Ramkrishna Pasumarthy

Achievable Casimirs and its implications on control of port-Hamiltonian systems

In this paper we extend results on interconnections of port-Hamiltonian systems to infinite-dimensional port-Hamiltonian systems and to mixed finite and infinite dimensional port-Hamiltonian systems. The problem of achievable Dirac structures is now studied for systems with dissipation, in the finite-dimensional, infinite-dimensional and the mixed finite and infinite-dimensional case. We also characterize the set of achievable Casimirs and study its application for the control of port-Hamiltonian systems.

On stability of time delay Hamiltonian systems

Stability of a class of nonlinear systems, called port-Hamiltonian systems, in the presence of time delay in the communication between the plant and controller is studied. The delay parameter is an unknown function which varies with time and for which the upper bounds on the magnitude and variation are known. The presence of delay may destroy the port-Hamiltonian structure of the system. Because of this, stability of the time delay systems is not obvious. We thus propose a theory to test the stability of port-Hamiltonian systems with time delay. The stability problem considered here, relies on the construction of a Lyapunov-Krasovskii (LK) functional based on the Hamiltonian of the port-Hamiltonian system. Based on the LK functional, we derive some sufficient conditions for the system to be asymptotically stable in presence of uncertain delays.

Dynamics and control of 2D SpiderCrane: A controlled Lagrangian approach

In this paper we present control of a multicable suspended mechanism called the ‘2D SpiderCrane’ based on controlled Lagrangian approach. SpiderCrane does not have any conventional heavy mobile components by virtue of which high transfer speeds are achievable. Using the method of controlled Lagrangian a control law is developed based on continuous-time kinetic and potential energy shaping. Simulations are carried out in MATLAB.

Identification and Multivariable Gain-Scheduling Control for Cloud Computing Systems

This paper presents the dynamic modeling and performance control of a Web server hosted on a private cloud. The cloud hosting Web server is a variable capacity system with two control inputs: 1) the number of virtual machines (VMs), which is indicative of the capacity of the cloud, and 2) the admission control used for regulating workload. As the workload and the hosting conditions change frequently, the linear parameter-varying (LPV) framework is well suited to derive the model. For the hosted Web server, we obtain an multiple input multiple output (MIMO) LPV model with performance metrics such as the response time and the throughput, which is then converted to polytopic LPV form using tensor product transformation. Finally, we design a gain scheduled linear quadratic regulator controller for performance guarantees with optimal cost of VMs. The identification, validation, and control experiments are demonstrated on the open source Eucalyptus cloud platform. The HTTP requests are generated using customized synthetic workload generator tool.

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.

A novel approach for phase identification in smart grids using Graph Theory and Principal Component Analysis

Consumers with low demand, like households, are generally supplied single-phase power by connecting their service mains to one of the phases of a distribution transformer. The distribution companies face the problem of keeping a record of consumer connectivity to a phase due to uninformed changes that happen. The exact phase connectivity information is important for the efficient operation and control of distribution system. We propose a new data driven approach to the problem based on Principal Component Analysis (PCA) and its Graph Theoretic interpretations, using energy measurements in equally timed short intervals, generated from smart meters. We propose an algorithm for inferring phase connectivity from noisy measurements. The algorithm is demonstrated using simulated data for phase connectivities in distribution networks.

An LPV approach to performance modeling of a web server on a private cloud

This paper presents dynamic modeling of a webserver hosted on a private cloud using grey box identification technique. In contrast to the results in literature, we model the web-server as a linear parameter varying (LPV) state space system valid around several well defined operating regions. We programmatically generate synthetic HTTP load based on open source workload tool called httperf to obtain response time as performance metric. Finally, we validate the models on test data by conducting experiments in the actual Eucalyptus cloud environment.

Towards Analog Memristive Controllers

Memristors, initially introduced in the 1970s, have received increased attention upon successful synthesis in 2008. Considerable work has been done on modeling and applications in specific areas, however, very little is known on the potential of memristors for control applications. Being nanoscopic variable resistors, it is intuitive to think of using them as a variable gain. The main contribution of this paper is the development of a memristive analog gain control framework and theoretic foundation of a control strategy which can be implemented using this framework. Analog memristive controllers may find applications in control of large array of miniaturized devices where robust and adaptive control is needed due to parameter uncertainty and ageing issues.

Performance guarantees via pole placement for a webserver hosted on a private cloud

In this paper we apply pole placement techniques to meet the performance objectives of a web server hosted on a private cloud. The web server is modeled as a switched system with models developed for several well defined operating regions using system identification technique. We then obtain the conditions for placement of exact and regional poles in desired locations using full state feedback to guarantee performance and stability. The experiments are performed on the open source Eucalyptus based cloud setup.