Sensitivity properties of multirate feedback control systems, basedon eigenstructure assignment

Some sampled-data systems, e.g., fly-by-wire control schemes, have a necessarily multirate structure, various input and/or outputs sampled at different rates. When considering a multirate system which has parameter uncertainty, it is important to examine ways in which the full freedom of the multivariable design can be utilized to minimize the sensitivity to parameter variations. Given the accompanying problems induced by intersample ripple disturbance. This note examines the design capabilities of a class of multirate systems with multiple input and fixed state sampling rates (MIFS), based on eigenstructure assignment. Although the use of eigenstructure assignment for continuous and single rate discrete systems is well understood, the eigenstructure assignment for the design of multirate feedback systems is an open topic of research. Accepting that the problems of intersample ripple are often magnified through multirate control, there are advantages in terms of increased freedom for minimizing sensitivity and optimizing robustness to parameter variations. A special feature of the MIFS class of multirate systems is the ability to introduce extra design freedom in the eigenproblem by a suitable choice of eigenstructure assignment and sample rates. The criteria for the selection of minimum sample rates to produce this extra freedom, and the implication that this has on the eigenstructure assignment problem, are outlined. The improved insensitivity properties are demonstrated using an example comparing the performance of multirate and corresponding single rate designs     

Comparative study of discretization zero dynamics behaviors in two multirate cases

It is well known that the existence of unstable zero dynamics is recognized as a major barrier in many control systems. When the usual digital control with zero-order hold (ZOH) or fractional-order hold (FROH) input is used, unstable zero dynamics inevitably appear in the discrete-time model even though the continuous-time system with relative degree more than two is of minimum phase. This paper investigates the zero dynamics, as the sampling period tends to zero, of sampled-data models composed of a generalized sample hold function (GSHF), a continuous-time nonlinear plant and a sampler in cascade. More precisely, we show how an approximate sampled-data model can be obtained for nonlinear systems with two special GSHF cases such that sampled zero dynamics of the resulting model can be arbitrarily placed. Further, two GSHFs with appropriate parameters provide nonlinear zero dynamics as stable as possible, or with improved stability properties even when unstable, for a given continuous-time plant. It is also shown that the intersample behavior arising from the multirate input can be localised by appropriately selecting the design parameters based on the stability condition of the zero dynamics. The results presented here generalize well-known ideas from the linear to nonlinear cases.     

Interactive control system design by a mixedH∞-parameter space method

This paper presents an interactive graphical method to determine sets of stabilizing controllers satisfying any combination of constraints on the sensitivity, complementary sensitivity, and input sensitivity transfer functions. The method is limited to single-input/single-output systems but offers significant advantages over current H^∞ methods. It can handle pure time delays in an exact manner. The weighting functions need not be rational. By virtue of producing the required parameter space region for the frequency response criteria, subsequent direct time-domain optimization is possible. The controllers obtained are of lower order for comparable performance than those produced by current H^∞ techniques. The method is particularly well suited to robust control problems, where frequency domain constraints emerge from the analysis of uncertainties in the system, and also to suboptimal problems, where the frequency-domain loop shaping is used to achieve time-domain specifications     

Event-driven intermittent control

An intermittent controller with fixed sampling interval is recast as an event-driven controller. The key aspect of intermittent control that makes this possible is the use of basis functions, or, equivalently, a generalised hold, to generate the intersample open-loop control signal. The controller incorporates both feedforward events in response to known signals and feedback events in response to detected disturbances. The latter feature makes use of an extended basis-function generator to generate open-loop predictions of states to be compared with measured or observed states. Intermittent control is based on an underlying continuous-time controller; it is emphasised that the design of this continuous-time controller is important, particularly in the presence of input disturbances. Illustrative simulation examples are given.     

A function space approach to sampled data control systems andtracking problems

This paper presents a new framework for hybrid sampled data control systems. Instead of considering the state only at sampling instants, this paper introduces a function piece during the sampling period as the state and gives an infinite-dimensional model with such a state space. This gives the advantage that sampled data systems with built-in intersample behavior can be regarded as linear, time-invariant, discrete-time systems. As a result, the approach makes it possible to introduce such time-invariant concepts as transfer functions, poles, and zeros to the sampled data systems even with the presence of the intersample behavior. In particular, tracking problems can be studied in this setting in a simple and unified way, and ripples are completely characterized as a mismatch between the intersample reference signal and transmission zero directions. This leads to the internal model principle for sampled data systems     

Preserving the autocovariance of texture tilings using importance sampling

By-example aperiodic tilings are popular texture synthesis techniques that allow a fast, on-the-fly generation of unbounded and non-periodic textures with an appearance matching an arbitrary input sample called the “exemplar”. But by relying on uniform random sampling, these algorithms fail to preserve the autocovariance function, resulting in correlations that do not match the ones in the exemplar. The output can then be perceived as excessively random. In this work, we present a new method which can well preserve the autocovariance function of the exemplar. It consists in fetching contents with an importance sampler taking the explicit autocovariance function as the probability density function (pdf) of the sampler. Our method can be controlled for increasing or decreasing the randomness aspect of the texture. Besides significantly improving synthesis quality for classes of textures characterized by pronounced autocovariance functions, we moreover propose a real-time tiling and blending scheme that permits the generation of high-quality textures faster than former algorithms with minimal downsides by reducing the number of texture fetches.     

Towards a multiresolution approach to linear control

We develop a multiresolution approximation framework for linear control. We construct a multiresolution analysis of the set of input functions of a linear system. The approximation of an input u at a scale j is defined as the input u/sub j/ of minimal energy such that the trajectories of the system associated with u and u/sub j/ coincide on a grid of step length 2/sup -j/. We propose a set of wavelet functions which generate this multiresolution analysis. These functions, called control theoretic wavelets, satisfy useful properties for the representation of control inputs of a linear system. As an example of application of our multiresolution approximation framework, we propose a method for efficient encoding of control inputs with regard to several criteria.     

Event‐triggered adaptive backstepping control for parametric strict‐feedback nonlinear systems

This paper proposes a novel adaptive backstepping control method for parametric strict‐feedback nonlinear systems with event‐sampled state and input vectors via impulsive dynamical systems tools. In the design procedure, both the parameter estimator and the controller are aperiodically updated only at the event‐sampled instants. An adaptive event sampling condition is designed to determine the event sampling instants. A positive lower bound on the minimal intersample time is provided to avoid Zeno behavior. The closed‐loop stability of the adaptive event‐triggered control system is rigorously proved via Lyapunov analysis for both the continuous and jump dynamics. Compared with the periodic updates in the traditional adaptive backstepping design, the proposed method can reduce the computation and the transmission cost. The effectiveness of the proposed method is illustrated using 2 simulation examples.     

Uniform bounded input bounded output stability of fractional‐order delay nonlinear systems with input

The bounded input bounded output (BIBO) stability for a nonlinear Caputo fractional system with time‐varying bounded delay and nonlinear output is studied. Utilizing the Razumikhin method, Lyapunov functions and appropriate fractional derivatives of Lyapunov functions some new bounded input bounded output stability criteria are derived. Also, explicit and independent on the initial time bounds of the output are provided. Uniform BIBO stability and uniform BIBO stability with input threshold are studied. A numerical simulation is carried out to show the system's dynamic response, and demonstrate the effectiveness of our theoretical results.     

Minimization of a regulated response to a fixed input

The problem of minimizing a regulated output due to a specific bounded input is solved in the SISO (single-input single-output) discrete-time case. It is shown that, in most situations, the optimal solution will not exist, but given any ϵ>0, it is possible to find a suboptimal solution with performance within ϵ of the optimal performance. The proposed approach is extended to the problem of shaping the error transient response. It is shown how time-domain templates can be used in this problem in the same way that frequency-weighting functions are used in the H^∞ and H² problems     

Output transient trajectory shaping control for a class of nonlinear systems

This paper presents a transient trajectory shaping (TTS) control method for the SISO strict feedback nonlinear systems. The TTS control refers to explicitly constraining the system output tracking error transient trajectories within predesigned time‐varying boundaries while they are converging to equilibrium. By this method, the boundaries of system output transient trajectories can be designed a priori according to the system transient control performance requirements in both symmetric and asymmetric ways. With a class of time‐varying boundary functions, control laws can be devised by utilizing the enhanced differential unbounded function techniques. Such control laws can ascertain that the system output tracking errors travel within their respectively predesigned time‐varying boundaries while converging to origin. To handle the control input exaggeration issue in TTS, input constraint control techniques are proposed to effectively reduce the required control input magnitude for second‐order systems. A numerical example is utilized to show the effectiveness of the proposed TTS control methods. Copyright © 2013 John Wiley & Sons, Ltd.     

A general framework for linear periodic systems with applicationsto H∞ sampled-data control

The authors present a framework for dealing with continuous-time periodic systems. The main tool is a lifting technique which provides a strong correspondence between continuous-time periodic systems and certain types of discrete-time time-invariant systems with infinite-dimensional input and output spaces. Despite the infinite dimensionality of the input and output spaces, a lifted system has a finite-dimensional state space if the original system does. This fact permits rather constructive methods for analyzing these systems. As a demonstration of the utility of this framework, the authors use it to describe the continuous-time (i.e., intersample) behavior of sampled-data systems, and to obtain a complete solution to the problem of parameterizing all controllers that constrain the L² -induced norm of a sampled-data system to within a certain bound     

Mixing exact and importance sampling propagation algorithms in dependence graphs

In this article a new algorithm is presented for the propagation of probabilities in junction trees. It is based on a hybrid methodology. Given a junction tree, some of the nodes carry out an exact calculation, and the other an approximation by Monte Carlo methods. For the exact calculation we will use Shafer/Shenoy method and for the Monte Carlo estimation a general class of importance sampling algorithms is used. We briefly study how to apply this sampler on the clusters in a junction tree. The basic algorithm and some of its variations are presented, depending on the family of functions to which we apply the importance sampler: potentials or/and messages in the tree. An experimental evaluation is carried out, comparing their performance with the well-known likelihood weighting approximated algorithm. This family of methods shows a very promising performance. © John Wiley & Sons, Inc.     

Generalized sample hold functions-frequency domain analysis ofrobustness, sensitivity, and intersample difficulties

Over the past 5 years, there has been substantial interest in the use of generalized sample hold functions for control. In this correspondence, the authors use a tool, which is novel in this context, namely, amplitude modulation theory. The authors employ this tool to analyze the quantitative and qualitative features of the intersample behavior in a frequency domain setting. This offers new theoretical and practical insights into the method. The authors' conclusion is that the perceived benefits come at substantial cost which makes its practical use questionable     

Interpolazione ed approssimazione simultanea di un insieme di dati di funzione e derivate prima e seconda. Descrizione del programma midia

The problem of the least square fitting with fixed constraints is here solved in the general case of mixed data, i.e. functions and/or derivatives up to the second order. Given a set of linearly independent functions, the coefficients, the error matrix and the variance of the linear combination at any given point are determined. The abscissa and function (or derivatives) values can be reduced in any interval and the metric is consequently transformed. Making use of a sub-matrices method, the decrease of the weighted sum of the square of the residual for fits with higher number of functions is proved. The MIDIA code, which applies the obtained formulae, has been written in FORTRAN language for the IBM-7094 computer. As independent functions the most common polynomials (monomials, Legendre, Hermite, Chebychev etc.…) are used. The program fits successively higher degree polynomials to input data and at each step the weighted sum of the square of the residual is given, and the one which will occur at the next step is predicted. The tabulation gives the values of the linear combination, of its first and second derivatives and of their standard deviations at any mesh point. If the number of input data is too large for an unique interpolation, an automatic disposal for grouping them is provided.      

Frequency domain approach for designing sampling rates for system identification

This paper considers the problem of joint determination of input spectra and sampling rate for linear system identification. The concept of an ‘input spectrum preserving sampler’ is introduced and it is shown that, for this sampler, the usual anti-aliasing filter is optimal, and that joint optimal design of input spectrum and sampling rate may be readily performed in the frequency domain.     

Improved prescribed performance control for nonaffine pure‐feedback systems with input saturation

This work considers an input and output constraint control problem for pure‐feedback systems with nonaffine functions possibly being in‐differentiable. A locally semibounded and continuous condition for nonaffine functions is presented to guarantee the controllability, and the nonaffine system is transformed to an equivalent pseudoaffine one based on the mild condition. Combined with backstepping technique, a novel prescribed performance controller with new performance functions is constructed to circumvent high frequency chattering in control input. An auxiliary system with bounded compensation term is utilized in this paper, successfully avoiding the overrun of control input. The methodology achieves the desired transient and steady‐state performance and presents excellent robustness against the system uncertainty. Finally, two numerical simulations are performed to demonstrate the effectiveness of the proposed approach.     

含状态和输入时滞的模糊系统的隶属函数依赖的稳定与镇定

研究一类含有状态时滞和输入时滞的T-S模糊系统的稳定性分析和镇定问题.首先,构造一个含三重积分的Lyapunov-Krasovskii(L-K)泛函,利用一个近期提出的二重积分不等式和基于辅助函数的积分不等式处理积分项.为了得到更为放松的时滞依赖的稳定性结果,考虑隶属度函数的边界信息,选择分段隶属函数去近似隶属度函数,同时引入松弛矩阵,以线性矩阵不等式(LMIs)形式给出保守性较小的隶属函数依赖的稳定性准则;然后,基于前提不匹配技术,结合Finsler引理,首次提出含状态和输入时滞的模糊系统的状态反馈控制器的设计方法,该模糊控制器不要求与模糊系统拥有相同的隶属度函数和模糊规则数目,从而提高设计的灵活性;最后,通过给出3个仿真算例表明所提出方法的先进性和有效性.     

煤矿高压电网单相接地漏电故障选线方法研究

新型高压电网单相接地漏电故障选线方法采用电流谐波故障诊断法、零序有功功率法和暂态零序电流互积求和法设定故障测度隶属函数和权重系数隶属函数;采用模糊理论将3种方法各自的隶属函数和权重系数隶属函数进行融合,计算出多判据选线方法下的线路故障测度,从而可判断出单相接地漏电故障线路。Matlab/Simulink仿真结果验证了该方法的正确性。     

Fuzzy algorithmic simulation of reliability: Control and correction resource optimization

Fuzzy models of reliability of algorithmic procedure based on membership functions that depend on parameters affecting the algorithm correct performance are considered. Statements of optimization problems of correction and control resources of linear algorithms with respect to reliability-cost criteria are formalized. The solution of the stated problems is illustrated by an example. The novelty of the approach consists in the fact that it does not use any statistical data and optimize parametric reliability of the system by choosing the control and correction resources in order to ensure the required or maximal possible correction level of performance for the given instability of input parameters.