fuzzy law. Then, we simulate the algorithms to evaluate the results.

scholarly journals Simulation of a Steam Injected Gas Turbine Plant Control System

1997 ◽  
Author(s):  
Shusheng Zang ◽  
Jaqiang Pan
Keyword(s):  
Gas Turbine ◽  
Flow Rate ◽  
Controller Design ◽  
Dynamic Performance ◽  
Linear Quadratic Regulator ◽  
Linear Quadratic ◽  
Turbine Plant ◽  
Fuel Flow ◽  
Lqr Controller ◽  
Gas Turbine Plant

The design of a modern Linear Quadratic Regulator (LQR) is described for a test steam injected gas turbine (STIG) unit. The LQR controller is obtained by using the fuel flow rate and the injected steam flow rate as the output parameters. To meet the goal of the shaft speed control, a classical Proportional Differential (PD) controller is compared to the LQR controller design. The control performance of the dynamic response of the STIG plant in the case of rejection of load is evaluated. The results of the computer simulation show a remarkable improvement on the dynamic performance of the STIG unit.

Optimal Error-Clamping Design for Position-Based Visual Servoing of a 2-DOF Model Helicopter

2011 ◽  
Author(s):  
M. Alizadeh ◽  
C. Ratanasawanya ◽  
M. Mehrandezh ◽  
R. Paranjape
Keyword(s):  
Visual Servoing ◽  
Degrees Of Freedom ◽  
Vision System ◽  
Physical Space ◽  
Linear Quadratic Regulator ◽  
Image Plane ◽  
Reference Trajectory ◽  
Linear Quadratic ◽  
Feed Forward ◽  
Model Helicopter

A vision-based servoing technique is proposed for a 2 degrees-of-freedom (dof) model helicopter equipped with a monocular vision system. In general, these techniques can be categorized as image- and position-based, where the task error is defined in the image plane in the former and in the physical space in the latter. The 2-dof model helicopter requires a configuration-dependent feed-forward control to compensate for gravitational forces when servoing on a ground target. Therefore, a position-based visual servoing deems more appropriate for precision control. Image information collected from a ground object, with known geometry a priori, is used to calculate the desired pose of the camera and correspondingly the desired joint angles of the model helicopter. To assure a smooth servoing, the task error is parameterized, using the information obtained from the linearaized image Jacobian, and time scaled to form a moving reference trajectory. At the higher level, a Linear Quadratic Regulator (LQR), augmented with a feed-forward term and an integrator, is used to track this trajectory. The discretization of the reference trajectory is achieved by an error-clamping strategy for optimal performance. The proposed technique was tested on a 2-dof model helicopter capable of pitch and yaw maneuvers carrying a light-weight off-the-shelf video camera. The test results show that the optimized controller can servo the model helicopter to a hovering pose for an image acquisition rate of as low as 2 frames per second.

Linear Quadratic Regulator Method in Vision-Based Laser Beam Tracking for a Mobile Target Robot

Robotica ◽  
2020 ◽  
pp. 1-11
Author(s):  
Yun Ling ◽  
Jian Wu ◽  
Weiping Zhou ◽  
Yubiao Wang ◽  
Changcheng Wu
Keyword(s):  
Control System ◽  
Laser Beam ◽  
Tracking Control ◽  
Error Control ◽  
Linear Quadratic Regulator ◽  
Lyapunov Theory ◽  
State Function ◽  
Linear Quadratic ◽  
Mobile Target ◽  
Beam Tracking

SUMMARY This paper proposes a novel laser beam tracking mechanism for a mobile target robot that is used in shooting ranges. Compared with other traditional tracking mechanisms and modules, the proposed laser beam tracking mechanism is more flexible and low cost in use. The mechanical design and the working principle of the tracking module are illustrated, and the complete control system of the mobile target robot is introduced in detail. The tracking control includes two main steps: localizing the mobile target robot with regards to the position of the laser beam and tracking the laser beam by the linear quadratic regulator (LQR). First of all, the state function of the control system is built for this tracking system; second, the control law is deduced according to the discretized state function; lastly, the stability of the control method is proved by the Lyapunov theory. The experimental results demonstrate that the Hue, Saturation, Value feature-extracting method is robust and is qualified to be used for localization in the laser beam tracking control. It is verified through experiments that the LQR method is of better performance than the conventional Proportional Derivative control in the aspect of converge time, lateral error control, and distance error control.

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