scholarly journals Critical parameters for the robust stabilization of the inverted pendulum with reaction delay: State feedback versus predictor feedback

2021 ◽  
Author(s):  
Balazs A. Kovacs ◽  
Tamas Insperger
Keyword(s):  
State Feedback ◽  
Inverted Pendulum ◽  
Robust Stabilization ◽  
Critical Parameters

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.

Robust Stabilizing Controller Design for Inverted Pendulum System

2014 ◽  
Vol 71 (1) ◽  
Author(s):  
Hazem I. Ali
Keyword(s):  
Steady State ◽  
Time Domain ◽  
State Feedback ◽  
Inverted Pendulum ◽  
Controller Design ◽  
H Infinity ◽  
Pendulum System ◽  
Stabilizing Controller ◽  
Inverted Pendulum System ◽  
System Uncertainties

In this paper the design of robust stabilizing state feedback controller for inverted pendulum system is presented. The Ant Colony Optimization (ACO) method is used to tune the state feedback gains subject to different proposed cost functions comprise of H-infinity constraints and time domain specifications. The steady state and dynamic characteristics of the proposed controller are investigated by simulations and experiments. The results show the effectiveness of the proposed controller which offers a satisfactory robustness and a desirable time response specifications. Finally, the robustness of the controller is tested in the presence of system uncertainties and disturbance.

scholarly journals On finite-time robust stabilization via nonlinear state feedback

2018 ◽  
Vol 28 (16) ◽  
pp. 4951-4965 ◽  
Author(s):  
K. Zimenko ◽  
A. Polyakov ◽  
D. Efimov
Keyword(s):  
Finite Time ◽  
State Feedback ◽  
Robust Stabilization ◽  
Nonlinear State

scholarly journals Fuzzy Swing Up Control and Optimal State Feedback Stabilization for Self-Erecting Inverted Pendulum

IEEE Access ◽  
2020 ◽  
Vol 8 ◽  
pp. 6496-6504 ◽  
Author(s):  
Erwin Susanto ◽  
Agung Surya Wibowo ◽  
Elvandry Ghiffary Rachman
Keyword(s):  
State Feedback ◽  
Inverted Pendulum ◽  
Feedback Stabilization ◽  
Optimal State ◽  
Optimal State Feedback

Robust H∞ Control and Stabilization of Uncertain Switched Linear Systems: A Multiple Lyapunov Functions Approach

2005 ◽  
Vol 128 (3) ◽  
pp. 696-700 ◽  
Author(s):  
Zhijian Ji ◽  
Xiaoxia Guo ◽  
Long Wang ◽  
Guangming Xie
Keyword(s):  
Linear Systems ◽  
Lyapunov Functions ◽  
State Feedback ◽  
Robust Stabilization ◽  
Disturbance Attenuation ◽  
Control Synthesis ◽  
Linear Matrix ◽  
Multiple Lyapunov Functions ◽  
Switched Linear Systems ◽  
Switched State Feedback

This paper addresses robust H∞ control and stabilization of switched linear systems with norm-bounded time-varying uncertainties. First, based on multiple Lyapunov functions methodology, a sufficient condition is derived for robust stabilization with a prescribed disturbance attenuation level γ only by employing state-dependent switching rules. Then the robust H∞ control synthesis via switched state feedback is studied. It is shown that a switched state-feedback controller can be designed to stabilize the switched systems with an H∞-norm bound if a matrix inequality based condition is feasible. This condition can be dealt with as linear matrix inequalities (LMIs) provided that the associated parameters are selected in advance. All the results presented can be regarded as an extension of some existing results for both switched and nonswitched systems.

scholarly journals All Stabilizing State Feedback Controller for Inverted Pendulum Mechanism

2018 ◽  
Vol 51 (4) ◽  
pp. 346-351 ◽  
Author(s):  
Rahman Bitirgen ◽  
Muhsin Hancer ◽  
Ismail Bayezit
Keyword(s):  
State Feedback ◽  
Inverted Pendulum ◽  
Feedback Controller ◽  
State Feedback Controller

scholarly journals T-S Fuzzy System Controller for Stabilizing the Double Inverted Pendulum

2020 ◽  
Vol 2020 ◽  
pp. 1-9
Author(s):  
Boutaina Elkinany ◽  
Mohammed Alfidi ◽  
Redouane Chaibi ◽  
Zakaria Chalh
Keyword(s):  
State Feedback ◽  
Inverted Pendulum ◽  
Fuzzy Controller ◽  
Pendulum System ◽  
Great Ability ◽  
Control Approach ◽  
Feedback Model ◽  
Inverted Pendulum System ◽  
System Controller ◽  
Fuzzy State

This article provides a representation of the double inverted pendulum system that is shaped and regulated in response to torque application at the top rather than the bottom of the pendulum, given that most researchers have controlled the double inverted pendulum based on the lower part or the base. To achieve this objective, we designed a dynamic Lagrangian conceptualization of the double inverted pendulum and a state feedback representation based on the simple convex polytypic transformation. Finally, we used the fuzzy state feedback approach to linearize the mathematical nonlinear model and to develop a fuzzy controller H ∞ , given its great ability to simplify nonlinear systems in order to reduce the error rate and to increase precision. In our virtual conceptualization of the inverted pendulum, we used MATLAB software to simulate the movement of the system before applying a command on the upper part of the system to check its stability. Concerning the nonlinearities of the system, we have found a state feedback fuzzy control approach. Overall, the simulation results have shown that the fuzzy state feedback model is very efficient and flexible as it can be modified in different positions.

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