In this paper, we present a method to design a hybrid fuzzy logic controller (FLC) for a magnetic levitation system (MLS) based on the linear feedforward control method combined with FLC. MLS has many applications in industry, transportation, but the system is strongly nonlinear and unstable at equilibrium. The fast response linear control law ensures that the ball is kept at the desired point, but does not remain stable at that point in the presence of noise or deviation from the desired position. The controller that combines linear feedforward control and FLC is designed to ensure ball stability and increase the system's fast-response when deviating from equilibrium and improve control quality. Simulation results in the presence of noise show that the proposed control law has a fast and stable effect on external noise. The advantages of the proposed controller are shown through the comparison results with conventional PID and FLC control laws.

This paper focuses on synthesizing sliding mode control (SMC) for flexible-joint manipulators (FJM) based on serial invariant manifolds in order to increase the control quality for the system. SMC based on the serial invariant manifolds is proposed. The control law is found based on synergetic control theory (SCT) and analytical design of aggregated regulators (ADAR) method. In order to improve the control quality due to the effect of the stiffness value between two links in the system, a mechanism for constructing manifolds is built. The time response of the outer loop manifolds close to the actuator will be larger in the next round. The control quality of the system can be pre-evaluated through the parameters of the designed manifolds. Global stability is demonstrated by using the Lyapunov function in the design process. Finally, the effectiveness of the proposed controller based on SCT is demonstrated by numerical simulation results and compared with the traditional SMC.

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