A nonlinear optimal control approach for underactuated offshore cranes

ABSTRACT

The article proposes a nonlinear optimal control approach for the model of boom cranes being mounted on vessels. The dynamic model of the boom cranes undergoes approximate linearisation with the use of Taylor series expansion around a temporary operating point which is recomputed at each iteration of the control method. For the approximately linearised model, an H-infinity feedback controller is designed. The linearisation procedure relies on the computation of the Jacobian matrices of the state-space model of the system. For the computation of the controller's feedback gains, an algebraic Riccati equation is solved at each time step of the control method. The new nonlinear optimal control approach achieves fast and accurate tracking for all state variables of the boom cranes, under moderate variations of the control inputs. The stability properties of the control scheme are proven through Lyapunov analysis.

KEYWORDS:

• Boom cranes
• nonlinear H-infinity control
• nonlinear optimal control
• global stability
• Lyapunov analysis

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

This work was supported by Grant Ref. 3671 ‘Control and estimation of dynamical nonlinear and partial differential equation systems’ of the Unit of Industrial Automation of the Industrial Systems Institute’.