Passivity And Control Design For Time-delay Stochastic Port-Hamilton Systems

Time delay and interference exist in many practical systems which will make the per-formance of the system decrease. So it is very necessary to consider the effects of delay and interference in the nonlinear systems. However, due to the complexity of the nonlinear system and the influence of time delay, the difficult of the controller design and stability analysis process of the system are increase. Fortunately, the viewpoints and methods of the generalized Hamilton system provide a good channel to solve these problems. The physical meaning of the Hamilton system is clear, and the Hamilton function is its generalized energy, so it can be expressed as a Lyapunov function for the system under some conditions. In the control design of the actual system such as the electric power system and the mechanical system, the methods based on Hamilton function have been widely used. In addition, gen-eralized Hamilton system's structure is simple and it also has some good properties, such as invariance and passivity. However, for stochastic and time-delay system, some properties such as passivity are not satisfied. Therefore, the passive control problem of stochastic Port-Hamilton systems with time delay is studied, and the controller design of stochastic power system with time delay is discussed. The main conclusions include the following two parts:1) The passive control of stochastic Hamilton system with time delay.Firstly, the stochastic passive condition is given for the stochastic Hamilton system with time delay in this paper. Secondly, we proved that the structure of the system and the form of the output function can be kept under a certain coordinate transformation. Thirdly, the stochastic generalized canonical transformation of the system is defined and then the stochastic passivity conditions of the systems is proposed. Finally, we can prove the system is stable based on the obtained results.2) The control design for stochastic power system with time delay based on Hamilton system theory.Firstly, based on the actual structure of the power system, and through the delay pre-feedback, the system is expressed as a form of dissipative Hamiltonian system. Then, based on the obtained Hamilton system form and Hamilton function method, the H_? control problem is solved. Finally, a simulation example is given to verify the correctness of the conclusion.