To effectively restrain the lateral vibration caused by the guide rail excitation and improve the ride comfort of the car system, a state-weighted linear quadratic regulator (LQR) control strategy is proposed. Firstly, based on the active control model of the 4-DOF car system with actuators distributed diagonally along the center of the car frame, an LQR controller for lateral vibration of high-speed elevator car systems is designed. Furthermore, in view of the tedious and time-consuming of the empirical method to choose state-weighted matrix Q, stepping quantum genetic algorithm (SQGA) is proposed to improve the performance of the controller. Finally, the time-frequency characteristic curves of the lateral vibration acceleration and the vibration displacement of the car system are compared and analyzed by MATLAB to verify the effectiveness of the proposed controller.

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To effectively suppress the longitudinal vibration of the car under the conditions of high-speed operation and emergency braking, and improve the ride comfort of the car system, this paper proposes an adaptive fuzzy inverse optimal output feedback control strategy. Firstly, the dynamic model of the high-speed elevator system is established and the nonlinear dynamic model is approximated by the fuzzy logic system, and the auxiliary system model is established. Fuzzy state observer is designed to estimate the unmeasurable state. Furthermore, an adaptive inverse optimal output feedback controller based on fuzzy observer is designed by using adaptive backstepping technology and inverse optimal control principle. The stability analysis shows that the proposed adaptive fuzzy inverse optimal output feedback control strategy not only ensures the stability of the car attitude of high-speed elevator but also realizes the inverse optimization of the target cost function. Finally, the acceleration time–frequency response analysis of the two typical stages of high-speed elevator uniform running and emergency braking is carried out, and the numerical results are compared with the linear quadratic controller optimized by stepping quantum genetic algorithm (GA-LQR) and controller based on the state-dependent Ricatti equation (SDRE). The analysis verifies the effectiveness of the controller.