Linear Quadratic Regulator Design for Position Control of an Inverted Pendulum by Grey Wolf Optimizer

The inverted pendulum system (IPS) is considered the milestone of many robotic-based industries. In this paper, a new variant of variable structure adaptive fuzzy (VSAF) is used with new reduced linear quadratic regulator (RLQR) and feedforward gain for enhancing the stability of IPS. The optimal determining of VSAF parameters as well as Q and R matrices of RLQR are obtained by using a modified grey wolf optimizer with adaptive constants property via particle swarm optimization technique (GWO/PSO-AC). A comparison between the hybrid GWO/PSO-AC and classical GWO/PSO based on multi-objective function is provided to justify the superiority of the proposed technique. The IPS equipped with the hybrid GWO/PSO-AC-based controllers has minimum settling time, rise time, undershoot, and overshoot results for the two system outputs (cart position and pendulum angle). The system is subjected to robustness tests to ensure that the system can cope with small as well as significant disturbances.

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Proportional Double Derivative Linear Quadratic Regulator Controller Using Improvised Grey Wolf Optimization Technique to Control Quadcopter

Applied Sciences ◽

10.3390/app11062699 ◽

2021 ◽

Vol 11 (6) ◽

pp. 2699

Author(s):

Mohamad Norherman Shauqee ◽

Parvathy Rajendran ◽

Nurulasikin Mohd Suhadis

Keyword(s):

Optimization Technique ◽

Linear Quadratic Regulator ◽

Lower Percentage ◽

Grey Wolf Optimizer ◽

Grey Wolf ◽

Linear Quadratic ◽

Yaw Control ◽

Hybrid Controller ◽

Lqr Controller ◽

Optimal Values

A hybrid proportional double derivative and linear quadratic regulator (PD2-LQR) controller is designed for altitude (z) and attitude (roll, pitch, and yaw) control of a quadrotor vehicle. The derivation of a mathematical model of the quadrotor is formulated based on the Newton–Euler approach. An appropriate controller’s parameter must be obtained to obtain a superior control performance. Therefore, we exploit the advantages of the nature-inspired optimization algorithm called Grey Wolf Optimizer (GWO) to search for those optimal values. Hence, an improved version of GWO called IGWO is proposed and used instead of the original one. A comparative study with the conventional controllers, namely proportional derivative (PD), proportional integral derivative (PID), linear quadratic regulator (LQR), proportional linear quadratic regulator (P-LQR), proportional derivative and linear quadratic regulator (PD-LQR), PD2-LQR, and original GWO-based PD2-LQR, was undertaken to show the effectiveness of the proposed approach. An investigation of 20 different quadcopter models using the proposed hybrid controller is presented. Simulation results prove that the IGWO-based PD2-LQR controller can better track the desired reference input with shorter rise time and settling time, lower percentage overshoot, and minimal steady-state error and root mean square error (RMSE).

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Optimal Design of Hybrid Optimization Technique for Balancing Inverted Pendulum System

WSEAS TRANSACTIONS ON SYSTEMS ◽

10.37394/23202.2020.19.19 ◽

2020 ◽

Vol 19 ◽

Keyword(s):

Inverted Pendulum ◽

Optimization Technique ◽

Research Work ◽

Linear Quadratic Regulator ◽

Optimization Techniques ◽

Grey Wolf Optimizer ◽

Linear Quadratic ◽

Pendulum System ◽

Inverted Pendulum System ◽

New Variant

Inverted Pendulum system is one of the most exciting problems in control theory. In this research work, a new variant of Grey Wolf optimizer (GWO) via Particle Swarm Optimization (PSO) based on Adaptive Constants (AC) is proposed. The proposed technique (GWO/PSO-AC) is tested via twenty-three benchmark functions and compared to GWO based on PSO without adaptive constants (GWO/PSO). The suggested technique shows superiority in determining the optimal solutions for the well-established benchmark test functions with high computing performance compared to alternative techniques. The proposed GWO/PSO-AC technique, is employed to tune the parameters of the Variable Structure Adaptive Fuzzy (VSAF) controller in addition to the Reduced Linear Quadratic Regulator (RLQR) suggested by the authors. Both controllers are used to stabilize the cart position and to swing up the pendulum angle. The RLQR has an advantage over regular LQR, which is, the numberof the required parameters to obtain the required LQR gains is reduced. The proposed technique is compared with two optimization techniques. The proposed technique achieves high performance for both the cart position and the pendulum angle. The attained results are very promising.

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Neural Network Based Contact Force Control Algorithm for Walking Robots

Sensors ◽

10.3390/s21010287 ◽

2021 ◽

Vol 21 (1) ◽

pp. 287

Author(s):

Byeongjin Kim ◽

Soohyun Kim

Keyword(s):

Neural Network ◽

Contact Force ◽

Force Control ◽

Control Algorithm ◽

Position Control ◽

Linear Quadratic Regulator ◽

Walking Robots ◽

Test Model ◽

Linear Quadratic ◽

Contact Force Control

Walking algorithms using push-off improve moving efficiency and disturbance rejection performance. However, the algorithm based on classical contact force control requires an exact model or a Force/Torque sensor. This paper proposes a novel contact force control algorithm based on neural networks. The proposed model is adapted to a linear quadratic regulator for position control and balance. The results demonstrate that this neural network-based model can accurately generate force and effectively reduce errors without requiring a sensor. The effectiveness of the algorithm is assessed with the realistic test model. Compared to the Jacobian-based calculation, our algorithm significantly improves the accuracy of the force control. One step simulation was used to analyze the robustness of the algorithm. In summary, this walking control algorithm generates a push-off force with precision and enables it to reject disturbance rapidly.

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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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Comparison of Control Methods for Two-Link Planar Flexible Manipulator

Volume 6: 13th International Conference on Multibody Systems, Nonlinear Dynamics, and Control ◽

10.1115/detc2017-67937 ◽

2017 ◽

Author(s):

Joseph Bowkett ◽

Rudranarayan Mukherjee

Keyword(s):

Position Control ◽

Linear Quadratic Regulator ◽

Flexible Manipulator ◽

Linear Quadratic ◽

Large Space ◽

Loop Control ◽

Command Shaping ◽

Aerospace Applications ◽

Control Command ◽

Low Stiffness

While the majority of terrestrial multi-link manipulators can be considered in a purely kinematic sense due to their high stiffness, the launch mass restrictions of aerospace applications such as in-orbit assembly of large space structures result in low stiffness links being employed, meaning dynamics can no longer be ignored. This paper seeks to investigate the suitability of several different open and closed loop control techniques for application to the problem of end effector position control with minimal vibration for a low stiffness space based manipulator. Simulations of a representative planar problem with two flexible links are used to measure performance and sensitivity to parameter variation of: model predictive control, command shaping, and command shaping with linear quadratic regulator (LQR) feedback. An experimental testbed is then used to validate simulation results for the recommended command shaped controller.

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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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Iterative Linear Quadratic Regulator (ILQR) Controller for Trolley Position Control of Quanser 3DOF Crane

Indian Journal of Science and Technology ◽

10.17485/ijst/2015/v8i16/75369 ◽

2015 ◽

Vol 8 (16) ◽

Cited By ~ 2

Author(s):

Muhammad Faisal ◽

Mohsin Jamil ◽

Qasim Awais ◽

Usman Rashid ◽

Muhammad Sami Syed Omer Gilani ◽

...

Keyword(s):

Position Control ◽

Linear Quadratic Regulator ◽

Linear Quadratic

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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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