Robust control approach for handling matched and/or unmatched uncertainties in port-controlled Hamiltonian systems

Abstract

This study considers the problem of robust interconnection and damping assignment passivity-based control approach (IDA-PBC) for underactuated mechanical systems from two points of view. First, the robustness of IDA-PBC in the presence of non-vanishing matched and unmatched uncertainties is analysed and sufficient conditions are derived to ensure ultimate boundedness of system. Second, the robust control design is provided by adding a new control input to the former controller designed by IDA-PBC, such that asymptotic stability of the closed-loop system in the face of non-vanishing matched uncertainties is fulfilled. Finally, the proposed robust controller is evaluated through simulations of two practical examples, i.e. an inertia wheel pendulum and a single-link elastic joint robot. The simulation outcomes clearly reveal the effectiveness of the presented robust controller.

Keywords

• nonlinear control systems
• stability
• uncertain systems
• pendulums
• control system synthesis
• closed loop systems
• robust control
• damping
• asymptotic stability
• unmatched uncertainties
• port-controlled hamiltonian systems
• robust interconnection
• damping assignment passivity-based control approach
• ida-pbc
• underactuated mechanical systems
• robust control design
• control input
• closed-loop system
• matched uncertainties
• presented robust controller
• robust control approach