Switching surface design via linear matrix inequality and Ackermann’s formula for a linearized inverted pendulum system

<span lang="EN-US">A new approach based on linear matrix inequality (LMI) technique for stabilizing the inverted pendulum is developed in this article. The unknown states are estimated as well as the system is stabilized simultaneously by employing the observer-based controller. In addition, the impacts of the uncertainties are taken into consideration in this paper. Unlike the previous studies, the uncertainties in this study are unnecessary to satisfy the bounded constraints. These uncertainties will be converted into the unknown input disturbances, and then a disturbance observer-based controller will be synthesized to estimate the information of the unknown states, eliminate completely the effects of the uncertainties, and stabilize inverted pendulum system. With the support of lyapunov methodology, the conditions for constructing the observer and controller under the framework of linear matrix inequalities (LMIs) are derived in main theorems. Finally, the simulations for system with and without uncertainties are exhibited to show the merit and effectiveness of the proposed methods.</span>

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Closed-loop model validation for an inverted pendulum experiment via a linear matrix inequality approach

Proceedings of the 36th IEEE Conference on Decision and Control ◽

10.1109/cdc.1997.657741 ◽

2002 ◽

Cited By ~ 3

Author(s):

Li Chen ◽

R. Smith

Keyword(s):

Linear Matrix Inequality ◽

Model Validation ◽

Closed Loop ◽

Inverted Pendulum ◽

Linear Matrix ◽

Loop Model ◽

Matrix Inequality ◽

Linear Matrix Inequality Approach ◽

Pendulum Experiment

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Control of interconnected systems with sensor delay based on decentralized adaptive neural dynamic surface method

Proceedings of the Institution of Mechanical Engineers Part I Journal of Systems and Control Engineering ◽

10.1177/0959651820966529 ◽

2020 ◽

pp. 095965182096652

Author(s):

Barmak Beigzadehnoe ◽

Zahra Rahmani ◽

Alireza Khosravi ◽

Behrooz Rezaie

Keyword(s):

Neural Network ◽

Large Scale ◽

Chemical Reactor ◽

Interconnected Systems ◽

Linear Matrix ◽

Dynamic Surface ◽

Control Laws ◽

Surface Design ◽

Pendulum System ◽

Inverted Pendulum System

In this article, an adaptive neural network is proposed for the tracking control problem of unknown nonlinear interconnected systems with inaccessible states and sensor delays based on dynamic surface strategy. The system has unknown nonlinearities and immeasurable states. Thus, a neural network state observer based on delayed outputs of subsystems is applied. The main difficulty in obtaining local observers’ gains is that undelayed outputs are not available. As a result, by utilizing proper Lyapunov–Krasovskii functionals in dynamic surface design procedures, the gains of local observers are given in terms of linear matrix inequalities. Then, appropriate changes in coordinates are defined using delayed outputs, observed states, and filtered virtual controls for the purpose of designing dynamic surface controllers. Subsequently, proper Lyapunov–Krasovskii functionals are introduced to deal with sensor delays and obtain control laws and stability criteria. Furthermore, the proposed decentralized control scheme can suitably conquer the decentralized tracking problem of unknown large-scale systems with sensor delays and guarantee that all the signals in the closed-loop interconnected systems be uniformly ultimately bounded. Finally, to show the effectiveness and efficiency of the proposed approach, the theoretic achievements are employed to design a controller for a double-inverted pendulum system and a cascade chemical reactor system.

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

Jurnal Teknologi ◽

10.11113/jt.v73.4444 ◽

2015 ◽

Vol 73 (6) ◽

Cited By ~ 1

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.

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