Development of a fuzzy-LQR and fuzzy-LQG stability control for a double link Rotary inverted pendulum.

*(English)*Zbl 1450.93031Summary: In this paper, a fuzzy based linear quadratic regulator (FLQR) and linear quadratic Gaussian (FLQG) controllers are developed for stability control of a double link rotary inverted pendulum (DLRIP) system. The aim of this work is to study dynamic performance analysis of both FLQR and FLQG controllers and to compare them with the classical LQR and LQG controllers, respectively. A dynamic mechanical simulation model of the DLRIP was obtained using both the numerically SimMechanics toolbox in MATLAB and the analytically dynamic nonlinear equations. To determine the control performance of the controllers, settling time \((\boldsymbol{T}_{\boldsymbol{s}})\), peak overshoot (PO), steady-state error \((\boldsymbol{E}_{\boldsymbol{ss}})\), and the total root mean squared errors (RMSEs) of the joint positions are computed. Furthermore, the dynamic responses of the controllers were compared based on robustness analysis under internal and external disturbances. To show the control performance of the controllers, several simulations were conducted. Based on the comparative results, the dynamic responses of both FLQR and FLQG controllers produce much better results than the dynamic responses of the classical LQR and LQG controllers, respectively. Moreover, the robustness results indicate that the FLQR and FLQG controllers under the internal and external disturbances were effective.

##### MSC:

93C42 | Fuzzy control/observation systems |

49N10 | Linear-quadratic optimal control problems |

93D05 | Lyapunov and other classical stabilities (Lagrange, Poisson, \(L^p, l^p\), etc.) in control theory |

70Q05 | Control of mechanical systems |

##### Keywords:

fuzzy linear quadratic regulator; linear quadratic Gaussian controllers; double link rotary inverted pendulum
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\textit{Z. B. Hazem} et al., J. Franklin Inst. 357, No. 15, 10529--10556 (2020; Zbl 1450.93031)

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