The active magnetic bearings (AMB) play an essential role in supporting the shaft of fast rotating machines and controlling the displacements in the rotors due to the deviation in the shaft. In this paper, an adaptive integral third-order sliding mode control (AITOSMC) is proposed. The controller suppresses the deviations in the rotor and rejects the system uncertainties and unknown disturbances present in the five DOF AMB system. The application of AITOSMC alleviates the problem of high-frequency switching called chattering, which would otherwise restrict the practical application of sliding mode control (SMC). Moreover, adaptive laws are also incorporated in the proposed approach for estimating the controller gains. Further, it also prevents the problem of overestimation and avoids the use of a priori assumption about the upper bound knowledge of total disturbance. The Lyapunov and homogeneity theories are exploited for the stability proof, which guarantees the finite-time convergence of closed-loop and output signals. The numerical analysis of the proposed strategy illustrates the effective performance. Furthermore, the comparative analysis with the existing control schemes demonstrates the efficacy of the proposed controller.

This paper focuses on controlling traction for a four-wheel electric vehicle by using the longitudinal slip ratio control technique. By keeping the slip ratio value inside an optimal limit, it can be ensured that the maximum driving force is obtainable by increasing the friction force between tire and road. The usefulness of the sliding mode control method is to provide robust performance from the parameter uncertainties at different road conditions. A control law is formulated based upon the Lyapunov stability approach to assure the sliding action. To satisfy the robustness, a vehicle model is made in Matlab, and it is simulated based on various parameter values. The slip ratios at different parameter values are plotted for open loop and closed loop. Then considering the vehicle kinematics and dynamics, a 3D CAD model using Catia is developed. Then exporting the model to Adams to use it as a plant model for the vehicle, co-simulation has been achieved by keeping the slip-based traction controller in Matlab/Simulink. Matlab/Simulink and Adams/View simulation validate the proposed method.

Active magnetic bearings (AMB) are used to suspend the rotor freely inside the stator to avoid any physical contact between them. Thus, it helps in significantly reducing the wear and tear that may cause a system breakdown. With the advancement of power electronics and the implementation of advanced control techniques, the use of AMB in industrial applications has increased. This paper proposes an optimal control strategy for the five degree of freedom (DOF) AMB system. The time-energy consumption of input is minimized by the application of a relatively new optimal control method called the pseudospectral method (PSM). Since the AMB is a nonlinear system, therefore the implementation of classical optimal control strategies becomes challenging. Thus, the PSM first transforms the optimal control problem at non-uniform nodes and converts it into a nonlinear programming problem, which is relatively easier to tackle. The PSM, as demonstrated in this paper, is able to find optimal solutions using relatively fewer grid points which in turn reduces the computational time and converges to the solution faster. The simulation analysis for the AMB system using two different types of PSM, that is, Legendre PSM and the Chebyshev PSM illustrates the optimal performance of the proposed strategy.