Goshaidas Ray

A new approach to the design of robust load-frequency controller for large scale power systems

Abstract A new method is presented for derivation of a robust controller for the load frequency controller of interconnected power systems with uncertain parameters. A combination of ‘Matching conditions’ and Lyapunov stability theory is adopted to implement a robust stabilizing controller. The stability analysis of the closed-loop interconnected systems for all admissible uncertainties is considered. The application of the proposed robust control scheme is considered through simulation studies of two-area power system model. Performance robustness of the proposed scheme is compared with the recent work of Wang et al. (1993, IEE Proc. C Vol. 140, pp. 11–16), and found to be very good.

Stability analysis for continuous system with additive time-varying delays: A less conservative result

This paper presents a less conservative result for stability analysis of continuous-time systems with additive delays by constructing a new Lyapunov-Krasovskii functional and utilizing free matrix variables in approximating certain integral quadratic terms in obtaining the stability condition in terms of linear matrix inequalities. Numerical example is provided to show the effectiveness of the proposed method compared to some recent results.

Decentralized Stabilization of Uncertain Systems With Interconnection and Feedback Delays: An LMI Approach

This note presents a broad LMI condition that can ascertain the stability of uncertain systems under decentralized feedback in the presence of interconnection and feedback delays. Based on the Lyapunovs direct approach with a four-term energy functional and a three-term quadratic formulation of the given state dynamics, this method has a larger search space than used so far. Numerical examples corroborate the superiority of this method vis-a-vis the existing ones for several subsets of the general problem.

Improved delay-range-dependent robust stability criteria for a class of Lur’e systems with sector-bounded nonlinearity

Abstract In this paper, the problem of delay-dependent stability of a class of uncertain Lur’e systems of neutral type with interval time-varying state delay and sector-bounded nonlinearity has been considered based on Lyapunov–Krasovskii functional approach. By constructing a candidate Lyapunov–Krasovskii (LK) functional, less conservative robust stability criteria are proposed in terms of linear matrix inequalities (LMIs). The reduction in conservatism of the proposed stability criteria over recently reported results is attributed to the candidate LK functional used in the delay-dependent stability analysis, and to the tighter bounding of the time-derivative of the functional without neglecting any useful terms using minimal number of slack matrix variables. The proposed analysis, subsequently, yields a stability condition in convex LMI framework, and is solved non-conservatively at boundary conditions using standard numerical packages. The effectiveness of the proposed stability criterion is demonstrated through standard numerical examples.

An Improved Delay-Dependent Stability Criterion for a Class of Lur’e Systems of Neutral Type

In this paper, we consider the problem of delay-dependent stability of a class of Lur’e systems of neutral type with time-varying delays and sector-bounded nonlinearity using Lyapunov–Krasovskii (LK) functional approach. By using a candidate LK functional in the stability analysis, a less conservative absolute stability criterion is derived in terms of linear matrix inequalities (LMIs). In addition to the LK functional, conservatism in the proposed stability analysis is further reduced by imposing tighter bounding on the time-derivative of the functional without neglecting any useful terms using minimal number of slack matrix variables. The proposed analysis, subsequently, yields a stability criterion in convex LMI framework, and is solved nonconservatively at boundary conditions using standard LMI solvers. The effectiveness of the proposed criterion is demonstrated through a standard numerical example and Chua’s circuit.

Robust Stability Criteria for Uncertain Neutral Systems with Interval Time-Varying Delay

In this paper, we consider the problem of robust stability of a class of linear uncertain neutral systems with interval time-varying delay under (i) nonlinear perturbations in state, and (ii) time-varying parametric uncertainties using Lyapunov-Krasovskii approach. By constructing a candidate Lyapunov-Krasovskii (LK) functional, that takes into account the delay-range information appropriately, less conservative robust stability criteria are proposed in terms of linear matrix inequalities (LMI) to compute the maximum allowable bound for the delay-range within which the uncertain neutral system under consideration remains asymptotically stable. The reduction in conservatism of the proposed stability criterion over recently reported results is attributed to the fact that time-derivative of the LK functional is bounded tightly without neglecting any useful terms using a minimal number of slack matrix variables. The analysis, subsequently, yields a stability condition in convex LMI framework, that can be solved non-conservatively at boundary conditions using standard LMI solvers. The effectiveness of the proposed stability criterion is demonstrated through standard numerical examples.

State feedback stabilization of uncertain linear time‐delay systems: A nonlinear matrix inequality approach

A nonlinear matrix inequality is derived as a stabilizability condition of linear uncertain time-delay systems. This inequality is seen as a less conservative one as well as efficient for numerical computation than the existing results as seen when solving by cone-complementary algorithm. Copyright

Stability Criteria for Nonlinearly Perturbed Load Frequency Systems With Time-Delay

In this paper, new criteria are presented for ascertaining delay-dependent stability of networked multi-area load frequency control (LFC) systems with feedback loop delay in presence of unknown and time-varying exogenous load disturbance. The proposed stability criteria are based on Lyapunov-Krasovskii (LK) functional approach, and they are expressed in linear matrix inequality (LMI) framework. Since the unknown exogenous load disturbance in the power system (cause) ultimately affects the evolution of the state variables of the system (effect), in the reported stability criteria, the load disturbance is mathematically modelled as a norm-bounded nonlinear time-varying function of current and delayed state vectors, and subsequently incorporated into the delay-dependent stability analysis. Two cases of time-delays are considered in the stability analysis: time-varying single feedback-loop delay element and time-invariant multiple feedback-loop delay elements. In addition, to realize less conservative stability criteria with minimal number of decision variables, in the stability analysis, tighter integral inequalities, viz., reciprocal convex combination lemma (for time-varying delay case) and Jenson integral inequality (for time-invariant delay case) are employed. The proposed results are illustrated on standard benchmark LFC systems, and supported suitably by simulation results.

Design of Robust Load Frequency Controller: H ∞ Loop Shaping Approach

Abstract In this article, a robust load frequency controller is designed by adopting H ∞ loop shaping design procedure given in [1]. Using a selected pre-compensator, the singular values of the nominal system are modified to satisfy the requirements for closed-loop performance specifications along with the sufficient robust stability margin of the system. The design of stabilizing controller for the perturbed plant is performed in the framework of normalized coprime factors of the shaped plant. This method does not require an iterative procedure for robust stability margin and thus improves the computational efficiency. The real μ-analysis is adopted to ensure the robust stability of the system. The effectiveness of the method has been demonstrated through the simulation studies of a two-area interconnected power system.

Design of a robust load—frequency controller for interconnected power systems based on the singular-value decomposition method

Abstract A robust control scheme is presented for the load—frequency control of an interconnected power system with uncertain parameters. A combination of the singular-value decomposition (SVD) technique and the Riccati equation approach is adopted to design a robust controller. Stability analysis of the closed-loop interconnected system for all admissible uncertainties is considered. The effectiveness of the proposed robust control scheme has been verified through simulation studies on a two-area power system model. The performance robustness of the proposed control algorithm is compared with recent results and found to be much better.