This paper focuses on the tracking control problem of Magnetic Levitation System (MLS). MLS is highly unstable nonlinear system, in the process of operation, MLS needs to have strong robustness and anti-interference ability. Due to disturbance and parameter uncertainties in MLS, it is complex to obtain the exact dynamics of MLS, and it is difficult to design a suitable controller. The dynamic equation of the system is established by Lagrange equation, and then we propose an adaptive Sliding Mode Control (SMC) based on Radial Basis Function Neural Network (RBFNN). Because of the parameter uncertainties and disturbance in MLS, RBFNN is used to approximate the unknown dynamics in MLS. The stability of the closed-loop system is strictly proved by using the Lyapunov stability theory, which can achieve the uniform ultimate boundedness (UUB) of the signals of the closed-loop MLS. MATLAB environment is used to verify the performance of the proposed controller. Considering disturbance, parameter change, or unmodeled dynamics in MLS, proposed controller is compared with other nonlinear controllers, simulation results verify the effectiveness of the proposed approach.

This paper proposes an $H_{\infty }$ observer based on descriptor systems to estimate the state of charge (SOC). The battery’s open-current voltage is chosen as a generalized state variable, thereby avoiding the artificial derivative calculation of the algebraic equation for the SOC. Furthermore, the observer’s dynamic performance is saved. To decrease the impacts of the uncertain noise and parameter perturbations, nonlinear $H_{\infty }$ theory is implemented to design the observer. The sufficient conditions for the $H_{\infty }$ observer to guarantee the disturbance suppression performance index are given and proved by the Lyapunov stability theory. This paper systematically gives the design steps of battery SOC $H_{\infty }$ observers. The simulation results highlight the accuracy, transient performance, and robustness of the presented method.

The coupling between variables in the multi-input multi-output (MIMO) systems brings difficulties to the design of the controller. Aiming at this problem, this paper combines the particle swarm optimization (PSO) with the coefficient diagram method (CDM) and proposes a robust controller design strategy for the MIMO systems. The decoupling problem is transformed into a compensator parameter optimization problem, and PSO optimizes the compensator parameters to reduce the coupling effect in the MIMO systems. For the MIMO system with measurement noise, the effectiveness of CDM in processing measurement noise is analyzed. This paper gives the control design steps of the MIMO systems. Finally, simulation experiments of four typical MIMO systems demonstrate the effectiveness of the proposed method.

The characteristic of a flexible system with weak damping is that the amplitude characteristics show a large change, and the situation on the Nyquist chart is extremely complicated. Due to the existence of weak damping, the perturbation range of the flexible modal parameters allowed by the system is greatly compressed, and the robust stability is reduced, which brings challenges to the control design. To deal with this problem, the traditional H-inf loop shaping method often leads to the controller instability and poor robustness. In order to improve the stability margin of the system, increase the robustness and stability, and solve the problem of the instability of H-infcontrollers, this paper proposes a robust comprehensive design method based on phase control. In this method, by using the closed-loop pole configuration corresponding to the flexible mode at low frequency, the phase control is realized. Through the phase control, the apex of the Nyquist curve of the weakly damped mode of the system is limited to the Right half plane. The H-inf weighting function relaxes the pole configuration requirements, reduces the conservativeness of strict positive real, and combines the phase control with the H-inf optimization solution to obtain a robust and self-stable H-inf controller. A specific design example is given. The simulation results show that this control method has extremely high robustness. This design example can provide a certain degree of robust design for other weakly damp.