Krishna Chaitanya Kosaraju

Control using new passivity property with differentiation at both ports

Port Hamiltonian systems are usually passive with respect to port variables that are power conjugate (eg: voltage and current, force and velocity) and this lead to energy shaping control methods. But systems with ‘dissipation obstacle’ cannot be controlled using these port variables and therefore we need to search for alternative passive maps. One option is within the Brayton Moser framework, where passivity is obtained by differentiating one of the port variables. This has led to power shaping methods for control, but the solutions (if exists) obtained impose constraints on the physical parameters of the system. In this paper, starting from the Brayton Moser framework we present a new passivity property with differentiation at both the port variables. Further using this new passive map, a PI like controller is proposed and presented using parallel RLC circuit and transmission line system with non zero boundary conditions as examples.

Power-Based Methods for Infinite-Dimensional Systems

In this chapter we aim to extend the Brayton Moser (BM) framework for modeling infinite-dimensional systems. Starting with an infinite-dimensional port-Hamiltonian system we derive a BM equivalent which can be defined with respect to a non-canonical Dirac structure. Based on this model we derive stability and new passivity properties for the system. The state variables in this case are the “effort” variables and the storage function is a “power-like” function called the mixed potential. The new property is derived by “differentiating” one of the port variables. We present our results with the Maxwell’s equations, and the transmission line with non-zero boundary conditions as examples.

Stability Analysis of Constrained Optimization Dynamics via Passivity Techniques

In this letter, we present passivity-based convergence analysis of continuous time primal-dual gradient method for convex optimization problems. We first show that a convex optimization problem with only affine equality constraints admits a Brayton Moser formulation. This observation leads to a new passivity property derived from a Krasovskii-type storage function. Second, the inequality constraints are modeled as a state dependent switching system. Using tools from hybrid systems theory, it is shown that each switching mode is passive and the passivity of the system is preserved under arbitrary switching. Finally, the two systems: 1) one derived from the Brayton Moser formulation and 2) the state dependent switching system, are interconnected in a power conserving way. The resulting trajectories of the overall system are shown to converge asymptotically, to the optimal solution of the convex optimization problem. The proposed methodology is applied to an energy management problem in buildings and simulations are provided for corroboration.

Building HVAC systems control using power shaping approach

Heating, Ventilating and Air-conditioning (HVAC) control systems play an important role in regulating indoor air temperature to provide building occupants a comfortable environment. Design of HVAC control system to provide an optimal balance between comfort and energy usage is a challenging problem. This paper presents a framework for control of building HVAC systems using a methodology based on power shaping paradigm that exploits passivity theory. The controller design uses Brayton-Moser formulation for the system dynamics wherein the mixed potential function is the power function and the power shaping technique is used to synthesize the controller by assigning a desired power function to the closed loop dynamics so as to make the equilibrium point asymptotically stable. The methodology is demonstrated using two example HVAC subsystems - a two-zone building system and a heat exchanger system.