Optimal Fractional Order Proportional—Integral—Differential Controller for Inverted Pendulum with Reduced Order Linear Quadratic Regulator

This paper focuses on a comparative study of a reduced order linear quadratic regulator control (ROLQR) and conventional variable frequency hysteresis controller (HC) for power factor correction, and their performances are compared. A prototype of front-end AC–DC converter followed by DC–DC Cuk converter controlled by a dSPACE signal processor was set up for 60 watts. Experimental results are presented to validate the simulation results. Simulation and experimental results reveal that ROLQR control can achieve good output voltage regulation and also provide improved robustness in shaping the input current in the presence of load variations when compared to conventional HC.

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

International Journal of Nonlinear Sciences and Numerical Simulation ◽

10.1515/ijnsns-2018-0029 ◽

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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Stabilizing and Swinging-Up the Inverted Pendulum Using PI and PID Controllers Based on Reduced Linear Quadratic Regulator Tuned by PSO

International Journal of System Dynamics Applications ◽

10.4018/ijsda.2015100104 ◽

2015 ◽

Vol 4 (4) ◽

pp. 52-69 ◽

Cited By ~ 17

Author(s):

M. E. Mousa ◽

M. A. Ebrahim ◽

M. A. Moustafa Hassan

Keyword(s):

Pid Controller ◽

Inverted Pendulum ◽

Research Work ◽

Linear Quadratic Regulator ◽

Nonlinear Problems ◽

Pid Controllers ◽

Linear Quadratic ◽

Swarm Optimization ◽

Feed Forward ◽

Forward Gain

The inherited instabilities in the Inverted Pendulum (IP) system make it one of the most difficult nonlinear problems in the control theory. In this research work, Proportional –Integral and Derivative (PID) Controller with a feed forward gain is used with Reduced Linear Quadratic Regulator (RLQR) for stabilizing the Cart Position and Swinging-up the Pendulum angle. Tuning the Controllers' gains is achieved by using Particle Swarm Optimization (PSO) Technique. Obtaining the combined PID controllers' gains with a feed forward gain and RLQR is a multi-dimensions control problem. The Proposed Controllers give minimum Settling Time, Rise Time, Undershoot and Over shoot for both the Cart Position and the Pendulum angle. A disturbance with different amplitudes is applied to the system, and the results showed the robustness of the systems based on the tuned controllers. The overall results are promising.

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Design of hybrid sliding mode controller based on fireworks algorithm for nonlinear inverted pendulum systems

Advances in Mechanical Engineering ◽

10.1177/1687814016684273 ◽

2017 ◽

Vol 9 (1) ◽

pp. 168781401668427 ◽

Cited By ~ 4

Author(s):

Te-Jen Su ◽

Shih-Ming Wang ◽

Tsung-Ying Li ◽

Sung-Tsun Shih ◽

Van-Manh Hoang

Keyword(s):

Inverted Pendulum ◽

Sliding Mode ◽

Linear Quadratic Regulator ◽

Sliding Mode Controller ◽

Proportional Integral Derivative ◽

Linear Quadratic ◽

Pendulum System ◽

Fireworks Algorithm ◽

Simulation Process ◽

Inverted Pendulum System

The objective of this article is to optimize parameters of a hybrid sliding mode controller based on fireworks algorithm for a nonlinear inverted pendulum system. The proposed controller is a combination of two modified types of the classical sliding mode controller, namely, baseline sliding mode controller and fast output sampling discrete sliding mode controller. The simulation process is carried out with MATLAB/Simulink. The results are compared with a published hybrid method using proportional–integral–derivative and linear quadratic regulator controllers. The simulation results show a better performance of the proposed controller.

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DYNAMICS BASED CONTROL OF A SKID STEERING MOBILE ROBOT

Jurnal Ilmu Komputer dan Informasi ◽

10.21609/jiki.v9i2.381 ◽

2016 ◽

Vol 9 (2) ◽

pp. 70 ◽

Cited By ~ 1

Author(s):

Osama Elshazly ◽

Hossam Abbas ◽

Zakarya Zyada

Keyword(s):

Mobile Robot ◽

Inverse Dynamics ◽

Linear Quadratic Regulator ◽

Nonlinear Controller ◽

Linear Quadratic ◽

Reduced Order ◽

Lqr Control ◽

Control Schemes ◽

Skid Steering ◽

Drive Model

In this paper, development of a reduced order, augmented dynamics-drive model that combines both the dynamics and drive subsystems of the skid steering mobile robot (SSMR) is presented. A Linear Quadratic Regulator (LQR) control algorithm with feed-forward compensation of the disturbances part included in the reduced order augmented dynamics-drive model is designed. The proposed controller has many advantages such as its simplicity in terms of design and implementation in comparison with complex nonlinear control schemes that are usually designed for this system. Moreover, the good performance is also provided by the controller for the SSMR comparable with a nonlinear controller based on the inverse dynamics which depends on the availability of an accurate model describing the system. Simulation results illustrate the effectiveness and enhancement provided by the proposed controller.

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

International Journal of Nonlinear Sciences and Numerical Simulation ◽

10.1515/ijnsns-2017-0139 ◽

2018 ◽

Vol 19 (3-4) ◽

pp. 379-389 ◽

Cited By ~ 3

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.

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