A Family of Robust Simultaneous Controllers With Tuning Parameters Design for a Set of Port‐Controlled Hamiltonian Systems

Abstract

This paper investigates the robust simultaneous stabilization (RSS) and robust adaptive simultaneous stabilization (RASS) problem for a set of port‐controlled Hamiltonian (PCH) systems. Some results for designing a family of robust simultaneous controllers with tuning parameters for such systems are proposed. Firstly, using the dissipative Hamiltonian structural properties, these systems are combined to generate an augmented PCH system, and two simultaneous stabilization controllers with parameters are designed for the systems: one is a robust controller and the other is adaptive. Secondly, an algorithm for solving the tuning parameters’ ranges of controller is proposed with symbolic computation. Finally, a numerical example is studied by applying the method obtained in this paper to a set of PCH systems with external disturbance. The effectiveness of the proposed control method is verified by simulations. Compared with conventional simultaneous stabilization control, the controller obtained in this paper not only has strong robustness for a set of systems, but also can optimize the robustness for the systems by adjusting the parameters’ values.

Multi-Objective Robust Control for Vehicle Active Suspension Systems via Parameterized Controller

“…Then we propose an algorithm to find the ranges of parameters in the controller (10) via solving the parameters of α (x, a) in condition (9) by using cylindrical algebraic decompositions (CAD), which is one method of symbolic computation [35]. The solving turning parameters (STP) algorithm is proceeded as follows [29].…”

“…However, so many hard constraints in controller design could not even be achieved. A family of robust simultaneous controllers with tuning parameters for a set of dissipative Hamiltonian systems has been proposed [29], [30].…”

Robust Control of Permanent Magnet Synchronous Machine Based on Passivity Theory

“…where e is the time constant of the low pass filter introduced for realizability. It results the electrical dynamics (5) and the behaviour of input disturbance u ed defined by (6). The variation of parameters is modelled within the disturbance variable u v =̇q e ΔR +q e ΔD e .…”

“…The compensation of these effects is performed through additional control terms computed by disturbance observers. A PBC based on port‐controlled Hamiltonian structure is developed . Actuator saturation is considered .…”