Chenming Li

A two-level control scheme for velocity limitation in mechanical systems is proposed, based on the Udwadia–Kalaba and diffeomorphism theory. First, a dynamic model incorporating equality constraints is developed. Considering uncertainties, the first-level robust control algorithm is designed. Second, using diffeomorphism theory, the system state is transformed, and the second-level control strategy is formulated to ensure compliance with inequality constraints. Furthermore, through Lyapunov stability analysis, the uniform boundedness and uniform ultimate boundedness of the system are validated. This control scheme constrains system velocity within the desired range and reduces the amplitude of velocity fluctuations. Finally, simulation-based validation on a nonlinear system confirms the effectiveness of the proposed control approach.

This article proposes a generalized Udwadia-Kalaba control method to simultaneously handle equality and speed inequality constraints. First, a dynamic model that includes both of these constraints is established, and the state transformation is carried out through diffeomorphism state transition theory. At the same time, limitations are imposed on the difference between the estimated state variables designed in this article and the actual state variables. Then, a robust control strategy is designed to ensure that the equality constraints and speed inequality constraints are satisfied. By utilizing the Lyapunov approach, the uniform boundedness and uniform ultimate boundedness of the dynamical system are demonstrated. Finally, the feasibility of the proposed method was verified through an uncertain long-distance belt conveyor system.

Based on the theory of viscoelasticity, a nonlinear dynamic model of the long-distance belt conveyor system is established considering PMSMs (Permanent Magnet Synchronous Motors). Then, a constraint following robust control is designed to accurately control the start and stop of the belt conveyor. The analysis then examines the speed, tension, and other parameters at critical positions during the startup phases with different desired speed curves. The parking phase is also investigated by dividing into four cases including unloaded free parking, fully loaded free parking, unloaded emergency parking, and fully loaded emergency parking. On this basis, four temperature conditions are set to study the slip ratio for the parking process: room temperature, extremely low temperature, monthly low temperature, and monthly high temperature. By comparing with traditional controllers, the proposed model-based underactuated controller can effectively improve the aforementioned metrics under various operating conditions, contributing to the safe and stable operation of long-distance nonlinear belt conveyors.

In order to achieve the stability and safety of the autonomous vehicle while reducing the control cost, a driving strategy for uncertain autonomous vehicle is presented. There are many uncertainties in the autonomous vehicle driving, and the boundary of the uncertainty maybe unknown. To solve this problem, a gated leakage type adaptive robust control based on the tracking deviation is developed. The salient feature of the control lies in the novel leakage mechanism designs. The leakage mechanism is designed to provide gated value for the leakage to prevent excessive control effort. The control system ensures the performance of the autonomous vehicle in terms of lateral and yaw displacement, which in turn prevents the vehicle from sideslip even in uncertainty. Compared with the constant leakage type adaptive robust control and Linear Quadratic Regulator (LQR) control, the effectiveness and superiority of the proposed control method are verified

A novel generalized Udwadia–Kalaba (GUK) control method is proposed in this paper to effectively deal with the constraint-following problem with comprehensive constraints, be it equality constraints or inequality constraints. Fully considering the complex application scenario in practice which encompasses both clear and feasible trajectory, the equality constraints and inequality constraints are simultaneously applied to design rational and reliable controller. Specifically, a state transformation function is introduced to describe the inequality constraints. Further, the dynamic model with comprehensive constraints is established based on the GUK theory. Then, a corresponding constraint-following control is presented to render the system performance, uniform boundedness and uniform ultimate boundedness. The effectiveness of the GUK control is verfied by the stability analysis based on Lyapunov minimax apprach and experimental verification of unmanned underwater vehicle (UUV). The desired control performances of UUV, constraint-following and collision avoidance, can be achieved. As an illustrative application, the UUV is designed to navigate through narrow sea trenches. Meanwhile, through comparative analysis with the linear quadratic regulator method and UK method, the superiority of this approach is demonstrated.