Stabilizing Tracking Control Strategies For Dynamic Periodic Orbit Of Underactuated TORA Systems

Underactuated mechanical systems(UMS)are mechanical control systems with fewer control inputs than the number of configuration variables.Control of UMS is currently an active and challenging field due to the lack of control inputs and their broad applications in transportation vehicles,robotics and aerospace vehicles.Translational oscillator with rotational actuator(TORA)system consisting of one unactuated translational cart and an actuated rotational proof-mass is a benchmark of UMS.The conventional research work for TORA system mainly focuses on stabilizing control of equilibrium points.This thesis focuses on its dynamic periodic orbit tracking control,the main contents include:Firstly,based on the Euler-Lagrange equation,the dynamics of inclined TORA system is discussed,particularly,dynamics and control problems of TORA system are focused.In addition,two kinds of typical dynamic periodic orbits are designed,namely,translational cart and rotational proof-mass tracking their dynamic periodic orbits respectively,and translational cart tracking dynamic periodic orbit while rotational proof-mass being stabilized at the fixed angle.Secondly,by utilizing virtual constraints technique,the periodic orbits for translational cart and rotational proof-mass are designed,and a virtual constraints equation between translational cart and rotational proof-mass is also presented.Then,a proper control Lyapunov function is designed.A virtual constraints based controller is derived to realize the desired periodic orbits tracking according to Lyapunov's second stability theory.The performance and feasibility of the proposed control design methodology are illustrated and analyzed with numerical simulations.Thirdly,different from the virtual constraints design methodology,the energy based control scheme is proposed to steer translational cart tracking its periodic orbit only.Based on the principle of energy conservation,the overall system energy is included in the control Lyapunov function for deriving the controller to realize the periodic orbit tracking.In addition,the control design process is concise.Simulation results demonstrate the feasibility and advantage of the energy based control scheme comparing to the virtual constraints based methodology.Finally,an experimental platform for TORA is developed.The friction model for the translational motion of cart is identified.Consequently,the feedforward compensation idea is employed to redesign the energy based control scheme,which leads to an energy based controller with friction compensation.Simulation results and the experimental results demonstrate its efficiency and practicability.The design principle of periodic orbits tracking and the design methodologies with friction compensation for underactuated TORA system can be extended to the design and implementation for other underactuated systems.