Yiming Wu, He Chen and Tong Yang Yiming Wu, He Chen and Tong Yang Additional information is available at the end of the chapter

Additional information is available at the end of the chapter

http://dx.doi.org/10.5772/intechopen.71383

#### **Abstract**

In the presence of persistent perturbations in both unactuated and actuated dynamics of crane systems, an observer-based robust control method is proposed, which achieves the objective of trolley positioning and cargo swing suppression. By dealing with the unactuated and unknown perturbation as an augmented state variable, the system dynamics are transformed into a quasi-chain-of-integrators form based on which a reduced-order augmented-state observer is established to recover the perturbations appearing in the unactuated dynamics. A novel sliding manifold is constructed to improve the robust performance of the control system, and a linear control law is presented to make the state variables stay on the manifold in the presence of perturbations in unactuated dynamics. A Lyapunov function candidate is constructed, and the entire closed-loop system is proved rigorously to be exponentially stable at the equilibrium point. The effectiveness and robustness of the proposed observer-based robust controller are verified by numerical simulation results.

**Keywords:** underactuated systems, overhead cranes, observer-based control, Lyapunov methods, motion control
