An estimation algorithm for multirate sampled digital control systems

We consider multirate digital control systems which consist of an interconnection of a continuous-time nonlinear plant (described by ordinary differential equations) and a digital lifted controller (described by ordinary difference equations). The input to the digital controller consists of the multirate sampled output of the plant and the input to the continuous-time plant consists of the multirate hold output of the digital controller. We show that when quantizer nonlinearities are neglected, then under reasonable conditions (which exclude the critical cases), the stability properties (in the Lyapunov sense) of the trivial solution of the nonlinear multirate digital control system can be deduced from the stability properties of the trivial solution of its linearization. When quantizer nonlinearities are not neglected, corresponding results can be established for Lagrange stability rather than Lyapunov stability of an equilibrium.

Part 1 Computers in control systems: historical development digital computer interfacing structure of a digital control loop interface units data representation and aliasing. Part 2 The z-transformation: definition of the z-transform z-transform properties inverse z-transform pulse of z-transfer functions of systems discrete approximations numerical integration pole-zero mapping modified z-transform multi-rate sampling systems analysis of multi-rate systems fast-slow multi-rate systems closed-loop multi-rate systems. Part 3 Analysis of sampled-data control systems z-transformation of systems stability in discrete systems time domain analysis root locus analysis frequency domain analysis. Part 4 Digital compensator design: continuous domain design digital design digital root locas design state feedback design digital PID control disign deadbeat response design optimal control design controller design in the presence of noise. Part 5 Real-time computer control systems: hardware requirements the digital computer and peripheral equipment the real-time clock interface units software aspects controller implementation programming languages system design co-ordination sampling rate selection and quantization errors computer/device communications interrupt handling multi-tasking and background/foreground. Part 6 Advances in computer control: artificial intelligence expert systems examples of expert systems knowledge based systems in control engineering conventional controller design methods manual control methods fuzzy sets and rule-based control basic fuzzy operations fuzzy relations fuzzy control algorithms parallel processing techniques parallel computers algorithms for parallel (MIMD) computers programming parallel computers performance of parallel computers parallel processing in control engineering matrix algebra numerical integration fault tolerance. Appendices: Table of laplace and z-transforms continuous second-order systems response specifications frequency response characteristics the transputer and occam occam overview transputer systems and occam configuration vibration control of a flexible cantilever system simulation modelling and state estimation controller design user interface solutions.

This paper discusses a new design method for state feedback multirate control with current estimator. A computationally effective multirate digital control scheme, in which the control outputs are calculated based only on the state estimates at sampling instants, is presented. It is shown that the states of the redesigned state feedback multirate control system match the states of conventional state feedback multirate control system at every sampling instant. The redesigned method is applied to a HDD servo control systems. The experimental results show that the performance of the redesigned multirate system is similar to that of the conventional multirate design in terms of open loop bandwidth, phase margin and gain margin.

This paper presents an analytic design of multirate controllers to guarantee stable haptic interaction and high fidelity. When the reflective force is computed by using slowly simulated virtual model, the control frequency of the conventional controller becomes low. This increases the zero-order-hold effect, and makes the system unstable. We propose a multirate control method to reduce the zero-order-hold effect. The multirate controller is implemented by adding a high frequency controller to the conventional controller. The high-frequency controller is designed to compensate the energy generated by the conventional controller. The stability analysis of the multirate haptic control system shows that the stiffness of the virtual model can be increased while maintaining the stability. A nonlinear virtual coupling is designed using this multirate control scheme. The multirate controller is evaluated by mathematical analysis and experiments.

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.

This paper is concerned with haptic simulation in multi-user virtual environments in which the users can haptically interact in a shared virtual world from separate workstations over an Ethernet local-area Network (LAN). High-fidelity haptic rendering requires a minimum control update rate of 1000Hz which is beyond the capability of popular network protocols such as the UDP and TCP/IP. Consequently, a multi-rate control strategy is adopted in which local force-feedback loops are executed at higher rates than data packet transmission between the user workstations. Two control architectures, i.e. centralized and distributed, are presented and their stability margins are compared. Two methods for mathematical modelling and analysis of the proposed multi-rate haptic control systems are examined. Analytical and experimental results demonstrate that the distributed control architecture is superior to the centralized controller from performance and stability perspectives. This is confirmed through experiments with a dual-user dual-finger haptic rendering platform.

Variance-constrained H∞ state estimation for time-varying multi-rate systems with redundant channels: The finite-horizon case

In haptic communication via the network, transmission period is not able to be designed uniquely since it restricted by the line bandwidth, transmission protocol, hardware constraints and so on. To address this problem, downsampling is often employed. Additionally, to enhance the performance of downsampled system, multirate control is proposed. However, the quantitative analysis on downsampling and multirate control are not treated. Therefore, this paper treats downsampling and multirate control system, and performs quantitative analysis by using hybrid parameter. In order to reveal the most effective combination of holder and single or multirate, holders (ZOH, DFOH and PFOH) are considered explicitly, and it is formulated to Laplace domain. The effectiveness of each combination is verified through experiments.

This brief is concerned with the joint state and fault estimation problem for a class of multi-rate systems with dynamical bias. To reflect real practice, the multi-rate sampling is considered which allows the sensor sampling rate and the state update rate to be different. The sensor is subject to the sensor fault that changes according to a dynamic equation. Instead of applying the traditional lifting technique, we introduce a time-varying delay into the measurement equation so as to transform the multi-rate systems into single-rate ones. The aim of this brief is to develop a joint state and fault estimation algorithm with minimized estimation error covariance. The recursion of the estimation error covariance is first derived, and appropriate estimator gains are then characterized that minimizes the estimation error covariance. A simulation example on the DC servo system is given to confirm the usefulness of the developed recursive state and fault estimation algorithm.

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.

The intense requirements of high-speed implementations of MultiDimensional (MD) Digital Signal Processing (DSP) systems justify the Application Specific Integrated Circuits (ASIC) designs and/or multiprocessor implementations. MD retiming has been recently proposed to improve the circuitry performance in high-level synthesis of single-rate MD DSP systems. This paper has conducted new theoretical analysis of MD multirate DSP systems modeled in data-flow graphs, and proposes intercalation of MD multirate systems so that unified MD retiming operations can be applied on multidimensional multirate DSP systems. By retiming and intercalation, full intra-iteration parallelism is achieved and functional elements can be executed simultaneously on circuits for the generic class of MD multirate DSP systems.KeywordsMultirate Signal ProcessingMD Data Flow GraphMultidimenional Retiming

A frequency analysis procedure for single and multirate sampled-data control systems is presented. The method is taking the inter-sample behaviour into account, and for a sinusoidal input the system power gain is calculated. Also the close correspondence between this method and the principal gain for continuous-time MIMO systems is discussed. Finally our method is illustrated on a sampled-data SISO system.

Internet-based control is the way of monitoring and adjusting plants from a remote site over the Internet. The major challenge of this new kind of control systems is how to deal with Internet time delay. Our recent study illustrated that there is a great potential to overcome Internet time delay from the control system architecture aspect such as by using multi-rate control schemes. In this paper, we formulate a new class of dual-rate control systems with Internet time delay at both feedback and feed-forward channels and investigate their asymptotic stability properties. Some new necessary and sufficient criteria of asymptotic stability for such dual-rate control systems are established. Two examples are given to illustrate the effectiveness of the theoretical results.

This paper focus on the digital control system for bearingless permanent magnet rotor motors. The bearingless permanent magnet synchronous motor (BPMSM) is an innovational type of motor, as bearingless motors have all advantages of magnetic bearings, they play an important role in solving difficult problems of special electric drives in life science, chemical processing industry, semiconductor manufacturing industry, foodstuff processing industry, and so on. In the paper, based on the basic working principle of BPMSM, the mathematics models of the radial forces and rotation part on BPMSM are deduced by adopting rotor magnetic field oriented control (FOC) strategy. A digital vector control system according to the demand of decoupling is designed and presented using DSP technique. An experimental platform of digital control system is developed to meet the need, The experiment results have shown that the steady suspension of the rotor is realized and the speed of the rotor can be continuously adjusted within the range of 0-3000 r/min.

The Hubble Space Telescope (HST) is designed to carry five major scientific instruments to collect imagery, spectrographic, and photometric astronomical data. The Pointing Control System is to achieve pointing accuracies and line of sight jitter levels an order of magni-tude less than can be achieved with ground mounted telescopes. In addition, the HST must be able to acquire and track solar system targets with apparent motion up to 0."21/s. Such targets include planetary satellites, planetary surface features and comets. It is to perform this tracking with an accuracy under 0."03 at the maximum rate. Tracking of solar objects by the Space Telescope accounts for the effects of velocity aberration and parallax, as well as solar targeting a celestial object in a science instrument aperture. The design of the Pointing Control System solar object tracking features is discussed, with emphasis on the special timing and granulation problems inherent with a sampled data, multi-rate digital control system.