Dina Shona Laila

A note on input-to-state stabilization for nonlinear sampled-data systems

We provide a framework for the design of L/sub /spl infin// stabilizing controllers via approximate discrete-time models for sampled-data nonlinear systems with disturbances. In particular, we present sufficient conditions under which a discrete-time controller that input-to-state stabilizes an approximate discrete-time model of a nonlinear plant with disturbances would also input-to-state stabilize (in an appropriate sense) the exact discrete-time plant model.

Sampled-Data Control of Nonlinear Systems

This chapter provides some of the main ideas resulting from recent developments in sampled-data control of nonlinear systems. We have tried to bring the basic parts of the new developments within the comfortable grasp of graduate students. Instead of presenting the more general results that are available in the literature, we opted to present their less general versions that are easier to understand and whose proofs are easier to follow. We note that some of the proofs we present have not appeared in the literature in this simplified form. Hence, we believe that this chapter will serve as an important reference for students and researchers that are willing to learn about this area of research.

A Refined Hilbert–Huang Transform With Applications to Interarea Oscillation Monitoring

This paper focuses on the refinement of standard Hilbert-Huang transform (HHT) technique to accurately characterize time varying, multicomponents interarea oscillations. Several improved masking techniques for empirical mode decomposition (EMD) and a local Hilbert transformer are proposed and a number of issues regarding their use and interpretation are identified. Simulated response data from a complex power system model are used to assess the efficacy of the proposed techniques for capturing the temporal evolution of critical system modes. It is shown that the combination of the proposed methods result in superior frequency and temporal resolution than other approaches for analyzing complicated nonstationary oscillations.

Discrete-time Lyapunov-based small-gain theorem for parameterized interconnected ISS systems

Input-to-state stability (ISS) of a feedback interconnection of two discrete-time ISS systems satisfying an appropriate small gain condition is investigated via the Lyapunov method. In particular, an ISS Lyapunov function for the overall system is constructed from the ISS Lyapunov functions of the two subsystems. We consider parameterized families of discrete-time systems that naturally arise when an approximate discrete-time model is used in controller design for a sampled-data system.

Monitoring of inter-area oscillations under ambient conditions using subspace identification

The damping of inter-area oscillations is a major concern for many power system operators. This paper presents a novel method for monitoring of inter-area oscillations based on system identification using subspace techniques and modal analysis. The method enables the detection of oscillatory modes as well as the damping and frequency of those from ambient data recorded during normal operation of the power system. Through modal observability which is also estimated, the parts of the grid participating in an oscillation mode can be determined. The method is suitable for real-time implementation. The paper demonstrates application of the method to measurements from the Nordic power system and to synthetic data. The technique can be used to increase operator situational awareness and provide early warning in case of potential for unstable inter-area mode oscillations.

Input-to-state stability for discrete-time time-varying systems with applications to robust stabilization of systems in power form

Input-to-state stability (ISS) of a parameterized family of discrete-time time-varying nonlinear systems is investigated. A converse Lyapunov theorem for such systems is developed. We consider parameterized families of discrete-time systems and concentrate on a semiglobal practical type of stability that naturally arises when an approximate discrete-time model is used to design a controller for a sampled-data system. An application of our main result to time-varying periodic systems is presented, and this is used to solve a robust stabilization problem, namely to design a control law for systems in power form yielding semiglobal practical ISS (SP-ISS).

Changing supply rates for input-output to state stable discrete-time nonlinear systems with applications

We present results on changing supply rates for input-output to state stable discrete-time nonlinear systems. Our results can be used to combine two Lyapunov functions, none of which can be used to verify that the system has a certain property, into a new composite Lyapunov function from which the property of interest can be concluded. The results are stated for parameterized families of discrete-time systems that naturally arise when an approximate discrete-time model is used to design a controller for a sampled-data system. We present several applications of our results: (i) a LaSalle criterion for input to state stability (ISS) of discrete-time systems; (ii) constructing ISS Lyapunov functions for time-varying discrete-time cascaded systems; (iii) testing ISS of discrete-time systems using positive semidefinite Lyapunov functions; (iv) observer-based input to state stabilization of discrete-time systems. Our results are exploited in a case study of a two-link manipulator and some simulation results that illustrate advantages of our approach are presented.

Adaptive Cruise Control System: Comparing Gain-Scheduling PI and LQ Controllers

Abstract Over the recent years, a considerable growth in the number of vehicles on the road has been observed. This increases importance of vehicle safety and minimization of fuel consumption, subsequently prompting manufacturers to equip cars, with more advanced features such as adaptive cruise control (ACC)or collision avoidance and collision warning system (CWS). This paper investigates two control applications design namely the gain scheduling proportional-integral (GSPI) control and gain scheduling Linear Quadratic (GSLQ)control for ACC, covering a high range speed. The control system consist of two loops in cascade, with the inner loop controlling the vehicle speed and the outer loop switching between the cruise control (CC) and the ACC mode and calculating the reference speed. A nonlinear dynamic model of the vehicle is constructed and then a set of operating points is determined and then a of linear models is extracted in operating point. For each operating point, PI and LQ controllers are obtained off-line. An integrated Simulink model including the nonlinear dynamic vehicle model and the ACC controller (either PI or LQ) was used to test the controllers in various traffic scenarios. Comparison results between the two controllers applications is provided to show the validity of the design.

Lyapunov based small-gain theorem for parameterized discrete-time interconnected ISS systems

Input-to-state stability (ISS) of a feedback interconnection of two discrete-time ISS systems satisfying an appropriate small gain condition is investigated via the Lyapunov method. In particular, an ISS Lyapunov function for the overall system is constructed from the ISS Lyapunov functions of the two subsystems. We consider parameterized families of discrete-time systems that naturally arise when an approximate discrete-time model is used to design a controller for a sampled-data system.

Nonlinear damping computation and envelope detection using Hilbert transform and its application to power systems wide area monitoring

An important feature of an oscillation is the damping characterization. For a system, the damping characteristic of the oscillation that occurs on its states or outputs gives the information of the stability of the system. There are various techniques to compute the damping ratio of a linear model of a system, but the tools that apply to nonlinear systems are scarce. In this paper, we utilize the Hilbert transform of nonlinear and nonstationary oscillatory signals to compute the instantaneous damping of the signals. The technique is applied to the computation of the damping ratio of power systems signals that contain inter area oscillations. This damping computation is important for power system monitoring.