Stability Control For A Class Of Under-actuated Systems

Under-actuated systems are characterized by the fact that they have fewer actuators than the degrees-of-freedom (DOF) to be controlled. Because they have many advantages, which include decreasing the number of actuators, lighting the system, reducing the cost, etc., they have become more and more valuable in both theory and applications. The content of the research includes the following five parts:1. A detailed comment on the present development of under-actuated systems is given, and the problems of under-actuated mechanical systems are analyzed. Then, the objective of this dissertation is proposed.2. Based on Lagrange mechanics, the mathematical model of a class of under-actuated systems-Overhead Cranes and linear Inverted Pendulum are established. A normal state equation model of the class is deduced.3. A sliding mode control approach is proposed based on the overhead crane and linear inverted pendulum system, the design steps and the principle of choosing parameters are given. Also theoretically analyses are presented to prove all the sliding mode surfaces are asymptotically stable, and then the simulation and experimental results verify the validity of the method.4. Ignore the mathematical model of bridge crane concrete, puts forward a single input rule fuzzy control method, stability analysis and design process of the fuzzy rules, the dynamic parameter selection principle and system are described in this paper, finally, through MATLAB software simulation for the proposed method is verified.5. For the jitter problem of the underactuated systems, with overhead crane system as a model, put forward a kind of input shaping method, the running state of the system can be improved effectively, the simulation results verify the validity of the proposed method.6. The main conclusions are summarized and the possible avenues of further issues about the control methods for under-actuated systems are addressed.