Weighted sliding mode control of a flexible one-link arm

A new design for controlling a flexible one-link manipulator based on a variable structure theory is presented. Using an assumed-mode method, the plant model is derived. The discontinuous control law based on the variable structure system theory for the noncolocated manipulator tip position control is then designed. By decomposing the inequality that guarantees the global reaching condition into a set of inequalities each containing one variable concerned, one can assign separate gains to each of these variables. In this way separate weighting is achieved for specific error to obtain the desired performance. If some of the inequalities are allowed to be equalities, as is done in the simulation, the algorithm can be as simple as a PID controller, yet still possess the properties of a sliding mode controller