Continuous sliding mode controllers for multi-input multi-output systems

Abstract

© 2018, Springer Nature B.V. This paper develops new continuous sliding mode controllers for multi-input multi-output mechanical systems in the presence of unknown, but bounded uncertainties in the given forces and in the masses. Assuming the absence of the uncertainties, a reference control input is first calculated using the fundamental equation of constrained motion that causes the system trajectories to exactly track the reference while minimizing a weighted L2 norm of the control effort. Next, in the presence of realistic uncertainties in the given forces and in the masses, two continuous sliding mode controllers are derived according to whether the mass matrix is diagonal or not. In the diagonal case, each element of the control vector is independently designed, while in the nondiagonal case the control vector is handled as a whole because its elements are coupled to one another. The two controllers are continuous because no signum functions are used. It is also shown that various forms of control input are possible depending on the control requirements among which a simple proportional-integral-derivative-type controller is exemplified in this paper. Two numerical examples serve to demonstrate the accuracy and robustness of the control methodology suggested herein.