Numeric Approach on Optimal Control for the Path Following System in Autonomous Vehicle

2019 ◽  
Author(s):  
Huyao Wu ◽  
Bin Ran
Keyword(s):  
Optimal Control ◽  
Control Strategies ◽  
Autonomous Vehicle ◽  
Path Following ◽  
Linear Quadratic Regulator ◽  
State Feedback Control ◽  
Linear Quadratic ◽  
The Road ◽  
Lqr Controller ◽  
Dynamic Errors

Abstract In this paper, the control strategies for Path Following System (PFS) in autonomous vehicle, which lets vehicle stay in the center of its lane is discussed, we will create a plant mechanical, mathematical and error dynamics model for the study of PFS, which is stabilized by the state-feedback control law, also considers the output where the sensor is made. We apply mainly an optimal control or configure a Linear-quadratic Regulator (LQR) for state space systems and compare it to that based on the Pole Assignment (PA). Combined with a typical operating scenario of the road, we mainly consider static and dynamic errors in the moving process, and how intensely the error fluctuates and how errors are related to the next time. Figures and data show that the LQR controller successfully adjusts and gives appropriate input to let the vehicle approach to centerline, errors and the steering angle required to negotiate a curved road are presented and analyzed, finally relevant conclusions are drawn.

scholarly journals FULL CAR ACTIVE DAMPING SYSTEM FOR VIBRATION CONTROL

2020 ◽  
Vol 6 (4) ◽  
pp. 1-17
Author(s):  
G. Yakubu ◽  
G. Sani ◽  
S. B. Abdulkadir ◽  
A. A.Jimoh ◽  
M. Francis
Keyword(s):  
Mathematical Model ◽  
Linear Quadratic Regulator ◽  
Active Damping ◽  
Settling Time ◽  
Linear Quadratic ◽  
Body Acceleration ◽  
The Road ◽  
Road Profile ◽  
Lqr Controller ◽  
Mass Displacement

Full car passive and active damping system mathematical model was developed. Computer simulation using MATLAB was performed and analyzed. Two different road profile were used to check the performance of the passive and active damping using Linear Quadratic Regulator controller (LQR)Road profile 1 has three bumps with amplitude of 0.05m, 0.025 m and 0.05 m. Road profile 2 has a bump with amplitude of 0.05 m and a hole of -0.025 m. For all the road profiles, there were 100% amplitude reduction in Wheel displacement, Wheel deflection, Suspension travel and body displacement, and 97.5% amplitude reduction in body acceleration for active damping with LQR controller as compared to the road profile and 54.0% amplitude reduction in body acceleration as compared to the passive damping system. For the two road profiles, the settling time for all the observed parameters was less than two (2) seconds. The present work gave faster settling time for mass displacement, body acceleration and wheel displacement.

scholarly journals Performance Comparisons Of Hybrid Fuzzy-LQR And Hybrid PID-LQR Controllers On Stabilizing Double Rotary Inverted Pendulum

2020 ◽  
Vol 1 (2) ◽  
pp. 71-80
Author(s):  
Jamilu Kamilu Adamu ◽  
Mukhtar Fatihu Hamza ◽  
Abdulbasid Ismail Isa
Keyword(s):  
Inverted Pendulum ◽  
Fuzzy Logic Controller ◽  
Linear Quadratic Regulator ◽  
State Feedback Control ◽  
Linear Quadratic ◽  
Trajectory Tracking Control ◽  
Stabilization Control ◽  
Full State Feedback ◽  
Lqr Controller ◽  
Rotary Inverted Pendulum

Double Rotary Inverted Pendulum (DRIP) is a member of the mechanical under-actuated system which is unstable and nonlinear. The DRIP has been widely used for testing different control algorithms in both simulation and experiments. The DRIP control objectives include Stabilization control, Swing-up control and trajectory tracking control. In this research, we present the design of an intelligent controller called “hybrid Fuzzy-LQR controller” for the DRIP system. Fuzzy logic controller (FLC) is combined with a Linear Quadratic Regulator (LQR). The LQR is included to improve the performance based on full state feedback control. The FLC is used to accommodate nonlinearity based on its IF-THEN rules. The proposed controller was compared with the Hybrid PID-LQR controller. Simulation results indicate that the proposed hybrid Fuzzy-LQR controllers demonstrate a better performance compared with the hybrid PID-LQR controller especially in the presence of disturbances.

Active Command-Steering Control of Tractor and Three Full Trailers for Tractor-Track Following

2006 ◽  
Author(s):  
Krishna Rangavajhula ◽  
H.-S. Jacob Tsao
Keyword(s):  
High Speed ◽  
Control Strategies ◽  
Linear Quadratic Regulator ◽  
Cost Effective ◽  
Steering Control ◽  
Linear Quadratic ◽  
Amplification Ratio ◽  
High Speeds ◽  
Lqr Controller ◽  
Optimal Linear

A key source of safety and infrastructure issues for operations of longer combination vehicles (LCVs) is off-tracking, which has been used to refer to the general phenomenon that the rear wheels of a truck do not follow the track of the front wheels and wander off the travel lane. In this paper, we examine the effectiveness of command-steering in reducing off-tracking during a 90-degree turn at low and high speeds in an articulated system with a tractor and three full trailers. In command steering, rear front axles of the trailers are steered proportionately to the articulation angle between the tractor and trailing units. We then consider several control strategies to minimize off-tracking and rearward amplification of this system. A minimum rearward amplification ratio (RWA), as a surrogate for minimum off tracking, has been used as the control criterion for medium to high speeds to arrive at an optimal Linear Quadratic Regulator (LQR) controller. As for low speeds, the maximum radial offset between the tractor and trailer 3 is minimized in the design of the controller. Robustness of the optimal controller with respect to tyre-parameter perturbations is then examined. Based on the simulation results, we find that, active command steering is very effective in reducing off tracking at low- as well as high-speed 90-degree turns. To achieve acceptable levels of RWA and off tracking, at least two of the three trailers must be actively command-steered. Among the three two-trailer-steering possibilities, actively steering trailers 1 and 2 is most cost-effective and results in the lowest RWA for medium- to high- speeds (at which RWA is important), and off-tracking is practically eliminated for all speed regimes considered.

scholarly journals A Hyperbolic Tangent Adaptive PID + LQR Control Applied to a Step-Down Converter Using Poles Placement Design Implemented in FPGA

2013 ◽  
Vol 2013 ◽  
pp. 1-8 ◽  
Author(s):  
Marcelo Dias Pedroso ◽  
Claudinor Bitencourt Nascimento ◽  
Angelo Marcelo Tusset ◽  
Maurício dos Santos Kaster
Keyword(s):  
Control Strategies ◽  
Linear Quadratic Regulator ◽  
Open Loop ◽  
Linear Quadratic ◽  
Hyperbolic Tangent ◽  
Dsp Builder ◽  
Loop Transfer Function ◽  
Lqr Controller ◽  
Step Down ◽  
Poles Placement

This work presents an adaptive control that integrates two linear control strategies applied to a step-down converter: Proportional Integral Derivative (PID) and Linear Quadratic Regulator (LQR) controls. Considering the converter open loop transfer function and using the poles placement technique, the designs of the two controllers are set so that the operating point of the closed loop system presents the same natural frequency. With poles placement design, the overshoot problems of the LQR controller are avoided. To achieve the best performance of each controller, a hyperbolic tangent weight function is applied. The limits of the hyperbolic tangent function are defined based on the system error range. Simulation results using the Altera DSP Builder software in a MATLAB/SIMULINK environment of the proposed control schemes are presented.

Robust stabilization control of a spatial inverted pendulum using integral sliding mode controller

2020 ◽  
Vol 0 (0) ◽  
Author(s):  
Ishan Chawla ◽  
Vikram Chopra ◽  
Ashish Singla
Keyword(s):  
Inverted Pendulum ◽  
Sliding Mode ◽  
Robust Stabilization ◽  
Linear Quadratic Regulator ◽  
Humanoid Robots ◽  
Sliding Mode Controller ◽  
Linear Quadratic ◽  
Integral Sliding Mode ◽  
Wide Range ◽  
Lqr Controller

AbstractFrom the last few decades, inverted pendulums have become a benchmark problem in dynamics and control theory. Due to their inherit nature of nonlinearity, instability and underactuation, these are widely used to verify and implement emerging control techniques. Moreover, the dynamics of inverted pendulum systems resemble many real-world systems such as segways, humanoid robots etc. In the literature, a wide range of controllers had been tested on this problem, out of which, the most robust being the sliding mode controller while the most optimal being the linear quadratic regulator (LQR) controller. The former has a problem of non-robust reachability phase while the later lacks the property of robustness. To address these issues in both the controllers, this paper presents the novel implementation of integral sliding mode controller (ISMC) for stabilization of a spatial inverted pendulum (SIP), also known as an x-y-z inverted pendulum. The structure has three control inputs and five controlled outputs. Mathematical modeling of the system is done using Euler Lagrange approach. ISMC has an advantage of eliminating non-robust reachability phase along with enhancing the robustness of the nominal controller (LQR Controller). To validate the robustness of ISMC to matched uncertainties, an input disturbance is added to the nonlinear model of the system. Simulation results on two different case studies demonstrate that the proposed controller is more robust as compared to conventional LQR controller. Furthermore, the problem of chattering in the controller is dealt by smoothening the controller inputs to the system with insignificant loss in robustness.

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 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.

Real-Time Control of a Rotary Inverted Pendulum using Robust LQR-based ANFIS Controller

2018 ◽  
Vol 19 (3-4) ◽  
pp. 379-389 ◽  
Author(s):  
Ishan Chawla ◽  
Ashish Singla
Keyword(s):  
Fuzzy Inference System ◽  
Inverted Pendulum ◽  
Fuzzy Inference ◽  
Sliding Mode ◽  
Linear Quadratic Regulator ◽  
Linear Quadratic ◽  
Inference System ◽  
Wide Range ◽  
Lqr Controller ◽  
Rotary Inverted Pendulum

AbstractFrom the last five decades, inverted pendulum (IP) has been considered as a benchmark problem in the control literature due to its inherit nature of instability, non-linearity and underactuation. Its applicability in wide range of practical systems, demands the need of a robust controller. It is found in the literature that wide range of controllers had been tested on this problem, out of which the most robust being sliding mode controller while the most optimal being linear quadratic regulator (LQR) controller. The former has a problem of discontinuity and chattering, while the latter lacks the property of robustness. To address the robustness issue in LQR controller, this paper proposes a novel robust LQR-based adaptive neural based fuzzy inference system controller, which is a hybrid of LQR and fuzzy inference system. The proposed controller is designed and implemented on rotary inverted pendulum. Further, to validate the robustness of proposed controller to parametric uncertainties, pendulum mass is varied. Simulation and experimental results show that as compared to LQR controller, the proposed controller is robust to variations in pendulum mass and has shown satisfactory performance.

Harmonic Current Distortion Using the Linear Quadratic Regulator for a Grid-Connected Photovoltaic System

2021 ◽  
Vol 29 (1) ◽  
Author(s):  
Oscar Andrew Zongo ◽  
Anant Oonsivilai
Keyword(s):  
Control Strategies ◽  
Harmonic Distortion ◽  
Linear Quadratic Regulator ◽  
Photovoltaic System ◽  
Voltage Source ◽  
Linear Quadratic ◽  
Grid Current ◽  
Harmonic Currents ◽  
Low Pass ◽  
Low Pass Filters

This paper presents a comparison between a proportional-integral controller, low pass filters, and the linear quadratic regulator in dealing with the task of eliminating harmonic currents in the grid-connected photovoltaic system. A brief review of the existing methods applied to mitigate harmonic currents is presented. The Perturb & Observe technique was employed for maximum power point tracking. The PI control, low pass filters, and the linear quadratic regulator are discussed in detail in terms of their control strategies. The grid current was analyzed in the system with all three of the controllers applied to control the voltage source inverter of the solar photovoltaic system connected to the grid through an L filter and LCL filter and simulated in MATLAB/SIMULINK. The simulation results obtained have proven the robustness of the linear quadratic regulator over other methods. The technique lowers the grid current total harmonic distortion from 7.85% to 2.13%.

scholarly journals Vehicle Optimal Control Design to Meet the 1.5 °C Target: A Control Design Framework for Vehicle Subsystems

Energies ◽  
2019 ◽  
Vol 12 (16) ◽  
pp. 3170
Author(s):  
Hu ◽  
Chen ◽  
Ding ◽  
Gu
Keyword(s):  
Optimal Control ◽  
Energy Savings ◽  
Control Strategies ◽  
Control Design ◽  
Paris Agreement ◽  
Design Framework ◽  
Control Effect ◽  
Linear Quadratic ◽  
Co2 Intensity ◽  
Light Duty Vehicle

Current studies have achieved energy savings of vehicle subsystems through various control strategies, but these control strategies lack a benchmark to measure whether these energy savings are sufficient. This work proposes a control design framework that uses the 1.5 °C target in the Paris Agreement as a benchmark to measure the adequacy of energy savings of vehicle subsystems. This control design framework involves two points. One is the conversion of the 1.5 °C target into a constraint on the energy consumption of a vehicle subsystem. The other is the optimal control design of the vehicle subsystem under this constraint. To describe the specific application of this control design framework, we conduct a case study concerning the control design of active suspension in a battery electric light-duty vehicle. By comparison with a widely used linear quadratic regulator (LQR) method, we find that this control design framework can both ensure the performance comparable to the LQR method and help to meet the 1.5 °C target in the Paris Climate Agreement. In addition, a sensitivity analysis shows that the control effect is hardly changed by battery electric vehicle market share and electricity CO2 intensity. This work might provide insight on ways that the automotive industry could contribute to the Paris Agreement.

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