This study focuses on linear dynamical systems whose dynamics are affine in the control input. Such dynamics are extensively considered to be rewritten into a canonical form, namely the passive port-Hamiltonian representation in order to further explore some structural properties such as interconnection and damping matrices, Hamiltonian storage function and dissipation term. | 4 Hoang Ngoc Ha A COMPARATIVE ANALYSIS OF PASSIVITY-BASED CONTROL APPROACHES WITH APPLICATION TO LINEAR DYNAMICAL SYSTEMS Hoang Ngoc Ha Duy Tan University; Abstract - This study focuses on linear dynamical systems whose dynamics are affine in the control input. Such dynamics are extensively considered to be rewritten into a canonical form, namely the passive port-Hamiltonian representation in order to further explore some structural properties such as interconnection and damping matrices, Hamiltonian storage function and dissipation term. On this basis, the passivity-based control design approaches including proportional controller and energy shaping controller are proposed for the purpose of stabilization. Interestingly, the energy shaping controller seems to be better since the controller gain accepts a larger domain of validity and can even be negative. A mass-spring-damper system is used to illustrate the proposed approach. Besides, numerical simulations are included in both the open loop and closed loop to compare the results. Key words - Port-Hamiltonian representation; modeling; passivitybased control; proportional controller; energy shaping controller. 1. Introduction This paper deals with the port-based modeling of general nonlinear dynamical systems [1–3] whose dynamics are described by a set of Ordinary Differential Equations (ODEs) and affine in the input u as follows: dx = f ( x ) + g ( x)u; x(t = 0) = xinit dt (1) where x = x(t ) is the state vector in the operating region D n ; f ( x) n expresses the smooth (nonlinear) function with respect to the vector field x . The input-state map and the control input are represented by g ( x) nxm and u , respectively. It is worth noting that many industrial applications of electrical, mechanical or biochemical engineering belong to this kind of systems [4–7]. Many control methodologies have been developed for the stabilization of the system (1) at a desired set-point x* .
