LMI-based Multiobjective Integral Sliding Mode Control for Rotary Inverted Pendulum System Under Load Variations

2015 ◽  
Vol 73 (6) ◽  
Author(s):  
Fairus, M. A. ◽  
Mohamed, Z. ◽  
Ahmad, M. N. ◽  
Loi, W. S.
Keyword(s):  
Nonlinear System ◽  
Inverted Pendulum ◽  
Sliding Mode ◽  
Space Representation ◽  
Linear Matrix ◽  
Pendulum System ◽  
Integral Sliding Mode ◽  
State Space Representation ◽  
Inverted Pendulum System ◽  
Rotary Inverted Pendulum

This paper presents a multiobjective integral sliding mode controller (ISMC) for a rotary inverted pendulum system under the influence of varying load. Firstly, the nonlinear system is approximated to facilitate the desired control design via extended linearization and deterministic approach. By using both of these techniques, the nonlinear system is formulated into a nonlinear state-space representation where the uncertainties are retained in the model. Next, the design objectives are formulated into linear matrix inequalities (LMI) which are then solved efficiently through convex optimization algorithms. With proper selection variables, numbers of the decision variables for LMIs are reduced. Hence, it will reduce the numerical burden and believes the calculated values more viable in practice. Finally, simulation works are conducted and comparison is made between the proposed controller, such as normal ISMC and LQR. The simulation results illustrate the effectiveness of the proposed controller and the performance is evaluated through integral of absolute-value error (IAE) performance index. 

scholarly journals Multibody Modeling and Balance Control of a Reaction Wheel Inverted Pendulum Using LQR Controller

2021 ◽  
Vol 1 (1) ◽  
pp. 84-89
Author(s):  
Ümit Önen ◽  
Abdullah Çakan
Keyword(s):  
State Space ◽  
Inverted Pendulum ◽  
Balance Control ◽  
Space Representation ◽  
Reaction Wheel ◽  
Linear Quadratic ◽  
Pendulum System ◽  
State Space Representation ◽  
Inverted Pendulum System ◽  
Lqr Controller

In this study, modeling and LQR control of a reaction wheel inverted pendulum system is described. The reaction wheel inverted pendulum model is created by using a 3D CAD platform and exported to Simscape Multibody. The multibody model is linearized to derive a state-space representation. A LQR (Linear-quadratic regulator) controller is designed and applied for balance control of the pendulum. The results show that deriving a state-space representation from multibody is an easy and effective way to model dynamic systems and balance control of the reaction wheel inverted pendulum is successfully achieved by LQR controller. Results are given in the form of graphics.

scholarly journals PSO-Based Integral Sliding Mode Controller for Optimal Swing-Up and Stabilization of the Cart-Inverted Pendulum System

2021 ◽  
Vol 18 (2) ◽  
pp. 88-97
Author(s):  
T.J. Shima ◽  
H.A. Bashir
Keyword(s):  
Control System ◽  
Inverted Pendulum ◽  
Sliding Mode ◽  
Pso Algorithm ◽  
Track Length ◽  
Sliding Mode Controller ◽  
Pendulum System ◽  
Integral Sliding Mode ◽  
Inverted Pendulum System ◽  
Optimal Values

An integral sliding mode controller (ISMC) which employs particle swarm optimization (PSO) algorithm to search for optimal values of the parameters of the integral sliding manifold as well as the gains of the controller is proposed in this work. We considered the swing-up and stabilization of the cart-inverted pendulum system which is assumed to be affected by uncertainties. First, we determined the swing-up and stabilization conditions of the control system by using the internal dynamics of the cart-inverted pendulum system and sliding mode dynamics. A PSO algorithm is then used to search for the optimal values of the ISMC design parameters that satisfy the stabilization condition with the aim of improving the transient performance of the control system. To mitigate the chattering phenomenon, a saturation function of the integral sliding variable was used in the discontinuous control law. Simulation results on swing-up and stabilization of the cart-inverted pendulum system revealed improvement in transient behaviour by reducing settling time (by 52.61%), overshoots (by 45.56%) and required track length for cart movement (by 68.34%).

Robust Adaptive Super-twisting Sliding Mode Stability Control for Underactuated Rotary Inverted Pendulum with Experimental Validation

2021 ◽  
Author(s):  
Omid Mofid ◽  
Khalid A Alattas ◽  
Saleh Mobayen
Keyword(s):  
Inverted Pendulum ◽  
Control Method ◽  
Sliding Mode ◽  
Lyapunov Stability Theory ◽  
Stability Control ◽  
Control Technique ◽  
Control Procedure ◽  
Pendulum System ◽  
Inverted Pendulum System ◽  
Rotary Inverted Pendulum

Abstract In this paper, an adaptive proportional-integral-derivative (PID) sliding mode control method combined with super-twisting algorithm is designed for the stabilization control of rotary inverted pendulum system in the appearance of exterior perturbation. The state-space model of rotary inverted pendulum in the presence of exterior disturbance is obtained. Then, the super-twisting PID sliding mode controller is designed for finite time stability control of this underactuated control system. The upper bounds of perturbation are presumed to be unknown; accordingly, the adaptive control procedure is taken to approximate the uncertain bound of the external disturbances. The stability control of rotary inverted pendulum system is proved by means of the Lyapunov stability theory. In order to validate accuracy and efficiency of the recommended control technique, some simulation outcomes are prepared and compared with other existing method. Moreover, experimental results are implemented to show the success of the proposed method.

Underactuated rotary inverted pendulum control using robust generalized dynamic inversion

2020 ◽  
Vol 26 (23-24) ◽  
pp. 2210-2220 ◽  
Author(s):  
Ibrahim M Mehedi ◽  
Uzair Ansari ◽  
Abdulrahman H Bajodah ◽  
Ubaid M AL-Saggaf ◽  
Belkacem Kada ◽  
...  
Keyword(s):  
Inverted Pendulum ◽  
Sliding Mode ◽  
Switching Control ◽  
Tracking Performance ◽  
Dynamic Inversion ◽  
State Variables ◽  
Pendulum System ◽  
Inverted Pendulum System ◽  
Rotary Inverted Pendulum ◽  
Control Part

The article applies the robust generalized dynamic inversion control methodology to the problem of stabilizing upright equilibrium configuration of the under-actuated rotary inverted pendulum system while tracking rotary motion of the actuated arm. The proposed robust generalized dynamic inversion control law comprised equivalent and switching control parts. The equivalent control part works to enforce a virtual constraint dynamics of the controlled state variables by means of Moore–Penrose generalized inversion. The switching control part is of the sliding mode type, and it improves robustness against unmodeled system dynamics, parametric uncertainties, and external disturbances. The robust generalized dynamic inversion control design on the linearized model of the under-actuated rotary inverted pendulum is shown to guarantee semi-global asymptotically stable tracking performance. Numerous computer simulations and experiments are conducted on the Quanser rotary inverted pendulum system, revealing that the proposed algorithm has better convergence and tracking performance than conventional sliding mode and generalized dynamic inversion control strategies when both are applied separately.

Analysis and modeling of an inverted pendulum system

2021 ◽  
Author(s):  
Keyword(s):  
Mathematical Model ◽  
Nonlinear System ◽  
Inverted Pendulum ◽  
System Analysis ◽  
Dimensional System ◽  
Two Dimensional ◽  
System Operation ◽  
Pendulum System ◽  
Inverted Pendulum System ◽  
Two Dimensional System

A nonlinear system, which consists of an inverted pendulum mounted on a cart with an electric drive, is considered. A mathematical model is created, its analysis and modeling of the investigated two-dimensional system operation is carried out. Keywords mathematical model; inverted pendulum; system analysis; state space

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

2017 ◽  
Vol 9 (1) ◽  
pp. 168781401668427 ◽  
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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