Comparative Study of Optimal Controller Application on Nonlinear Systems

Borgohain, Niku; Buragohain, Mrinal

doi:10.1007/978-981-15-9829-6_32

Cited by 1 publication

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“…The beam consists of two parts; the first part of the beam consists of a rigid shaft, while the other part rotates up and down on which the ball moves freely on it [10].…”

Section: Introductionmentioning

confidence: 99%

Performance Comparison of the Ball and Beam System using Linear Quadratic Regulator Controller

Umar¹,

Mu’azu²,

Haruna³

et al. 2023

PID Control for Linear and Nonlinear Industrial Processes

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This paper proposes the performance comparison of a linear quadratic regulator (LQR) controller for the ball and beam system (BBS). The BBS is a standard benchmark control system, which has two degree-of-freedom (2 DOF). It is an open loop and a highly nonlinear unstable system. This makes its parameter difficult to be estimated accurately, hence designing a controller for it is a challenging task. MatheThe BBS was modelled using Euler–Lagrange modeling technique, while the LQR controller was used for the stabilization of the ball on the beam. Simulation was done in MATLAB/Simulink 2022b environment, and the results simulated showed that for the two weighting matrices (Q and R), the state weighting matrix had a higher penalty on the ball displacement, ball velocity, beam angle, and beam angular velocity at lower values of Q. For the state weighting matrix had a better effect of penalty performance on the BBS with lower values. Also, as the diagonal element of the state weighting matrix Q increases from 0.1 to 20, the values of the optimal controller K increase, the reduced Ricatti matrix P increases, and the estimated eigenvalues E reduce. This implies that the ball displacement, ball velocity, beam angle, and beam angular velocity are better at lower values of Q.

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“…The beam consists of two parts; the first part of the beam consists of a rigid shaft, while the other part rotates up and down on which the ball moves freely on it [10].…”

Section: Introductionmentioning

confidence: 99%