Robust Stability Evaluation of Sampled-Data Control Systems with a Sector Nonlinearity

The robust stability criterion for sampled-data control systems with a sector nonlinearity was presented in our previous papers (1996, 1998). Although it is applicable only to the sampled-data control system of a certain class, a usual discrete-time control system belongs to this type of class. The criterion contains the robust stability condition in regard to the nonlinear allowable band (sector) for continuous-time systems and the linear allowable gain band (interval set) for discrete-time systems. The paper focuses primarily on the concept of robust stability in order to analyze a nonlinear element by the linear gain band, in other words, the validity of Aizerman's conjecture extended into discrete-time systems.

Bifurcation and Chaos in Nonlinear Sampled-Data Control Systems

Many of nonlinear control systems are sampled-data system, i.e. the continuous-time nonlinear plants are controlled by digital controllers. So it is important to investigate that if the solution of the discrete-time output regulation problem is effective to sampled-data nonlinear control systems. Recently a feedforward neural network based approach to solving the discrete regulator equations has been presented. This approach leads to an effective way to practically solve the discrete nonlinear output regulation problem. In this paper the approach is used to sampled-data nonlinear control system. The simulation of the sampled-data system shows that the control law designed by the proposed approach performs much better than the linear control law does.

In this paper, we provide a novel defence strategy for a nonlinear sampled-data control system under zero-dynamics attacks. In a sampled data structure, sampling zeros induced by discretization make a system vulnerable to deception attacks. we analyze the dissipativity in the zero-dynamics part of the system equipped with a multi-rate setup and find conditions on sampling rates to neutralize the attacker's target plan. We show that, under some mild conditions, using multi-rate sampling in the nonlinear sampled-data system not only preserves the dissipativity property of the intrinsic zero-dynamics but also stabilizes the extrinsic zero-dynamics induced by the sample and hold process, and as a result attenuate the effects of attacks on the system stability. Finally, a numerical example is used to illustrate the effectiveness of the proposed approach.

In this literature, a data pre-processing circuit designs and analyses for an infrared image seeker of a subsonic cruise missile are proposed.The flight speed of the missile is 250m/s.Therefore, automatic contrast control and automatic brightness control are usually needed to keep wanted contrast and brightness for best image properties in target recognition and tracking; especially for the missile at the terminal approaching phase to prevent signal saturation.Signal saturation implies target lost.The major parameters of imaging systems for contrast and brightness controls include average, maximum and minimum of gray level of the whole picture in the sampling interval.Therefore, the overall system is a complicated nonlinear sampled-data control system.It is difficult to describe, analyze and design the system.In this literature, the overall system is first decomposed into two linearized sampled-data control systems to get needed loop compensations, and verified by a special range-dependent testing signal to the overall system secondly.The controlled system is further verified by a thermal plate and real flight testing.Testing results give the proposed method can provide effective way to analyze and design the considered system. Minimal (MIN) Brightness Maximal (MAX) BrightnessD/A APC Control Signal(60Hz) CCD Focal Plane Array Pre-Processing Circuits AGC Control Circuit APC Control Circuit Amplifier Circuit A/D D/A AGC Control Signal(60Hz) Addressing for Desired Cell (256x256x60Hz) Micro-Processor MAX/ MIN/ AVG Digital Filters for APC Digital Filters for AGC

<div class="htmlview paragraph">In this work we study the stability of digital controls of flexible/Vibratory aerospace/automobile systems by the graph norm technique, occurring in sampled-data control systems due to sampling period variations. To do so, this work tries to establish regions (graphs) of stability and instability in a Banach Space, the distances (norms) between them and a given design to detect analytically and/or numerically its margins of stability or conditions of instability. Based on that, we sketch the first steps for a design methodology of stable digital controllers of flexible/vibratory systems embedded in a sampled-data system with adjustable sampling periods of A/D and D/A converters. A short tutorial about the graph norm technique is also given and some theoretical results as well numerical results are shown. This work was done in two folds to unmask the stability secrets hidden in a general sampled-data control system, until today not revelated. The first part we have used the graph norm and at the second part we made use of the Liapunov stability theory.</div>

In this paper, we develop a discrete-time controller for continuous-time nonlinear plant. The exact dynamics of the plant are unknown, but some bounds of the dynamics are assumed. The controller consists of a supervisory controller and an adaptive fuzzy controller. The supervisory controller is designed to guarantee the boundedness of the state, and the adaptive fuzzy controller is designed to control the state to track a given trajectory. More specifically, the supervisory controller is constructed from the bounds of the plant dynamics in such a way that once the state moves outside the stable region, the supervisory controller will take action to draw it back. The adaptive fuzzy controller is constructed from the measured state and control data using the nearest neighborhood clustering algorithm. Both the supervisory controller and the adaptive fuzzy controller operate at discrete-time points, whereas the plant keeps running continuously. We give rigorous proofs of the properties of this sampled-data nonlinear adaptive control system.

Stability and sensitivity of nonlinear sampled data systems

Theory of nonlinear control

Describes a graphical evaluation of the robust stability in a frequency domain based on the results from our previous papers in which Popov's criterion was expressed in an explicit form. The control system described herein is a feedback system with one time-invariant nonlinear element (a sector nonlinearity) in the forward path. By applying the small gain theorem that concerns L/sub 2/ gain in regard to a nonlinear subsystem with a free parameter, a robust stability condition for control systems with time-invariant nonlinearity is presented. Using this concept, we show a representation of an off-axis circle criterion on a Nyquist diagram, and propose an evaluation method of the stability from the relative position with the vector locus of the open loop frequency response characteristic.

Multirate, sampled-data control systems are analyzed in the frequency domain, taking the inter-sample behavior into account. The focus of the analysis is both on the rejection of disturbances within a certain frequency region, and on the robust stability properties. Due to the periodic behavior of such systems, a distinction is made between the performance frequency response (PFR) and the robust frequency response (RFR). The RFR is related to current frequency response approaches for sampled-data systems.

Output feedback stabilization of nonlinear dual-rate sampled-data systems via an approximate discrete-time model

This paper studies input/output stability of nonlinear sampled-data systems with a sector nonlinearity. A circle-criterion type of stability condition was derived previously, for the case where the sector nonlinearity is possibly time-varying and dynamical. In contrast, this paper deals with the case where it is time-invariant and memoryless, and gives a less conservative stability criterion for such a case. It is derived by applying the multiplier technique, and corresponds to the Popov criterion in the continuous-time setting. The arguments make use of the frequency-domain theory of sampled-data systems, and a sort of convexity in the frequency domain plays an important role. A method with the cutting-plane algorithm is provided for finding a multiplier that proves stability.

Popov-Type Criterion for Stability of Nonlinear Sampled-Data Systems

STABILITY AND SENSITIVITY OF NONLINEAR SAMPLED DATA SYSTEMS