Robust Control For Robot Based On The Linear State Equation

This thesis has studied the robust control problem of the robotic systems. First, the development history of the robotic dynamic model based on the Lagrange equation is introduced by an example of a two-joint robot. Second, the robotic dynamic model based on the Lagrange equation is transformed into a linear state equation via the linear feedback control technique, and a detailed transformation procedure is given. Third, for the given linear model, many control methods are used in designing controllers. Finally, for each approach, the numerical simulation is given to show a good effectiveness and ensure some performance requirement.These control approaches include computing torque control, the linear matrix inequality (LMI) method, the variable structure control, the robust optimal control and the robust control with friction under consideration. In particular, the computing torque control can guarantee the robotic system to be stable in three kinds of sences: the globally exponentially stable(GES), the globally asymptotically stable (GAS) and the globally uniformly ultimately bounded (GUUB). We adopt two kinds of methods to study the stability and the robustness of the robotic systems via the LMIs. The variable structure control can easily make the system to be GAS, and the robust optimal control translates the robust control problem into the optimal control problem. However, the robust control with friction embodies the uncertainty, and the controller is designed according to properties of frictions.