Krishna Vijayaraghavan

Nonlinear observer for simultaneous states and unknown parameter estimation

This paper presents the design of an observer for the simultaneous estimation of states and unknown parameter for a class of nonlinear systems whose nonlinearity satisfies a bounded Jacobian condition. The paper presents two alternate observers based on the structure of the system. The conditions for the existence of these observers can be expressed as a linear matrix inequality and solved using standard solvers. The case of time-varying parameter and multiple unknown parameter have also been investigated. The use of the developed methodology is demonstrated through illustrative examples.

Observer-based sensor fault estimation in nonlinear systems

Sensor bias faults and sensor gain faults are two important types of faults in sensor. Simultaneous estimation of these sensor faults in nonlinear systems in the presence of input disturbance and measurement noise is challenging and has not been adequately addressed in literature. Hence, this article develops an observer-based sensor fault estimation method for generalized sector-bounded nonlinear systems in the presence of input disturbance and measurement noise. A generalized sector-bounded nonlinearity was chosen because it encompasses a wide range of nonlinearities including Lipschitz, positive real, and dissipative. This article presents necessary and sufficient conditions to achieve a suboptimal cost for a cost function consisting of the sum of the square integrals of the estimation errors to the square integrals of the disturbances in the form of linear matrix inequality. The linear matrix inequality can be solved offline to explicitly calculate observer gain, and the resulting observer simultaneously estimates the system states as well as both bias and gain faults in the sensors. Compared to previous literature, the proposed methodology is designed to work in the presence of both input disturbance and measurement noise. Additionally, this article considers a generalized sector-bounded nonlinearity which encompasses a variety of different physical nonlinearities. Furthermore, the observer does not require the online solution of the Riccati equation and is thus computationally less intensive compared with the methods of extended Kalman filtering. The observer design procedure is demonstrated through two illustrative examples consisting of a fourth-order double spring–mass system and a third-order wind turbine power transmission mechanism.

Observer design for generalized sector-bounded noisy nonlinear systems

This article presents a new observer for a class of nonlinear systems, defined as a “generalized sector-bounded” nonlinear system, in the presence of both sensor and input disturbances. The generalized sector-bounded nonlinearity is shown to be a super-set of Lipschitz, bounded Jacobian, one-sided Lipschitz, monotonically increasing and dissipative nonlinearities. This article presents necessary and sufficient conditions for this observer to guarantee a desired minimum performance. The conditions for the observer are presented as a linear matrix inequality that can be solved offline using commercial solvers, and the solution to the linear matrix inequality is used to explicitly compute the observer gain. This article then extends these results to case where an additive nonlinearity appears in the sensor output. The use of the methodology developed in this article is demonstrated through illustrative examples. Compared to previous results on nonlinear observers, the proposed observer guarantees a global performance measure for a very general class of nonlinear systems and does not require online computation of the observer gain.

Adaptive nonlinear observer for state and unknown parameter estimation in noisy systems

This paper proposes a novel adaptive observer for Lipschitz nonlinear systems and dissipative nonlinear systems in the presence of disturbances and sensor noise. The observer is based on an H∞ observer that can estimate both the system states and unknown parameters by minimising a cost function consisting of the sum of the square integrals of the estimation errors in the states and unknown parameters. The paper presents necessary and sufficient conditions for the existence of the observer, and the equations for determining observer gains are formulated as linear matrix inequalities (LMIs) that can be solved offline using commercially available LMI solvers. The observer design has also been extended to the case of time-varying unknown parameters. The use of the observer is demonstrated through illustrative examples and the performance is compared with extended Kalman filtering. Compared to previous results on nonlinear observers, the proposed observer is more computationally efficient, and guarantees state and parameter estimation for two very broad classes of nonlinear systems (Lipschitz and dissipative nonlinear systems) in the presence of input disturbances and sensor noise. In addition, the proposed observer does not require online computation of the observer gain.

Generalised observer design for dissipative Lipschitz nonlinear systems in the presence of measurement noise

This paper presents two novel observer concepts. First, it develops a globally exponentially stable nonlinear observer for noise-free dissipative nonlinear systems. Second, for a dissipative nonlinear system with measurement noise, the paper develops an observer to guarantee a desired performance, namely an upper limit on the ratio of the square of the weighted L2 norm of the error to the square of the weighted L2 norm of the measurement noise. The necessary and sufficient conditions for both observers are reformulated as algebraic Riccati equations (AREs) so that standard solvers can be utilised. In addition, the paper presents necessary and sufficient conditions to be satisfied by the nonlinear system in order to ensure that the ARE (and hence the observer design problem) has a solution. The use of the methodology developed in this paper is demonstrated through illustrative examples. In literature, there is no previous observer for dissipative system that provides both necessary and sufficient conditions. Results for noisy system either rely on linearising the system about state trajectory (requiring initial estimates to be close to the actual states) or are for specialised systems that cannot be extended to dissipative systems.

Design of sliding observers for Lipschitz nonlinear system using a new time-averaged Lyapunov function

ABSTRACT This paper provides a procedure for designing a sliding mode observer for a nonlinear system in the presence of Gaussian input disturbances and sensor noises. The paper first proposes a novel candidate for Lyapunov stability, termed a Time-averaged Lyapunov (TAL) function. The TAL averages the Lyapunov analysis over a small finite time interval, allowing for intuitive analysis of noises and disturbance. The paper then provides the necessary and sufficient condition for the design of the sliding observer gainsusing the TAL in the form of Linear Matrix Inequality (LMI). The LMIs can then be explicitly solved offline using commercial LMI solvers. The paper compares the LMIs for the two observer designs to demonstrate the design of the sliding mode observer using TAL can greatly enhance the scope of observer design for nonlinear systems.

A comparative study of Extended Kalman Filter and an optimal nonlinear observer for state estimation

A recently developed nonlinear H∞ observer and Extended Kalman Filter (EKF) offer two filters for state estimation in nonlinear systems. The Riccati equation that arises while developing the nonlinear H∞ observer is compared with the Riccati equation arising from the Extended Kalman Filter (EKF). Variations between the two Riccati equations translate into the differences in the performance of these alternative estimation methods. The H∞ filter offers faster convergence of the estimation covariance at large estimation errors during the transience of the filter. The Extended Kalman Filter, on the other hand, maintains higher levels of optimality at steady state at the expense of higher computational load. An LMI formulation for the H∞ filter is also presented that allows leveraging the bound on the nonlinearity to seek a stable filter for nonlinear systems.

Wind Solar Hybrid Power System Modeling and Analysis

India has always been victim of power failures or blackouts and the recent July 2012 countrywide blackout is a perfect example for it. It is expected that due to the widening gap between supply and demand, such instances of power failure would occur more regularly in future. Such blackouts are also be foreseen in other parts of the world. The electricity grids in many countries are highly centralized and are mostly dependent on fossil-fuel based energy sources (coal, oil, natural gas etc). Due to the rapid rise in the living standards of developing countries such as India and China, there is an increase in demand for electricity for running various appliances, as well as for heating and air-conditioning equipment. Such an increased in demand places tremendous strain on ailing centralized grid burning fossil fuel. The use of renewable energy sources (such as solar and wind) could potentially allow large amount of demand to be met though alternative means and offset the demand on the grid.The advancement in technology has encouraged the implementation of renewable resources especially solar and wind. Hybrid power systems (HPS) that consist of these resources can significantly lower storage requirements. Furthermore, besides being cost-efficient, it is coherent to the weather conditions since solar and wind complement each other well. For highly efficient hybrid power systems to be developed, a significant degree of research must be applied to further their development. This includes tasks such as modeling these systems and applying proficient control algorithms to maximize efficiency. This paper focuses on simulation of an HPS consisting of a photovoltaic (PV) module, wind turbine (WT), and a lead acid battery through MATLAB/SIMULINK software. Moreover, a control algorithm is proposed, which leads to an efficient and autonomous operation of the HPS, along with maximizing power output from PV module and WT. The model and control system were tested using sample hourly solar radiation, temperature, and wind speed data to generate the power output from the PV module and WT, which was then processed through the proposed algorithm, to power a sample hourly load profile. The results indicate that a simple HPS can meet the type of load demand provided in an efficient and effective manner.© 2013 ASME