Finite-time port-controlled Hamiltonian design for second-order dynamical systems

Abstract

Finite-time design is not common in classical controllers, and the ones in the literature are not usually robust. The state-dependent differential Riccati equation (SDDRE) is an optimal nonlinear design in the company of a finite-horizon cost function that manipulates the terminal time using a weighting matrix of states. This method is sensitive to parametric model uncertainty, though its finite time characteristics can be augmented with other controllers. Port-controlled Hamiltonian (PCH) design can present a robust control law by defining the desired inertia matrix in the reference Hamiltonian function. The PCH is not finite-time; however, it can be modified using the suboptimal gain of the SDDRE controller. This paper combines the SDDRE and the PCH design to present a novel nonlinear controller with both finite-time and robust behavior toward parameter uncertainty in modeling. The finite-time behavior refers to the capability of controlling a system with different final times, as the input parameter to the system (or finishing a control task in a predefined time). The analytical stability proof of the proposed input law has been addressed using Lyapunov’s second method. The modified PCH is applied to second-order dynamical systems; as an illustrative example, a two-degree-of-freedom (DoF) inverted pendulum has been simulated and compared with a proportional–derivative (PD) control and a PCH with constant PD gains. A four-DoF robot arm was also simulated to highlight the application of the proposed method on complex systems. The introduced method outperformed the classical ones and showed finite-time regulation with different terminal times.