scholarly journals Linear and Non-Linear Control Design of Skid Steer Mobile Robot on an Embedded

2018 ◽  
Vol 7 (3) ◽  
pp. 185
Author(s):  
Jharna Majumdar ◽  
Sudip C Gupta ◽  
B Prassanna Prasath
Keyword(s):  
Mobile Robot ◽  
Pid Controller ◽  
Control Design ◽  
Linear Quadratic Regulator ◽  
Performance Comparison ◽  
Linear Control ◽  
Proportional Integral Derivative ◽  
Linear Quadratic ◽  
Non Linear ◽  
Lqr Controller

A detailed approach for a linear Proportional-Integral-Derivative (PID) controller and a non-linear controller - Linear Quadratic Regulator (LQR) is discussed in this paper. By analyzing several mathematical designs for the Skid Steer Mobile Robot (SSMR), the controllers are implemented in an embedded microcontroller - Mbed LPC1768. To verify the controllers, MATLAB-Simulink is used for the simulation of both the controllers involving motors - Maxon RE40. This paper compares between PID and LQR controller along with the performance comparison between Homogenous and Non-Homogenous LQR controllers.

Design and Analysis of Linear Quadratic Regulator for a Non-Linear Positioning System

2015 ◽  
Vol 761 ◽  
pp. 227-232 ◽  
Author(s):  
Tang Teng Fong ◽  
Zamberi Jamaludin ◽  
Ahmad Yusairi Bani Hashim ◽  
Muhamad Arfauz A. Rahman
Keyword(s):  
Physical System ◽  
Inverted Pendulum ◽  
Linear Quadratic Regulator ◽  
Upright Position ◽  
System Model ◽  
Optimum Control ◽  
Control Vector ◽  
Linear Quadratic ◽  
Non Linear ◽  
Lqr Controller

The control of rotary inverted pendulum is a case of classical robust controller design of non-linear system applications. In the control system design, a precise system model is a pre-requisite for an enhanced and optimum control performance. This paper describes the dynamic system model of an inverted pendulum system. The mathematical model was derived, linearized at the upright equilibrium points and validated using non-linear least square frequency domain identification approach based on measured frequency response function of the physical system. Besides that, a linear quadratic regulator (LQR) controller was designed as the balancing controller for the pendulum. An extensive analysis was performed on the effect of the weighting parameter Q on the static time of arm, balance time of pendulum, oscillation, as well as, response of arm and pendulum, in order to determine the optimum state-feedback control vector, K. Furthermore, the optimum control vector was successfully applied and validated on the physical system to stabilize the pendulum in its upright position. In the experimental validation, the LQR controller was able to keep the pendulum in its upright position even in the presence of external disturbance forces.

scholarly journals Elevation, pitch and travel axis stabilization of 3DOF helicopter with hybrid control system by GA-LQR based PID controller

2020 ◽  
Vol 10 (2) ◽  
pp. 1868 ◽  
Author(s):  
Ibrahim K. Mohammed ◽  
Abdulla I. Abdulla
Keyword(s):  
Pid Controller ◽  
Hybrid Control ◽  
Research Work ◽  
Linear Quadratic Regulator ◽  
Optimization Method ◽  
Feedback Gain ◽  
Algorithm Optimization ◽  
Linear Quadratic ◽  
Control Approach ◽  
Lqr Controller

This research work presents an efficient hybrid control methodology through combining the traditional proportional-integral-derivative (PID) controller and linear quadratic regulator (LQR) optimal controlher. The proposed hybrid control approach is adopted to design three degree of freedom (3DOF) stabilizing system for helicopter. The gain parameters of the classic PID controller are determined using the elements of the LQR feedback gain matrix. The dynamic behaviour of the LQR based PID controller, is modeled and the formulated in state space form to enable utlizing state feedback controller technique. The performance of the proposed LQR based LQR controller is improved by using Genetic Algorithm optimization method which are adopted to obtain optimum values for LQR controller gain parameters. The LQR-PID hybrid controller is simulated using Matlab environment and its performance is evaluated based on rise time, settling time, overshoot and steady state error parameters to validate the proposed 3DOF helicopter balancing system. Based on GA tuning approach, the simulation results suggest that the hybrid LQR-PID controller can be effectively adopted to stabilize the 3DOF helicopter system.

Controlling an Underactuated Two-Wheeled Mobile Robot: A Constraint-Following Approach

2019 ◽  
Vol 141 (7) ◽  
Author(s):  
Hui Yin ◽  
Ye-Hwa Chen ◽  
Dejie Yu
Keyword(s):  
Mobile Robot ◽  
Degrees Of Freedom ◽  
Control Design ◽  
Nonholonomic Constraints ◽  
Linear Quadratic Regulator ◽  
Wheeled Mobile Robot ◽  
Linear Quadratic ◽  
Control Goal ◽  
Standard Linear ◽  
Following Error

Controlling underactuated systems is a challenging problem in control engineering. This paper presents a novel constraint-following approach for control design of an underactuated two-wheeled mobile robot (2 WMR), which has two degrees-of-freedom (DOF) to be controlled but only one actuator. The control goal is to drive the 2 WMR to follow a set of constraints, which may be holonomic or nonholonomic constraints. The constraint is considered in a more general form than the previous studies on constraint-following control (hence including a wider range of constraints). No auxiliary variables or pseudo variables are required for the control design. The proposed control only uses physical variables. We show that the proposed control is able to deal with both holonomic and nonholonomic constraints by forcing the constraint-following error to converge to zero, even if the system is not initially on the constraint manifold. Using this control design, we investigate two cases regarding different constraints on the 2 WMR motion, one for a holonomic constraint and the other for a nonholonomic constraint. Simulation results show that the proposed control is able to drive the 2 WMR to follow the constraints in both cases. Furthermore, the standard linear quadratic regulator (LQR) control is applied as a comparison in the simulations, which reflects the advantage of the proposed control.

scholarly journals Optimized LQR-PID Controller Using Squirrel Search Algorithm for Trajectory Tracking of a 6-DoF Parallel Manipulator

2021 ◽  
Author(s):  
Chandan Choubey ◽  
Jyoti Ohri
Keyword(s):  
Trajectory Tracking ◽  
Pid Controller ◽  
Parallel Manipulator ◽  
Search Algorithm ◽  
Linear Quadratic Regulator ◽  
Absolute Error ◽  
Minimal Cost ◽  
Proportional Integral Derivative ◽  
Linear Quadratic ◽  
Mean Velocity

Abstract In 6 Degree of Freedom (DOF) parallel manipulator, trajectory tracking is one of the main challenges. To obtain the desired trajectory, the DC motor needs to generate optimal torque. So to obtain optimal torque, an optimized Linear Quadratic Regulator-Proportional–Integral–Derivative (LQR-PID) controller is presented in this paper. For optimizing the Q, R and gain parameters of LQR-PID controller, Squirrel Search Algorithm (SSA) is presented. In this algorithm, minimal cost function of LQR-PID controller is considered as objective function. The SSA based LQR-PID controller leads the motor to generate optimal torque that helps to attain the desired trajectory of 6-DOF parallel manipulator. Results of the work depicts that the SSA based LQR-PID controller achieves the best mean velocity, sum square error (SSE), integral square error (ISE) and integral absolute error (IAE).

scholarly journals PID AND LQR CONTROLLERS APPLIED TO THE INVERSE DYNAMICS OF A 3-DOF MANIPULATOR

2021 ◽  
Vol 7 (7) ◽  
Author(s):  
Josias Guimarães Batista ◽  
Darielson Araújo de Souza ◽  
Laurinda Lúcia Nogueira dos Reis ◽  
Antônio Barbosa de Souza Júnior
Keyword(s):  
Pid Controller ◽  
Inverse Dynamics ◽  
Production Systems ◽  
Linear Quadratic Regulator ◽  
Pid Controllers ◽  
Proportional Integral Derivative ◽  
Dynamics Model ◽  
Linear Quadratic ◽  
Inverse Dynamic ◽  
Industrial Manipulator

The application in the industrial manipulator robots has grown over the years making production systems increasingly efficient. Within this context, the need for efficient controllers is required to perform the control of these manipulators. In this work the PID controller (Proportional-Integral-Derivative) and LQR (Linear Quadratic Regulator) is presented from the inverse dynamics model of a RPP (Rotational - Prismatic - Prismatic) cylindrical manipulator. The inverse dynamic model which is modeled on Simulink together with a cascaded PID controller is presented. The PID and LQR results are also presented for joint independent and joint dependent control, i.e a controlled PID is used for each joint, controlling the trajectories and speeds at the same time. This paper has as main contributions the development of the manipulator dynamics model and the design of the LQR and PID controllers applied to the inverse dynamics model, which makes the system simpler to control.

scholarly journals Optimal Controller and Controller Based on Differential Flatness in a Linear Guide System: A Performance Comparison of Indexes

2015 ◽  
Vol 2015 ◽  
pp. 1-10 ◽  
Author(s):  
Fabio Abel Gómez Becerra ◽  
Víctor Hugo Olivares Peregrino ◽  
Andrés Blanco Ortega ◽  
Jesús Linares Flores
Keyword(s):  
New Technologies ◽  
Linear Quadratic Regulator ◽  
Performance Comparison ◽  
Differential Flatness ◽  
Linear Quadratic ◽  
Linear Guide ◽  
Performance Indexes ◽  
Lqr Controller ◽  
Guide System ◽  
Linear Slide

The use of linear slide system has been augmented in recent times due to features granted to supplement electromechanical systems; new technologies have allowed the manufacture of these systems with low coefficients of friction and offer a variety of types of sliding. In this paper, we present a comparison between the performance indexes of two techniques of control applying optimal control LQR (Linear Quadratic Regulator) acronym for STIs in English and the technique of differential flatness controller. The use of linear slide bolt of potency takes into account the dynamics of the DC motor; the Euler-Lagrange formalism was used to establish the mathematical model of the slide. Cosimulation via the MATLAB/Simulink-ADAMS virtual prototype package, including realistic measurement disturbances, is used to compare the performance indexes between the LQR controller versus differential flatness controller for the position tracking of linear guide system.

Two-degree-of-freedom multi-input multi-output proportional–integral–derivative control design: Application to quadruple-tank system

2018 ◽  
Vol 233 (3) ◽  
pp. 303-319
Author(s):  
Jatin Kumar Pradhan ◽  
Arun Ghosh ◽  
Chandrashekhar Narayan Bhende
Keyword(s):  
State Feedback ◽  
Control Design ◽  
Linear Quadratic Regulator ◽  
Linear Matrix ◽  
Feedback Gain ◽  
Matrix Inequality ◽  
Proportional Integral Derivative ◽  
Linear Quadratic ◽  
Proportional Integral Derivative Controller ◽  
Proportional Integral

This article is concerned with designing a 2-degree-of-freedom multi-input multi-output proportional–integral–derivative controller to ensure linear quadratic regulator performance and H∞ performance using a non-iterative linear matrix inequality–based method. To design the controller, first, a relation between the state feedback gain and proportional–integral–derivative gain is obtained. As the gains of proportional–integral–derivative controller cannot, in general, be found out from this relation for arbitrary stabilizing state feedback gain, a suitable form of the matrices involved in linear matrix inequality–based state feedback design is then chosen to obtain the proportional–integral–derivative gains directly. The special structure of the above matrices allows one to design proportional–integral–derivative controller in non-iterative manner. As a result, multi-objective performances, such as linear quadratic regulator and H∞, can be achieved simultaneously without increasing the computational burden much. To enhance the reference-input-to-output characteristics, a feedforward gain is also introduced and designed to minimize certain closed-loop H∞ performance. The proposed control design method is applied for multi-input multi-output proportional–integral compensation of a laboratory-based quadruple-tank process. The performance of the compensation is studied through extensive simulations and experiments.

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.

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