Time-varying Feedback Control Research Articles

Time-varying feedback control of nonaffine nonlinear systems without drift

Sufficient conditions are presented under which a general nonlinear system without drift is globally asymptotically stabilizable by time-varying state feedback. A novel approach is developed for the design of a time-varying smooth state feedback controller. The controller is explicitly constructed by using the bounded state feedback strategy (Lin, 1995, 1996) combined with Lyapunov technique as well as lossless systems theory. This work incorporates earlier global stabilization results (Coron, 1992; Pomet, 1992) for controllable affine systems without drift, which are known not to be smoothly stabilizable via any time-invariant state feedback.

Exponential stabilization of nonholonomic chained systems

This paper presents a feedback control scheme for the stabilization of two-input, driftless, chained nonholonomic systems, also called chained form. These systems are controllable but not asymptotically stabilizable by a smooth static-state feedback control law. In addition, exponential stability cannot be obtained with a smooth, time-varying feedback control law. Here, global, asymptotical stability with exponential convergence is achieved about any desired configuration by using a nonsmooth, time-varying feedback control law. The control law depends, in addition to the state and time, on a function which is constant except at predefined instants of time where the function is recomputed as a nonsmooth function of the state. The inputs are differentiable with respect to time and tend exponentially toward zero. For use in the analysis, a lemma on the exponential convergence of a stable time-varying nonlinear system perturbed by an exponentially decaying signal is presented. Simulation results are also shown.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Time-varying feedback for the stabilization of fixed modes in decentralized control systems

The decentralized structure of a large-scale control system imposes constraints on the feedback strategies that can be used. This may lead to fixed modes and structurally fixed modes. In this paper it is discussed to what extent decentralized time-varying feedback control strategies may eliminate fixed modes and structurally fixed modes.

An algorithm for non-linear space—Time nuclear reactor control

A novel multivariable control algorithm for non-linear space-time nuclear reactor dynamics is proposed in this paper. The multivariable control algorithm is based on a mathematical model of the nuclear reactor which includes: a single energy group of neutrons, delayed neutron precursors, iodine, xenon and thermal-hydraulic feedback. The multivariable control algorithm is composed of non-linear time-varying feedforward and feedback control signals, a reference model of the nuclear reactor and a dynamic observer. The non-linear proportional plus integral feedback controller forces the nuclear reactor to follow the response of the reference model. The dynamic observer estimates the unmeasurable state variables. The feedforward and feedback control signals are determined in a novel approach by specifying the form of the closed-loop response of the neutron density variables. By virtue of the multivariable control algorithm the closed-loop differential equations are linear and time-varying. A linear stability analysis for base-load and load-cycle operation indicates that the closed-loop system is stable provided that the thermal-hydraulic subsystem is inherently stable. The simulated dynamic response indicates that the multivariable control algorithm provides excellent response characteristics.

On the stability of linear time-varying feedback systems with random parameters

The problem of finding frequency-domain conditions which guarantee asymptotic stability with probability 1 of linear systems with a time-varying feedback controller and having white noise parameter variations is considered. It is shown that the stochastic version of the second method of Liapunov can be employed for deriving sufficient conditions for stability of such systems. Stability criteria are derived after taking into account restrictions on the gain as well as on the rate of change of the gain of the controller.

L p and Orlicz stability of a class of nonlinear timevarying feedback control systems

L p and Orlicz stability of a class of nonlinear timevarying feedback control systems

Stability and performance analysis of a certain class of nonlinear time varying feedback control systems

The partitioning technique and the state variable approach have been applied to analyze and to study the behaviour of a control system whose dynamic performance can in general be described by a nonlinear differential equation containing some linear, some nonlinear, and a forcing function terms. By placing suitable restrictions on the system equation, it was found that the state variables, which represent the state of the system, belong to an L 2 space. Under the assumed restrictions, the admissible system was found to satisfy the definition of asymptotic stability in the sense of Lyapunov. Utilizing two different definitions of the norm, the system trajectory was analyzed. During the interval of operation considered, expressions for the required norms were obtained inside which all possible states of system remain. Included will be found an example to illustrate the method presented.

Synthesis of feedback controls using optimization theory--An example

This paper illustrates the use of optimization theory in the synthesis of a linear time-varying feedback control by carrying out the design of an aircraft landing system. The optimization method employed is the Parametric Expansion Method. A number of different controls are synthesized by selecting different functional forms for the weighting factors appearing in the error index formulated from the performance requirements. These controls are compared by presenting the landing trajectories of the aircraft.