Robust Passivity Cascade Technique-Based Control Using RBFN Approximators for the Stabilization of a Cart Inverted Pendulum

This paper proposes a novel passivity cascade technique (PCT)-based control for nonlinear inverted pendulum systems. Its main objective is to stabilize the pendulum’s upward states despite uncertainties and exogenous disturbances. The proposed framework combines the estimation properties of radial basis function neural networks (RBFNs) with the passivity attributes of the cascade control framework. The unknown terms of the nonlinear system are estimated using an RBFN approximator. The performance of the closed-loop system is further enhanced by using the integral of angular position as a virtual state variable. The lumped uncertainties (NN—Neural Network approximation, external disturbances and parametric uncertainty) are compensated for by adding a robustifying adaptive rule-based signal to the PCT-based control. The boundedness of the states is confirmed using the passivity theorem. The performance of the proposed approach was assessed using a nonlinear inverted pendulum system under both nominal and disturbed conditions.

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Intelligent Swing-Up and Robust Stabilization via Tube-based Nonlinear Model Predictive Control for A Rotational Inverted-Pendulum System

Revista Politécnica ◽

10.33333/rp.vol45n1.05 ◽

2020 ◽

Vol 45 (1) ◽

pp. 49-64

Author(s):

Alvaro Prado ◽

Marco Herrera ◽

Oswaldo Menéndez

Keyword(s):

Predictive Control ◽

Nonlinear Model ◽

Closed Loop ◽

Inverted Pendulum ◽

Angular Position ◽

Loop System ◽

Invariant Sets ◽

Closed Loop System ◽

Pendulum System ◽

Inverted Pendulum System

The purpose of this paper is to introduce a new robust nonlinear model-based predictive control scheme applied to a rotational inverted-pendulum system. The rotational pendulum is composed by a mechanical arm attached to a free-motion pendulum (orthogonal to the arm), namely Furuta Pendulum. In principle, a Fuzzy controller enables the robotic arm bar to lift the rotational pendulum through oscillatory swing-up motion up to automatically achieve the upper equilibrium position in a prescribed stabilizing operation range. After the pendulum reaches the operating range, an intelligent control bypass system allows the transition between the swing-up motion controller and a robust predictive controller to maintain the angular position of the pendulum around the upward critical position. To achieve robust performance, a centralized control framework combines a triplet of control actions. The first one compensates for disturbances using the regulation trajectory ?feedforward control. The second control action corrects errors produced by modelling mismatch. The third controller assures robustness on the closed-loop system whilst compensating for deviations of the state trajectories from the nominal ones (i.e, disturbance-free). The control strategy provides robust feasibility despite constraints on the arm bar and pendulum's actuators are met. Such constraints are calculated on-line based on robust positively invariant sets characterised by polytopic sets (tubes). The proposed controller is tested in a series of simulations, and experimentally validated on a high-fidelity simulation environment including a rotational inverted-pendulum built for educational purposes. The results show that robust control performance is strengthened against disturbances of the closed-loop system benchmarked to inherently-robust linear and nonlinear predictive controllers.

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Fuzzy Control of an Inverted Pendulum

Volume 6: 16th Computers in Engineering Conference ◽

10.1115/96-detc/cie-1441 ◽

1996 ◽

Author(s):

Tuna Balkan ◽

Mehmet Emin Ari

Keyword(s):

Inverted Pendulum ◽

Fuzzy Controller ◽

Angular Position ◽

Upright Position ◽

Control Signal ◽

Position Measurement ◽

Pendulum System ◽

Inverted Pendulum System ◽

And Performance ◽

The Stability

Abstract An inverted pendulum system has been designed and constructed as a physical model of inherently unstable mechanical systems. The vertical upright position of a pendulum is controlled by changing the horizontal position of a cart to which the pendulum is hinged. The stability of the system has been investigated when a fuzzy controller is used to produce the control signal, while making a single measurement. It has been shown that by using simple fuzzy rules to allow real time computation with a single angular position measurement, the system can not be made absolutely stable. However, the stability and performance of the system have been considerably improved by shrinking the membership functions of angular position, computed angular velocity and control signal when inverted pendulum is very close to the vertical upright position.

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Design and implementation of adaptive control logic for cart-inverted pendulum system

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

10.1177/0959651818788148 ◽

2018 ◽

Vol 233 (2) ◽

pp. 164-178 ◽

Cited By ~ 2

Author(s):

Sandeep Hanwate ◽

Yogesh V Hote ◽

Akshit Budhraja

Keyword(s):

Adaptive Control ◽

Inverted Pendulum ◽

Control Logic ◽

External Disturbances ◽

Pendulum System ◽

Inverted Pendulum System ◽

Simulation Based ◽

Modelling Uncertainties ◽

Individual Candidate ◽

Supervisory Control System

In this article, an adaptive control logic is proposed to serve as a supervisory control system sufficient to curb the adverse effects due to modelling uncertainties and external disturbances. The control logic belongs to the class of adaptive control methodologies. The attractive attribute of this technique is that only the superior features of each individual candidate controller are obtained by applying appropriate weight to these controllers. In order to prove its effectiveness and applicability, the benchmark problem for stabilization of cart-inverted pendulum system is carried out using this technique. The system performance is tried against that with each individual candidate controllers existing techniques. In addition, the simulation-based analysis is strengthened by analysing the performance of a real-time cart-inverted pendulum system setup, stabilized using the proposed control logic.

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Design and Control of a Vertically Moving Base Inverted Pendulum using NARMA-L2 with Resilient backpropagation and Levenberg Marquardt backpropagation Training Algorithm

10.14293/s2199-1006.1.sor-.ppvnr50.v1 ◽

2020 ◽

Author(s):

Mustefa Jibril ◽

Messay Tadese ◽

Reta Degefa

Keyword(s):

Inverted Pendulum ◽

Moving Average ◽

Angular Position ◽

Control Analysis ◽

Training Algorithm ◽

Pendulum System ◽

Inverted Pendulum System ◽

Neural Network Controller ◽

Levenberg Marquardt ◽

Moving Base

In this paper, a vertically moving base inverted pendulum control analysis has been done using Matlab/Simulink Toolbox. Because the vertically moving base inverted pendulum system is nonlinear and highly unstable, a feedback control system is used to make the system controlled and stable. A nonlinear autoregressive moving average L2 controller which is a family of Neural Network controller is used with Resilient backpropagation and Levenberg Marquardt backpropagation Training Algorithm to improve the stability of the pendulum. Comparison of the vertically moving base inverted pendulum using NARMA-L2 with Resilient backpropagation and Levenberg Marquardt backpropagation Training Algorithm for tracking a desired angular position of the system using a step and random input signals and a promising results have been obtained succesfully.

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A Method of Robust Control for Nonlinear Inverted Pendulum System

Advanced Materials Research ◽

10.4028/www.scientific.net/amr.562-564.1650 ◽

2012 ◽

Vol 562-564 ◽

pp. 1650-1654

Author(s):

Ke Yong Shao ◽

Miao Miao Tian ◽

Qing Yu Wu

Keyword(s):

Bp Neural Network ◽

Inverted Pendulum ◽

Linear Part ◽

Parametric Uncertainty ◽

Control Law ◽

Pendulum System ◽

Nonlinear Part ◽

Inverted Pendulum System ◽

Coordinate Transfer ◽

Backstepping Algorithm

In this paper, the controller of inverted pendulum with parametric uncertainty and nonlinearity was proposed. The controller was composed of two terms. Control law of linear part of the system was obtained by Coordinate Transfer and Backstepping algorithm. To the nonlinear part and uncertainty of the system which are usually not accords with the form of Backstepping algorithm, a BP neural network was applied to the design of the controller. Method submitted in this paper was less restrictive to the form of the nonlinear system, and has a wider universality. At the end of the paper, simulations proved the effectiveness of the proposed method.

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