Finite-time stabilization and H∞ control of Port-controlled Hamiltonian systems with disturbances and saturation

The finite-time stabilization and finite-time H∞ control problems of Port-controlled Hamiltonian (PCH) systems with disturbances and input saturation (IS) are studied in this paper. First, by designing an appropriate output feedback, a strictly dissipative PCH system is obtained and finite-time stabilization result for nominal system is given. Second, with the help of the Hamilton function method and truncation inequality technique, a novel output feedback controller is developed to make the PCH system finite-time stable when IS occurs. Further, a finite-time H∞ controller is designed to attenuate disturbances for PCH systems with IS, and sufficient conditions are presented. Finally, a numerical example and a circuit example are given to reveal the feasibility of the obtained theoretical results.

Adaptive Robust Simultaneous Stabilization of Two Dynamic Positioning Vessels Based on a Port-Controlled Hamiltonian (PCH) Model

In this paper, the adaptive robust simultaneous stabilization problem of two ships is studied. Firstly, the water surface three-degree-of-freedom ship models are transformed into port-controlled Hamiltonian (PCH) models. Using a single output feedback controller, the two PCH systems are combined to generate an enhanced PCH system based on Hamiltonian structural attributes. Then, considering the situation with both external interference and structural parameter perturbation in the systems, an adaptive robust output feedback controller is designed to stabilize the two systems simultaneously. Finally, the effectiveness of the controller proposed in this paper is illustrated by a simulation example.

Stabilization via output feedback for a type of uncertain time-varying port-controlled Hamiltonian system based on linear matrix inequality approach

In this paper, the control of a type of uncertain time-varying port-controlled Hamiltonian (PCH) systems is investigated. As a matter of fact, the control method proposed in this paper is not based on passivity of PCH systems, but a general output equation is introduced inspired by the measured “information” in the systems in traditional control system theory and the problem of output feedback is considered. In this paper, a conception of p-quadratic stability of the type of PCH system is introduced, and the relationship between p-quadratic stability and Lyapunov stability is pointed out. Then, the problem for p-quadratic stabilization of the proposed system via static output feedback is solved in the following two cases, respectively. For the case of unperturbed output equation, a necessary and sufficient condition for the problem is derived in terms of two groups of linear matrix inequalities (LMIs); for the general case that the output equation also has time-varying perturbations, a sufficient condition for p-quadratic stable of closed-loop system is also given in terms of LMIs. It is also shown that conservatism can be greatly reduced when the perturbation variables in the uncertain PCH systems are restricted to vary within certain intervals. Finally, a numerical example is proposed in the end followed by a simulation to verify the effectiveness of the method proposed in this paper.

Water Level Control for Steam Generator in Nuclear Power Based on Port-Controlled Hamiltonian Method

This article designs the water level of steam generator control system applying PCH system modeling and control principle of Energy-Shaping. The basic principles of port-controlled Hamiltonian (PCH) system modeling and control principle of Energy-Shaping are provided, including passivity, dissipation and so forth. Meanwhile, port-controlled Hamiltonian (PCH) system, energy-shaping principle, matching method and its corresponding realization and stability analysis are presented. The water level of steam generator is accomplished; the controlled object is mathematically modeled with principle modeling method. Then the mathematic model is translated into PCH model. the proper Hamiltonian function is finely selected. The water level equilibrium point of steam generator system is respectively determined; the PCH controller based on energy-shaping method is ultimately obtained. The proposed modeling and control methods provide a potential idea for the other control methods applied method on steam generator system. Moreover, the proposed methods can be put into industrious process control.

Robust Simultaneous Stabilization Control Method for Two Port-Controlled Hamiltonian Systems: Controller Parameterization

This paper investigates robust simultaneous stabilization (RSS) control method for two port-controlled Hamiltonian (PCH) systems and proposes results on the design of simultaneous stabilization controller with parameters for such systems. Firstly, two PCH systems are studied. Using the dissipative Hamiltonian structural properties, the systems are combined to generate an augmented PCH system. When there are external disturbances in the systems, a robust controller with parameters is designed for the systems. Secondly, an algorithm for solving parameters of the controller is proposed with symbolic computation. Finally, an illustrative example is presented to show that the RSS controller obtained in this paper works very well.

Control Strategy of the DC Drive Systems Based on the State Error Port-Hamiltonian Theory

A novel state error port-controlled Hamiltonian (PCH) system method is presented for speed control the direct current (DC) separately excited motor. The unity power factor regulation of three phase pulse width modulated (PWM) rectifier is also implemented. Then, the state error PCH system control theory, the PCH model of the PWM rectifier and DC motor are proposed. Moreover, the control algorithm of the duty ratio switch function is presented for the PWM rectifier. Theoretical analysis and simulation results show that the controller has good speed tracking and unity power factor control performances.

Port-Controlled Hamiltonian Control of IM Based on Back-to-Back Converter

A method of port-controlled Hamiltonian (PCH) systems energy-shaping control is presented for the four-quadrant control problem of squirrel cage induction motor (IM) drive system. First, the PCH models of IM drive system are developed. Then, the PCH controllers are designed based on the control theory of closed-loop state error PCH system. The coordinated control of the grid-side and the motor-side are applied in Matlab/simulink, which the motor-side is started after the grid-side is achieved up to stable. The controlled system can be achieved that DC bus voltage controllable, unity power factor, energy bidirectional flow, IM run in the four-quadrant, etc.