Research On Nonlinear Control Of Underactuated System

Underactuated system is a special and important analytical mechanics system. Nowadays, more and more people have paid attention to the study of underactuated system.Nonholonomic systems represent a class of constrain underactuated systems. The research on nonholonomic system shows high significance both in theory and application.As a typical underactuated system, inverted pendulum system has widespread applications in real world. The article is devoted to nonlinear control of the two forms of underactuated systems, which is supported by the relevant background knowledge, current results, etc. The research results obtained by the author can be divided into three parts:1). Finite-time stabilization of a general class of nonholonomic dynamic systems.We presents control strategies for finite-time stabilization of a class of nonholonomic dynamic systems with unknown virtual control coefficients and system parameters.The minimal dilation degree technique and the terminal sliding mode control scheme with finite-time convergence are used to design the controllers. The systematic control strategy development involves the introduction of assistant transformations and the application of recursive terminal sliding mode structure. Depending on whether the system can be converted into a time-invariant linear system or not, two control schemes are proposed respectively guaranteeing that system states converge to zero in finite time.The effectiveness and the robust feature of the developed control approaches are testified by two practical examples: the simplified underactuated hovercraft system and the parking problem for a mobile robot of the unicycle type.2). Energy-based control for parallel-type double inverted pendulums with restricted cart rail length.The Newton-Euler method is used to establish the mathematical model of a paralleltype double inverted pendulums system(PDIPS). A new energy-based swinging up strategy is proposed for the PDIPS with restricted cart rail length. The controller is developed by a Lyapunov function in the form of two pendulums’ energy and the cart’s velocity. The way to swing up two pendulums is to drive the total energy of the two pendulums to its potential energy at the vertical position. The proposed controller can also make the speed of the cart converge to zero such that the restriction on the rail length is satisfied. The designed controller has a simple structure, good convergence performance and easy tuning parameters. We also illustrate the good performance of the proposed swing-up law through simulation and experiment.3). Adaptive trajectory tracking and balance control of the planner inverted pendulum.The nonlinear dynamical model of the planar inverted pendulum is developed with Lagrangian formulation firstly. Then based on the system energy, an adaptive trajectory tracking controller is proposed for stabilizing and tracking control of an underactuated planar inverted pendulum system. Compared with conventional control methods, the developed controller is put forward without approximately decoupling or linearizing the complicated nonlinear model of the planar inverted pendulum system. The designed adaptive controller is designed in the presence of system friction, air resistances and uncertainty parameters. Then the stability of the closed-loop system is proved. Finally, numerical simulation results demonstrate that the proposed control scheme provides high-performance adaptivity and is robust with regard to parametric variations and different initial states.