STABILITY AND SENSITIVITY OF NONLINEAR SAMPLED DATA SYSTEMS

Stability and sensitivity of nonlinear sampled data systems

Bifurcation and Chaos in Nonlinear Sampled-Data Control Systems

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.

The insertion of communication networks in closed-loop of digital control systems makes the system synthesis and analysis complex. In this paper, we consider the combination of classical reliability, risk and safety evaluation with typical control system through digital networked control systems. The main purpose is to study the influence of transmission delays and packet dropouts on the reliability of digital networked control systems by using a modified statistical method-Monte Carlo simulation. The behaviors of two types of fault are modelled by different statistical distribution. The control strategies we apply for digital control systems are Proportion Integration Differentiation control strategies, generated by Genetic Algorithm. In terms of a realistic system model, we evaluate and compare the influences on the reliability of digital networked control systems with different control strategies from quantitative aspect. Numerical examples are presented to illustrate the effectiveness and correctness of the approach.

Recently, the Plant Input Mapping (PIM) method was proposed as a digital-redesign (or an emulation) approach in digital control system design. This method guarantees stability of a redesigned digital control system for a wide range of sampling periods. In this paper the PIM method is applied to the design of a digital model-matching flight control system. In the model-matching control system design a plant must have no unstable zeros. However, unstable zeros appear for small sampling periods in a step invariance model of a continuous-time (CT) plant with the relative degree greater than two, even if the CT plant has no unstable zeros. Hence, in such a case, the direct-digital approach cannot be applied to the design of a digital model-matching control system. By contrast, the digital-redesign approach such as the Tustin's method or the PIM method is free from the problem. Simulation results for an unstable VTOL aircraft show that the proposed method gives better performance than the conventional design methods.

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

An optimal dual-rate digital redesign method is proposed that can be applied to continuous-time and fast-rate discrete-time control systems. The paper presents a technique, which relies on the solution of a dual-rate H2 discrete-time control problem, to convert such systems to either a slow-rate or a dual-rate sampled-data control system while guaranteeing closed-loop stability and performance in the discrete-time H2 sense. The proposed technique results in sampled-data control systems providing satisfactory closed-loop performances over an extended range of sampling rates, as compared with other widely used methods of digital redesign. Furthermore, the proposed digital redesign technique is useful in practice since it allows the designer to constrain the complexity of the digital controllers, thus resulting in low-order digital controllers easily implementable in software code and free of causality and real-time problems. Numerical examples provide a comparison of the proposed digital redesign technique with well-known approaches.

International Journal of Adaptive Control and Signal ProcessingVolume 12, Issue 7 p. 600-602 Book ReviewFree Access Digital Control Systems, P. N. Paraskevopoulos, Prentice Hall Inc., Hemel Hempstead, Herts, England, U.K., 1996, ISBN 0-13-341876-6, xv + 383pp., Price: £25.95 T. Chen, T. Chen Department of Electrical and Computer Engineering, The University of Alberta, Edmonton, Alberta, Canada T6G 2G7Search for more papers by this author T. Chen, T. Chen Department of Electrical and Computer Engineering, The University of Alberta, Edmonton, Alberta, Canada T6G 2G7Search for more papers by this author First published: 18 December 1998 https://doi.org/10.1002/(SICI)1099-1115(199811)12:7<600::AID-ACS509>3.0.CO;2-CAboutPDF ToolsRequest permissionExport citationAdd to favoritesTrack citation ShareShare Give accessShare full text accessShare full-text accessPlease review our Terms and Conditions of Use and check box below to share full-text version of article.I have read and accept the Wiley Online Library Terms and Conditions of UseShareable LinkUse the link below to share a full-text version of this article with your friends and colleagues. Learn more.Copy URL Share a linkShare onFacebookTwitterLinkedInRedditWechat No abstract is available for this article. References 1 Franklin, G. F., J. D., Powell and M. L. Workman, Digital Control of Dynamic Systems, Addison-Wesley, Reading, MA, 1990. 2 Aström, K. J. and B., Wittenmark, Computer Control Systems, Prentice-Hall, Englewood Cliffs; NJ, 1984. 3 Phillips, C. L. and H. T., Nagal, Digital Control System Analysis and Design, Prentice-Hall, Englewood Cliffs, NJ, 1990. 4 Ogata, K., Discrete-Time Control Systems, Prentice-Hall, Englewood Cliffs, NJ, 1987. 5 Chen, T. and B. A., Francis, Optimal Sampled-Data Control Systems, Springer, Berlin, 1995. Volume12, Issue7November 1998Pages 600-602 ReferencesRelatedInformation

Basing on lifting technology, this paper researches a design method for multirate sampled-data control system in the background of flight control system design, which consummates the theory of multirate sampled-date control system design for further steps, and provides a method to design multirate sampled-data controller. As the reason of uncertainty in the aircraft model and the need of different sampling frequencies in different control loops, H <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</inf> -optimal multirate sampled-data control is considered. First, multirate sampled-data control system is outlined, and then the signal description are presented. Because of multirate sampled-data system is time-variant, the direct digital controller design becomes difficult. The equivalent discrete time-invariant systems can be converted from the linear time-variant systems through lifting technology. Then the H <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</inf> discretization of multirate sampled-data systems is researched. After the sampled-data control system was lifted, the equivalent L <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</inf> [0, h) -induced norm is proven. Base on the above, the method of H <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</inf> -optimal multirate sampled-data control is summarized. A height control is simulated using a simplified aircraft model to illustrate the design. The simulation shows that the multirate Sampled-data control system can achieve the satisfactory objective accurately and optimally.

A digital closed-loop control system with all digital phase locked loop (ADPLL) is designed and optimized, in order to improve the bias stability and transient response of the gyroscope. The nonlinear mathematical models for the closed-loop amplitude and phase control system are established. The linearization method is applied to analyze the nonlinear models. The control parameters of the drive loop are optimized. The experimental results show that the phase deviation between the demodulation reference signal of the drive loop and the sense signal is less than 0.25° in the temperature range from-40°C to 60°C, within 0.15° of the variation. At room temperature, the overshoot amount of the gyroscope control system is 4.5% with setting time of 0.12s. The bias stability is 1.45°h. Compared to the analog control scheme, the digital control system has advantages of short setting time, small overshoot, short phase locked time, large locked range, high phase precision, etc.

TRANSPORT LAG in sampled-data control systems influences their stability. If this influence is studied as the function of transport lag and other system parameters, the design procedure becomes cumbersome. This paper, which applies Mitrovi?'s algebraic method,1?3 presents a new way to analyze and synthesize various sampled-data control systems such as the cyclic variable-rate, multirate, and those with nonsynchronized samplers. Other related problems are greatly facilitated by this method also.

The article discusses an approach that allows you to move from a discrete model of a digital controller to its analog representation, which provides analysis and synthesis of digital systems in the continuous domain, taking into account the quantization period. In the proposed method for the control system, a transition is made from the discrete z-region to the Laplace region. This approach makes it possible to consider the quantization time as an additional parameter of the digital control system settings, evaluate the influence of the selected quantization period not only on the behavior of the set for discrete at the moments of quantization, but also in between, to evaluate the temporal characteristics of the control system at any time. The analog representation of the digital controller enables the calculation of transients using MatLAB. The article provides examples of the synthesis for a digital control system in the frequency domain based on the frequency response characteristic of an open-loop control system taking into account the quantization period. The method can be used by automation specialists to analyze and setting digital control systems

With the development of modern automatic control technology, digital control technology has advanced technology and inherent advantages compared with traditional analog control technology. Therefore, the use of digital instrument and control system has become an inevitable trend of global nuclear power construction. Nuclear power embedded real-time operating system is an important part of digital instrument and control system in nuclear power plant. It is responsible for managing the hardware resources of the whole system and providing operation environment for application software. Its safety directly affects the safety of instrument and control system. This paper studies the application of embedded information technology in the safety of nuclear power plant, and puts forward a safety related scheme of embedded information system. The scheme fully considers the confidentiality, integrity and availability of information in the digital instrument and control system of nuclear power plant. The application results show that the scheme can meet the information security requirements of nuclear power instrument and control system, and has reference and guiding significance for the research and development of nuclear power embedded real-time operating system.

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

The authors consider sampled-data control systems which consist of an interconnection of a continuous-time nonlinear plant and a digital controller which has quantizers (but is otherwise linear), along with the required interface elements (A/D and D/A converters). In the present paper the authors study the qualitative effects of the quantizers and the plant nonlinearities of these systems.