Finite Time Convergence And Tracking Control Design Of Nonholonomic Systems

Nonholonomic systems represent a wide class of mechanical systems. The research on nonholonomic control systems shows high significance both in theory and application. The thesis gives a summary introduction to nonholonomic control systems, including relevant background knowledge, research status, current control approaches and results, etc. The finite-time convergence control problem and tracking control problem of nonholonomic controlsystems consist the main theme of the thesis. The research results obtained by the author can be divided into two parts:Part1. Finite-time convergence controller design of high-order generalized chained systemsIn the control system performance studying, convergence performance is a key indicator. And from the point of view of optimization, the method of finite-time convergence is optimal control method. The finite-time controller designing strategies can be focused on open loop controller, non-continuous and feedback controller, and continuous and feedback controller. In this thesis, based on variable structure control theory and using continuous and feedbackcontroller- terminal sliding mode technology, a finite-time convergence controller is constructed for high-order generalized chained systems with two control inputs. The study of this system is mainly motivated by the importance of chained systems in the theory of nonholonomic control.Consider following high-order generalized chained systemswhere y(t) is the n-dimensional state of the systems, u₁(t), u₂(t) are the control inputs. They are supposed to make y(t) converge to zero in finite time. At the same time, u₁(t),u₂(t) also become zero. Finally, the performance of the proposed control law is shown throughsimulated examples. The simulation results show the efficiency of the method.Part 2. Finite-time tracking controller design for a general class of nonholonomic systemsRecently, the tracking problem of nonholonomic systems has been a hotpot of the researchof mechanical control systems.Compared with the finite-time convergence problem, finite-time tracking of nonholonomic control systems is not put much enthusiasm on. In fact, the tracking problem is so similar to the convergence problem if you see tracking as the convergenceof the given trajectory. In this paper, a new model is proposed, which is powerful enough to include in itself many typical nonholonomic models such as chained form, power form, extended chained form, and underactuated surface vessel systems, etc. Using terminal sliding mode technology and series of transformations, the tracking controller is designed for a general class of nonholonomic systems and achieved global finite-time tracking. At the same time, the successful research of this model is proved that the method of the finite-time convergence control applies to a large class of nonholonomic control systems. Its effectiveness is demonstrated through simulations.