In this paper, a compound control scheme with linear active disturbance rejection control (LADRC) and nonlinear active disturbance rejection control (NLADRC) is designed to stabilize the speed control system of the marine engine. To deal with the high nonlinearity and the complex disturbance and noise conditions in marine engines, the advantages of both LADRC and NLADRC are employed. As the extended state observer (ESO) is affected severely by the inherent characteristics (cyclic speed fluctuation, cylinder-to-cylinder deviations, etc.) of the reciprocating engines, a cycle-detailed hybrid nonlinear engine model is adopted to analyze the impact of such characteristics. Hence, the controller can be evaluated based on the modified engine model to achieve more reliable performance. Considering the mentioned natural properties in reciprocating engines, the parameters of linear ESO (LESO), nonlinear ESO (NLESO), and the switching strategy between LADRC and NLADRC are designed. Finally, various comparative simulations are carried out to show the effectiveness of the proposed control scheme and the superiority of switching strategy. The simulation results demonstrate that the proposed control scheme has prominent control effects both under the speed tracking mode and the condition with different types and levels of load disturbance. This study also reveals that when ADRC related approaches are employed to the reciprocating engine, the impact of the inherent characteristics of such engine on the ESO should be considered well.

The wheel-side direct-driven transmission system (WDTS) is a new intelligent transmission technology, which has significant advantages in high-efficiency and few malfunctions for the electric bus. Based on the Lagrange–Maxwell equation, the WDTS electromechanical coupling dynamic model, whose effectiveness is verified by the PMSM speed, is constructed for analyzing the system torsional vibration destabilization characteristics. Then, by determining the resonance curve equation for the torsional vibration response amplitude of the WDTS with the direct multi-scale method, the influences of the torque ripple amplitude of the PMSM and the transmission clearance on the system torsional vibration stability are analyzed. The results indicate that the WDTS torsional vibration response shows complex nonlinear characteristics especially under the effect of the system transmission clearance, which has an important impact on the system stable operation. The research results can lay a theoretical foundation for the design of the WDTS of the electric bus.

In nanopositioning system, the compliant tripod stages have proved to have enormous advantages for out-of-plane (z/tip/ tilt) positioning in turns of compactness, simplicity in structure, and economic cost. However, most of the present-day compliant tripod stage undergo manufacturing problems due to a complicate structure, and little study has been carried out to formulate the tri-inputs and tri-outputs relationship, which is essential for precise positioning. Accordingly, this paper presents the quasi-static analysis of a novel compliant tripod stage with an equivalent plane model to achieve precise position analysis for nanopositioning. Three-plane compliant lever mechanisms and cylindrical flexure hinges with high length-diameter ratio are employed, which mitigate couple influence and enable easy fabrication via planar manufacturing processes. The spatial output motions of the compliant tripod stage are first split among inputs of the threeplane compliant lever mechanisms, where the lateral translations of the compliant tripod stage are included. Then the displacement equations of the plane compliant lever mechanism are formulated through Castigliano's second theorem. The model is further verified by finite element analysis. Finally, an experimental test system is set up and the test results validate the proposed approach.

Connecting joints are significant components in mechanical systems as well as the Cartesian flexible robotic manipulator (FRM) which consists of a flexible arm and a moving base through connecting joints. Uncertain factors, such as unqualified assembly, accidental collision, and longtime service, will reduce the restraint stiffness of the connecting joints and enhance the dynamic nonlinearity of the system subsequently. In this case, the traditional perfectly fixed restrained model cannot reflect the real property of the connecting joints. This paper focuses on the elasticity property of the connecting joints with uncertain restraint stiffness, which is defined as the elastically restrained connecting joints (ERCJ), and investigates the dynamic characteristics and restraint mechanism of the ERCJ. An elastic restrained model is proposed to describe the elasticity property of the connecting joints and determine the elastic restrained region of the ERCJ, and the frequency relationship equation in the elastic restrained region is simultaneously determined and verified. Based on the proposed elastic restrained model and Hamilton’s variational principle, the dynamic model and vibration displacement equation of the FRM with elastically restrained connecting joints (FRMERCJ) are established. The virtual prototype experiment of the FRMERCJ is conducted to verify the dynamic model and reveal the restraint mechanism of the ERCJ. The proposed elastic restrained model in this paper can accurately describe the elasticity property of the connecting joints, and the ERCJ is sensitive to motion velocities especially under higher velocities for higher-order vibrations in the initial stage. The results are meaningful for the dynamic analysis and vibration control of robotic manipulators.