In his talk, he will first introduce linear lossless systems. Properties of image representation and energy functions of such systems will be discussed. In his talk, he will mainly focus on state space realization of two kinds of lossless systems namely lossless positive real (LPR) and lossless negative imaginary (LNI) systems, from a given image/transfer function representation of the system. Examples of LPR systems are n-port lossless LC circuits with the voltages across and currents through the ports as external variables and examples of LNI systems are spring-mass systems with the displacements of and forces acting on a mass as external variables. The concept of Quadratic Differential Forms (QDFs) is made use of for the realization procedure. QDFs are quadratic functionals in the system variables and their derivatives. Scalars like total energy and Lagrangian of the system can be written as QDFs. It will be shown that realization of a LPR or a LNI system can be carried out iteratively via an appropriate decomposition of a QDF that corresponds to an energy function of the system. The algebra of univariate and bivariate polynomials is made use of in the approach for the realization.
Next, it will be shown that the realization procedure has relevance and applications in the areas of synthesis and analysis of electrical and mechanical networks. The state space realization of LPR systems that he will describe specifically leads to first Cauer synthesis of the network corresponding to the given image/transfer function representation. In addition, the realization procedure helps in the analysis of the network obtained by the first Cauer synthesis. It will be shown that the state space realization procedure of LNI systems gives a novel approach towards synthesis of a spring-mass system with the given input-output (Force-displacement) characteristics. This is particularly useful in the design of vehicle suspension systems.
Dr. Shodhan Rao received B.Tech and M.Tech degrees (dual degree) in Mechanical Engineering from Indian Institute of Technology (IIT), Bombay, India in 2002, specializing in Computer Aided Design and Automation. During his graduation in August 2002, he was awarded the institute silver medal for being the topper of his class consisting of 42 students. Between July 2002 and July 2003, he worked as a systems analyst in General Electric Aircraft Engines, Bangalore. Between August 2003 and December 2004, he worked as a Senior Research Fellow in a project on the control of underactuated manipulators in IIT, Bombay. He obtained Ph.D. degree in Electrical Engineering from the University of Southampton, U.K. in May 2009. The area of specialization of his Ph.D. thesis was ``Behavioural Systems Theory". Between May 2009 and April 2011, he worked as a post-doctorate researcher in the University of Twente, Netherlands in the areas of variable stiffness robotic actuators and stiffness control of prosthetic hands by means of neural interfaces. He is currently a post-doctorate researcher in the Center for Systems Biology at the University of Groningen, Netherlands. His research interests lie in the areas of behavioural systems theory, theory and modeling of chemical reaction networks and control of robotic actuators and manipulators.