(1990). ENERGY FUNCTION ANALYSIS FOR POWER SYSTEM STABILITY. Electric Machines & Power Systems: Vol. 18, No. 2, pp. 209-210.

Energy function analysis for power system stability

We present a differential geometric approach to the problem of fault detection and isolation for nonlinear systems. A necessary condition for the problem to be solvable is derived in terms of an unobservability distribution, which is computable by means of suitable algorithms. The existence and regularity of such a distribution implies the existence of changes of coordinates in the state and in the output space which induce an "observable" quotient subsystem unaffected by all fault signals but one. For this subsystem, a fault detection filter is designed.

A geometric approach to nonlinear fault detection and isolation

A Treatise on the Analytical Dynamics of Particles and Rigid Bodies: THE GENERAL THEORY OF ORBITS

“Spreadsheet simulation” refers to the use of a spreadsheet as a platform for representing simulation models and performing simulation experiments. This tutorial explains the reasons for using this platform for simulation, discusses why this is frequently an efficient way to build simulation models and execute them, describes how to setup a spreadsheet simulation, and finally examines some limitations on the use of spreadsheets for simulation.

Proceedings of the 2004 winter simulation conference

The different aspects of H, -estimation of linear, time-varying processes are considered, in both the continuous- and the discrete- time cases. The connection with differential-games is explained and the uniqueness and robustness issues are discussed. Four illustrative examples are given that demonstrate the various estimation schemes and compare the H, results with the correspondingl, solutions.

http://ieeexplore.ieee.org/iel5/1040/8509/00371384.pdf

H,-optimal estimation: a tutorial

Total energy shaping is a controller design methodology that achieves (asymptotic) stabilization of mechanical systems endowing the closed-loop system with a Lagrangian or Hamiltonian structure with a desired energy function - that qualifies as Lyapunov function for the desired equilibrium. The success of the method relies on the possibility of solving two PDEs which identify the kinetic and potential energy functions that can be assigned to the closed loop. Particularly troublesome is the partial differential equation (PDE) associated to the kinetic energy which is nonlinear and inhomogeneous and the solution, that defines the desired inertia matrix, must be positive-definite. In this note, we prove that we can eliminate or simplify the forcing term in this PDE by modifying the target dynamics and introducing a change of coordinates in the original system. Furthermore, it is shown that, in the particular case of transformation to the Lagrangian coordinates, the possibility of simplifying the PDEs is determined by the interaction between the Coriolis and centrifugal forces and the actuation structure. The examples of pendulum on a cart and Furuta's pendulum are used to illustrate the results.

http://www.esi2.us.es/~jaar/Datos/Articles/lhmnlc06.pdf

Total Energy Shaping Control of Mechanical Systems: Simplifying the Matching Equations Via Coordinate Changes

The expected value of the exponential of a weighted quadratic sum of the squares of the estimation error is minimized with respect to the state estimate subject to a Gauss-Markov system. The state estimates are assumed to be a function of the measurement history up to the stage time of the state vector. The estimator which optimizes this exponential cost criterion is linear but is not a conditional mean estimator such as the Kalman filter. This shows that the implications of Sherman's theorem are restricted to functions of the estimates which have access to the same measurement history such as in smoothing problems. In the solution process the expectation operation is replaced by an extremization operation allowing the formulation of a deterministic discrete time game. The saddle point estimator resulting from this game is the same as that obtained from the solution of an associated disturbance attenuation problem. This optimal stochastic estimator which generalizes the Kalman filter can feature the estimation error of certain states over others by the choice of the quadratic weighting matrices in the cost criterion. Correlation between the measurement and process noises is included. >

Optimal stochastic estimation with exponential cost criteria

Design and analysis of a spherical mobile robot

An estimator and smoother for a linear time varying system, over a finite time interval, are developed from a linear quadratic (LQ) game approach. The exogenous inputs composed of the measurement and process noise, and the initial state, are assumed to be finite energy signals whose statistics are unknown. The measure of performance is in the form of a disturbance attenuation function and the optimal estimator (smoother) bounds the attenuation function from above. The disturbance attenuation function is converted to a performance measure for a zero-sum LQ game and the exogenous inputs and the estimator are viewed as players in the game; the exogenous inputs attempt to worsen the estimate while the estimator tries to provide the most accurate estimate. The optimal estimator (smoother), restricted to a class of functions dependent on the measurement alone, is found to be unbiased and linear in structure. With a few mild assumptions, the results are extended to a linear time-invariant system on an infinite horizon, and the optimal estimator obtained is shown to satisfy an upper bound on the H ? norm.

A Linear-Quadratic Game Approach to Estimation and Smoothing

A path planning algorithm for a spherical mobile robot rolling on a plane is presented in this paper. The robot is actuated by two internal rotors that are fixed to the shafts of two motors. These are in turn mounted on the spherical shell in mutually orthogonal directions. The system is nonholonomic due to the nonintegrable nature of the rolling constraints. Further, the system cannot be converted into a chained form, and neither is it nilpotent nor differentially flat. So existing techniques of nonholonomic path planning cannot be applied directly to the system. The approach presented here uses simple geometrical notions and provides numerically efficient and intuitive solutions. We also present the dynamic model and derive motor torques for execution of the algorithm. Along the proposed paths, we achieve dynamic decoupling of the variables making the algorithm more suitable for practical applications.

https://www.cambridge.org/core/services/aop-cambridge-core/content/view/S0263574708004748

Ravi N. Banavar

Papers

Total Energy Shaping Control of Mechanical Systems: Simplifying the Matching Equations Via Coordinate Changes

Optimal stochastic estimation with exponential cost criteria

Design and analysis of a spherical mobile robot

A Linear-Quadratic Game Approach to Estimation and Smoothing

Motion analysis of a spherical mobile robot