同步多速率系统H∞控制的J-无损失共轭化设计

针对提升后同步多速率控制器存在的因果约束问题,利用J-无损失共轭因子同H_∞控制相关的性质,提出了同步多速率系统H_∞控制的J-无损失共轭化设计.这一方法将提升后同步多速率系统的H_∞控制问题转化成求解共轭因子的问题,即只需求解相关特征值和Lyapunov方程,就可得到满足因果约束条件的控制器和相应闭环系统的参数化形式,同时对提升控制器的因果约束转化为范数有界真有理稳定传递函数矩阵空间BH^∞中任意参数的因果约束,同常规的逼近     

Adaptive output feedback control of general MIMO systems using multirate sampling and its application to a cart–crane system

In adaptive output feedback control based on almost strictly positive real conditions, a technical difficulty arises when the multi-input multi-output (MIMO) system under consideration is non-square, and in particular, has less inputs than outputs. To overcome this, we propose the idea of multirate sampled-data control—by carefully choosing faster input sampling rates, we obtain a lifted discrete-time system, which has the same number of inputs and outputs and does not give rise to the causality constraint. The adaptive control strategy is then applied to the lifted system, resulting in a multirate adaptive output feedback controller which is implementable digitally and provides closed-loop stability under certain conditions. The results reported here are validated on an experimental cart–crane system.     

Identification of fast-rate models from multirate data

For a multirate sampled-data system consisting of a continuous-time process with or without a time delay, a sampler with period nT and a zero-order hold with period mT (m < n), we study the problem of identifying a fast single-rate model with sampling period mT based on multirate input-output data. This problem is solved in two steps: First, we identify a lifted state-space model for the multirate system by extending existing subspace identification algorithms to take into account the causality constraint in the lifted model; next, based on the lifted model, we extract a state-space model for the fast single-rate system. Such fast-rate models are useful for many applications such as inferential control. Other related topics discussed in the paper include observability of lifted models in the presence of time delay and time-delay estimation from multirate data. Finally, we apply and test the proposed algorithms to an experimental setup involving a continuously stirred tank heater.     

满足因果约束的多速率单值广义预测控制

针对输入更新频率和输出采样频率均不相同的多速率采样系统,提出一种多速率广义预测控制算法．通过采用在系统周期内根据不同的采样时刻构造扩展模型序列的方法,有效地解决了由于多速率采样而引起的因果约束问题．在此基础上,对算法的闭环稳定性进行了分析,仿真结果证明了算法的有效性．     

Multirate versions of sampled-data stabilization of nonlinear systems

The problem of state feedback sampled-data stabilization of nonlinear systems is considered under the “low measurement rate” constraint and in the presence of (not necessarily small) time delay in the measurement channel. A multirate control scheme is proposed that utilizes a numerical integration scheme to approximately predict the current state from the delayed measurements. For both the controller emulation approach and the approach based on approximate discrete-time model of the system, we show that under standard assumptions the closed-loop multirate sampled data system is asymptotically stable in the semiglobal practical sense. An illustrative example of sampled-data control of vertical take off and landing aircraft is discussed.     

Feedback control of linear systems by multirate pulse-widthmodulation

In this note, sampled-data methods for modeling and control design of pulse-width modulated systems are examined. Both single-rate and multirate approaches are considered. Local controllability and observability analyses of the sampled-data models are performed, and feedback linearizability conditions for the sampled-data models are derived. Multirate nonlinear state and output feedback designs are presented that permit asymptotic regulation or tracking     

A linear matrix inequality (LMI) approach to robust H/sub 2/ sampled-data control for linear uncertain systems

In this paper, we consider the H/sub 2/ sampled-data control for uncertain linear systems by the impulse response interpretation of the H/sub 2/ norm. Two H/sub 2/ measures for sampled-data systems are considered. The robust optimal control procedures subject to these two H/sub 2/ criteria are proposed. The development is primarily concerned with a multirate treatment in which a periodic time-varying robust optimal control for uncertain linear systems is presented. To facilitate multirate control design, a new result of stability of hybrid system is established. Moreover, the single-rate case is also obtained as a special case. The sampling period is explicitly involved in the result which is superior to traditional methods. The solution procedures proposed in this paper are formulated as an optimization problem subject to linear matrix inequalities. Finally, we present a numerical example to demonstrate the proposed techniques.     

非均匀采样数据系统的新型模型描述方法

提升技术是处理非均匀采样数据（Non-uniformly sampled-data,NUSD）系统的标准工具.然而,提升状态空间模型存在因果约束问题,相应的提升传递函数模型结构复杂,且参数数目过多.因此,它们不便于非均匀采样数据系统的辨识与控制.通过引入时变后移算子,本文提出了一种输入输出表达的新型模型描述方法.该模型能够克服提升系统模型的缺点,使得传统单率系统的辨识和控制方法能够推广到非均匀采样数据系统中.仿真结果表明了新模型的优越性和有效性.     

Modeling and Identification of Multirate Systems

Multirate systems are abundant in industry; for example, many soft-sensor design problems are related to modeling, parameter identification, or state estimation involving multirate systems. The study of multirate systems goes back to the early 1950s, and has become an active research area in systems and control. This paper briefly surveys the history of development in the area of multirate systems, and introduces some basic concepts and latest results on multirate systems, including a polynomial transformation technique and the lifting technique as tools for handling multirate systems, lifted state space models, parameter identification of dual-rate systems, how to determine fast single-rate models from dual-rate models and directly from dual-rate data, and a hierarchical identification method for general multirate systems. Finally, some further research topics for multirate systems are given.     

Block multirate input-output model for sampled-data control systems

A model for multirate sampled-data systems is presented. A detailed analysis of nonconventional sampled-data control systems (SDCS) is performed. The block multirate input-output model illustrates the control possibilities of multirate SDCS. It is obtained from either a transfer function matrix or a state variable representation. The model provides a direct way to represent, design, and understand either periodic or predictive controllers. A controller design methodology suitable for multivariable, multirate, nonsynchronous SDCS is also presented. The main feature is the freedom to achieve important objectives such as structure assignment, decoupling, and desired transient behavior, as well as reference matching, optimal control, or disturbance rejection     

Multirate sampled-data systems: computing fast-rate models

This paper studies identification of a general multirate sampled-data system. Using the lifting technique, we associate the multirate system with an equivalent linear time-invariant system, from which a fast-rate discrete-time system is extracted. Uniqueness of the fast-rate system, controllability and observability of the lifted system, and other related issues are discussed. The effectiveness is demonstrated through simulation and real-time implementation.     

Design of sampled-data critical control systems based on the fast-discretization technique

The fast-discretization is known as an approximate but efficient technique for design and analysis of sampled-data systems. In this paper, we propose a fast-discretization-based design for sampled-data critical control systems. Supposing a tracking problem or a slow-changing disturbance rejection problem, we assume that an exogenous input is a persistent and/or transient input with bound on the rate of change. It is shown that the critical constraint for such exogenous inputs can be given in the form of the inequality constraint on the unit step response. The design parameters are determined by a numerical search method subject to this constraint. However, instead of evaluating it strictly, we check the corresponding constraint which is obtained from the fast-discretized system. Although this approach is approximate, it provides an efficient numerical procedure for a computer-aided design. To show the validity of the proposed method, an example of a multi-objective critical control system design is presented.     

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     

Design of H 2 Controllers for Sampled-Data Systems with Input Time Delays

This paper presents a general framework based on lifting technique for sampled-data systems with input time delays. By analyzing the properties of operator-valued matrices of lifted systems with input time delays, an extended lifting technique is obtained. It is then shown that, with the proposed lifting technique, the complex behavior of the system can be illustrated by two simple lifted systems, which construct the extended lifted system. The extended lifted system has the same induced norm as that of the original system with an input time delay, since the proposed lifting technique is an isometric isomorphism. Through applying the proposed lifting technique to sampled-data systems with input time delays, the time-invariant discrete-time system with infinite-dimensional input and output spaces is obtained. The equivalent discrete-time system, which is derived from the extended lifted system, can satisfy the problem of H ₂ sampled-data control systems with input time delays. Simulation results are given to show that the proposed method can guarantee a more stable system response than the conventional H ₂ sampled-data controller for the sampled-data systems with the various input time delays.     

Suppressing intersample behavior in iterative learning control

Iterative Learning Control (ILC) is a control strategy to improve the performance of digital batch repetitive processes. Due to its digital implementation, discrete time ILC approaches do not guarantee good intersample behavior. In fact, common discrete time ILC approaches may deteriorate the intersample behavior, thereby reducing the performance of the sampled-data system. In this paper, a generally applicable multirate ILC approach is presented that enables to balance the at-sample performance and the intersample behavior. Furthermore, key theoretical issues regarding multirate systems are addressed, including the time-varying nature of the multirate ILC setup. The proposed multirate ILC approach is shown to outperform discrete time ILC in realistic simulation examples.     

Cost translation and a lifting approach to the multirate LQGproblem

It is shown how to translate an instance of a multirate sampled-data LQG problem into an equivalent, modified, single-rate, shift-invariant problem via a lifting isomorphism approach. Using this approach, one can solve the multirate LQG problem without using periodic system theory or solving periodic Riccati equations and without suffering any increases in state dimension. This translation procedure shows the correct way to translate RMS noise specification to the lifted domain for a multirate Q-design computer-aided-design package     

A new optimal multirate control of linear periodic andtime-invariant systems

The optimal multirate design of linear, continuous-time, periodic and time-invariant systems is considered. It is based on solving the continuous linear quadratic regulation (LQR) problem with the control being constrained to a certain piecewise constant feedback. Necessary and sufficient conditions for the asymptotic stability of the resulting closed-loop system are given. An explicit multirate feedback law that requires the solution of an algebraic discrete Riccati equation is presented. Such control is simple and can be easily implemented by digital computers. When applied to linear time-invariant systems, multirate optimal feedback optimal control provides a satisfactory response even if the state is sampled relatively slowly. Compared to the classical single-rate sampled-data feedback in which the state is always sampled at the same rate, the multirate system can provide a better response with a considerable reduction in the optimal cost. In general, the multirate scheme offers more flexibility in choosing the sampling rates     

Linear periodically time-varying discrete-time systems: Aliasing and LTI approximations

Linear periodically time-varying (LPTV) systems are abundant in control and signal processing; examples include multirate sampled-data control systems and multirate filter-bank systems. In this paper, several ways are proposed to quantify aliasing effect in discrete-time LPTV systems; these are associated with optimal time-invariant approximations of LPTV systems using operator norms.     

A new representation of the parameters of lifted systems

Lifting, i.e., discretization with built-in intersample behavior, is an emerging technique for the analysis and design of sampled-data systems. The applicability of the lifting technique, however, is severely limited owing to difficulties in dealing with the parameters of the lifted systems, which are operators over infinite-dimensional spaces rather than finite-dimensional matrices. In this paper, a new representation for the parameters of the lifted systems is proposed. The technical machinery developed in the paper based on this representation simplifies considerably algebraic manipulation over parameters of the lifted systems, thus extending the scope of applicability of the lifting technique. To illustrate the advantages of the proposed approach, the computational issues in the sampled-data H^∞ problem are considered