Modeling and Control of Ball and Beam System using Model Based and Non-Model Based Control Approaches

Keshmiri, Mohammad; Jahromi, Ali Fellah; Mohebbi, Abolfazl; Amoozgar, Mohammad Hadi; Xie, Wenfang

doi:10.21307/ijssis-2017-468

Cited by 75 publications

(48 citation statements)

References 12 publications

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“…For instance, in [15] genetic algorithm (GA) has been used for optimally selecting the weighting matrices of LQR for state feedback control design of multi machine power system. GA based LQR design for ball and beam position control application has been reported in [16], and the results are reported to be encouraging. Similarly, the stabilizing controller design for inverted pendulum is solved using particle swarm optimization (PSO) in [17].…”

Section: Introductionmentioning

confidence: 92%

Algebraic Riccati equation based Q and R matrices selection algorithm for optimal LQR applied to tracking control of 3rd order magnetic levitation system

Kumare¹,

Jerome²

2016

Archives of Electrical Engineering

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This paper presents an analytical approach for solving the weighting matrices selection problem of a linear quadratic regulator (LQR) for the trajectory tracking application of a magnetic levitation system. One of the challenging problems in the design of LQR for tracking applications is the choice of Q and R matrices. Conventionally, the weights of a LQR controller are chosen based on a trial and error approach to determine the optimum state feedback controller gains. However, it is often time consuming and tedious to tune the controller gains via a trial and error method. To address this problem, by utilizing the relation between the algebraic Riccati equation (ARE) and the Lagrangian optimization principle, an analytical methodology for selecting the elements of Q and R matrices has been formulated. The novelty of the methodology is the emphasis on the synthesis of time domain design specifications for the formulation of the cost function of LQR, which directly translates the system requirement into a cost function so that the optimal performance can be obtained via a systematic approach. The efficacy of the proposed methodology is tested on the benchmark Quanser magnetic levitation system and a detailed simulation and experimental results are presented. Experimental results prove that the proposed methodology not only provides a systematic way of selecting the weighting matrices but also significantly improves the tracking performance of the system.

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Section: Introductionmentioning

confidence: 92%

Algebraic Riccati equation based Q and R matrices selection algorithm for optimal LQR applied to tracking control of 3rd order magnetic levitation system

Kumare¹,

Jerome²

2016

Archives of Electrical Engineering

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“…Therefore, the (4) can be ignoredand the dynamic of the system is summarized to (5). ̈= …………………….……………...……………(5) The system equation can be represented throughstate space (6) and (7).…”

Section: …(2)mentioning

confidence: 99%

“…Some papers present the control study based on the mathematical model of the system, so several techniques are implemented and simulated. In [3] was used a pole placement control in the ball and beam system, in [4]was implemented a fuzzy approach and [5]presented PID (proportional, integral and derivative) and LQR (Linearquadratic regulator) technics. Another important fact about the ball and beam is that due to the simplicity of the plant, several authors present some changes in the model, e.g.in [6] the actuation system is changed,in [7], [8], [9] different types of sensors are used, as well as this work, that presents a change in the plant.…”

Section: Introductionmentioning

confidence: 99%

Control of a Modified Ball and Beam System Using Tracking System in Real Time with a DC Motor as an Actuator

Niro¹,

Kaneko²,

Mollon³

et al. 2017

IJAERS

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“…Although there are few variations of the ball and beam system hardware setup [1][2][3], the basic system dynamics and control principle is common to all of them: a ball is positioned on a beam, on which it can move in two directions from the beam center, left and right, or positive and negative. The beam is connected to a voltage driven servomotor that determines the rotation of the beam and consequently the movement and positioning of the ball.…”

Section: Introductionmentioning

confidence: 99%

Optimized PID Position Control of a Nonlinear System Based on Correlating the Velocity with Position Error

Muškinja

Rižnar

2015

Mathematical Problems in Engineering

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We examined a design approach for a PID controller for a nonlinear ball and beam system. Main objective of our research was to establish a nonmodel based control system, which would also not be dependent on a specific ball and beam hardware setup. The proposed PID controller setup is based on a cascaded configuration of an inner PID ball velocity control loop and an outer proportional ball position control loop. The effectiveness of the proposed controller setup was first presented in simulation environment in comparison to a hardware dependent PD cascaded controller, along with a more comprehensive study on possible design approach for optimal PID controller parameters in relation to main functionality of the controller setup. Experimental real time control results were then obtained on a laboratory setup of the ball and beam system on which PD cascaded controller could not be applied without parallel system model processing.

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Modeling and Control of Ball and Beam System using Model Based and Non-Model Based Control Approaches

Cited by 75 publications

References 12 publications

Algebraic Riccati equation based Q and R matrices selection algorithm for optimal LQR applied to tracking control of 3rd order magnetic levitation system

Algebraic Riccati equation based Q and R matrices selection algorithm for optimal LQR applied to tracking control of 3rd order magnetic levitation system

Control of a Modified Ball and Beam System Using Tracking System in Real Time with a DC Motor as an Actuator

Optimized PID Position Control of a Nonlinear System Based on Correlating the Velocity with Position Error

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