Switching Control Design For A Class Of Underactuated Systems

The underactuated systems are characterized by the fact that they have fewer actuators than the number of system state dimensions. Research on the control of underactuated systems is very valuable in both theory and applications in that the absence of control inputs has incomparable advantages in decreasing the number of actuators, saving energy, enhancing system flexibility, reducing weight and costs and so on. Meanwhile, since underactuated systems have the characteristics of high nonlinearity, strong coupling and change of the parameters, it is very difficult to control the underactuated systems.In this thesis,2 DOF inverted pendulum is taken as the research object, which was bought from the Canadian company of Quanser. The research objective is to extend the range of the swing rod angle on the basis of the switched system theory. The main contributions are as follows.First of all, based on Euler-Lagrange method, the dynamic model of underactuated systems is established. Also, the property of stability, controllability and observability for underactuated system is analyzed.Second, for linearized inverted pendulum model, LQR controller and pole placement controller are designed, and when the swing rod angle is relatively large, it can be brought back to the equilibrium position through the method of hard and soft switchings.The nonlinear model is also linearized based on the input-output linearization approach and multi-point LQR hard and soft switching controllers are constructed.Third, for linearized inverted pendulum model, state-feedback controller is designed using backstepping. In the design process, two positive constants can be adjusted arbitrarily, then the two constants are chosen based on the idea of hard and soft switchings, and the hard and soft switching controllers are constructed. The simulation also shows the effectiveness of the designed method.Finally, a hardware-in-loop simulation platform is builded, and the designed controller can hold the swing rod to stay in vertical position. Therefore, the experiment illustrates that the designed controller is feasible and effective.The conclusions and perspectives are presented in the end of the thesis.