Ripple-free deadbeat control for sampled-data systems

In this paper the ripple-free deadbeat control problem for sampled-data systems is considered. This control objective is to settle the error to zero for all time after some finite settling time, in other words to eliminate the ripples between the sampling instants in deadbeat control of sampled-data systems. The necessary and sufficient conditions to solve this problem are derived and related to the system type, and a method of constructing the ripple-free deadbeat control system is presented.     

Optimization of control input for deadbeat control systems

The aim of this paper is to deal with the problem of excessive control magnitude with deadbeat control systems. By the use of the transfer-function factorization approach, all stabilizing deadbeat controls are characterized in terms of control input. A formula is derived for the optimal control that minimizes the control input error for the specified settling time. The design procedure is essentially trade-offs between settling time and control input properties. As the bound of such trade-offs, the limiting value of the optimal performance index, as the settling time goes to infinity, is derived. This limit value plays an important role in fixing the most appropriate settling time.     

Output deadbeat control discrete-time multivariate systems

An algorithm is presented to compute output deadbeat controls for linear multivariable systems. The algorithm, based on quadratic optimization with no cost on control (cheap control), is numerically stable and covers the most general cases. The resulting controls are internally stable and are shown to drive the outputs of the system to zero in minimum time using state feedback. The central part of the algorithm is the construction of the nonunique state-cost matrix. Two alternatives are presented having different complexities and resulting in solutions having different properties     

Ripple-free deadbeat control of SISO discrete systems

The ripple-free deadbeat control problem for arbitrary (not necessarily stable) SISO linear discrete plants and reference signals is treated. It is established that a causal, stabilizing ripple-free deadbeat controller exists if and only if the zeros of the plant and the poles of the reference signal are disjoint, and a complete characterization of all such controllers is obtained. Solutions to two illustrative problems are presented.     

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     

Robust sampled-data control for Markovian jump linear systems

In this paper, we consider the problem of robust control for uncertain sampled-data systems that possess random jumping parameters which is described by a finite-state Markov process. The conditions for the existence of a stabilizing control and optimal control for the underlying systems are obtained. The desired controllers are designed which are in terms of matrix inequalities. Finally, a numerical example is given to show the potential of the proposed techniques.     

State covariance assignment for sampled-data feedback control systems

This paper proposes a new performance criterion of ‘covariance’ for sampled-data systems. A covariance of sampled-data systems is defined by taking account of inter-sample behaviour. An SCA (state covariance assignment) problem for sampled-data feedback control systems is also discussed, which is the counterpart of that for purely continuous or discrete-time feedback control systems. The SCA problem for sampled-data systems will be solved as a discrete-time SCA problem, where the discretization preserves the state covariance and is in two steps. In the first step, a certain sample time performance is required to ensure the inter-sample performance, and the output signal results to be discretized. The second step is to discretize the input signal.     

Takagi-Sugeno模糊连续系统的模糊采样控制

研究了T-S模糊连续系统的模糊采样控制问题．利用广义系统的描述方法、Lyapunov-Krasovikii泛函以及线性矩阵不等式(LMI)方法,建立了LMIs形式的依赖于采样时间间隔的模糊采样镇定条件,同时给出了模糊采样控制律的设计方法．所设计的模糊采样控制律可以镇定T-S模糊系统．而且,当连续时间模糊控制律可以镇定T-S模糊系统时,对于足够小的采样时间间隔,带有同样增益矩阵的模糊采样控制律也可以镇定T-S模糊系统．最后,通过两个仿真实例说明了所给方法的有效性．     

Multirate sampled-data control of two-time-scale systems

Two-time-scale decoupling is adopted to obtain slow and fast subsystems. Based on these subsystems, a multirate composite control strategy is derived. It is shown how a recently presented multirate scheme can be modified to handle slow, nonzero mean disturbances, by introducing time incremental models. The improvements with the given multirate control law are illustrated by an example     

A numerical method for deadbeat control of generalized state-space systems

In this paper we give a new numerical method for constructing a rank m correction BF to an n × n matrix A, such that the generalized eigenvalues of λE−(A+BF) are all at λ = 0. In the control literature, this problem is known as ‘deadbeat control’ of a generalized state-space system Ex_i+1 = Ax_i + Bu_i, whereby the matrix F is the ‘feedback matrix’ to be constructed.     

Output-feedback control of LPV sampled-data systems

In this paper, we address the analysis and the output-feedback synthesis problems for linear parameter-varying (LPV) sampled-data control systems with potentially variable sampling rates. We assume that the state-space matrices of the plant and the sampling interval depend on parameters that are measurable in real-time and vary in a compact set with bounded variation rates. We explore criteria such as the stability, the energy-to-energy gain (induced L 2 norm) and the energy-to-peak gain (induced L 2 -to- L X norm) of such sampled-data LPV systems using parameter-dependent Lyapunov functions. Based on these analysis results, the corresponding sampled-data output-feedback control synthesis problems are examined. Both analysis and synthesis conditions are formulated in terms of linear matrix inequalities (LMIs) that can be solved via efficient interior-point algorithms.     

Non-uniform sampled-data control of MIMO systems

In this paper, the problem of controlling MIMO plants where the pattern of measurements sampling and control actions delivering is not regular is tackled. Multirate control, time delay systems, missing data environments as well as limited computing and communication resources are on the grounds of these problems. There is an extensive literature on these topics. Different models are reviewed and, from the control viewpoint, model-based control design techniques are reported and new algorithms are proposed. Among the main challenges are the achievement of good performance and the avoidance of intersampling ripple. Both issues are considered and some results are discussed.     

On output deadbeat control of discrete-time multivariable systems

A necessary extension to the output deadbeat control algorithm of M.R. Marrani et al. (see ibid., vol.AC-34; p.644-8 (1989)) is presented. This extension is shown to provide particular theoretical insights when dealing with the case of a system with multiple stable transmission zeros. It is numerically straightforward to implement. Once the zeros have been calculated, the state zero directions can be determined independently. This method has particular advantages when dealing with the case of a plant with multiple stable transmission zeros     

Output-feedback control for sampled-data systems with variable sampling rate

In this paper, we propose design method of controller for sampled-data systems with variable sampling rate. First, we give design method for both H₂ and H_∞ controller. For H₂ control, performance of the system is introduced according to a standard sampled-data setting. A discrete-time H₂ control problem is employed for solving the original problem. Its solvability condition is then established as a parameter-dependent linear matrix inequality. A probabilistic approach is taken for coping with the parameter-dependency. H_∞ controller is designed by almost the same manner. Applying both results, we have design method for multi-objective control.     

Decentralised sampled-data control for large-scale systems with nonlinear interconnections

This paper presents a decentralised sampled-data control technique for a class of large-scale systems, which are considered to consist of linear subsystems and nonlinear interconnections. The decentralised sampled-data controller design problem is established using a closed-loop subsystem. Based on the controller design problem, the stability condition is derived for a closed-loop large-scale system, and the maximum interconnection bound is guaranteed to satisfy the stability condition. Also, its sufficient condition is formulated in terms of linear matrix inequalities. Finally, the effectiveness of the proposed technique is verified by using an example of the multi-machine power system.     

Robust extended dissipative control for sampled-data Markov jump systems

This paper investigates the problem of the sampled-data extended dissipative control for uncertain Markov jump systems. The systems considered are transformed into Markov jump systems with polytopic uncertainties and sawtooth delays by using an input delay approach. The focus is on the design of a mode-independent sampled-data controller such that the resulting closed-loop system is mean-square exponentially stable with a given decay rate and extended dissipative. A novel exponential stability criterion and an extended dissipativty condition are established by proposing a new integral inequality. The reduced conservatism of the criteria is demonstrated by two numerical examples. Furthermore, a sufficient condition for the existence of a desired mode-independent sampled-data controller is obtained by solving a convex optimisation problem. Finally, a resistance, inductance and capacitance (RLC) series circuit is employed to illustrate the effectiveness of the proposed approach.     

非线性采样控制系统的Lagrange稳定性

针对由具有外部慢时变输入信号的非线性被控对象和线性数字控制器构成的非线性采样系统,采用非线性跳跃系统方法及其线性化策略,得到了这类系统在理想离散化方式和无限字长数字控制器作用下(即不考虑量化因素)的Lagrange稳定(最终有界)条件.并指出,当考虑数字控制器和接口器件的非线性量化因素影响时,只要非线性量化环节及其相应偏导数有界,则所得稳定性结论仍然成立.