Continuous-time deadbeat control for sampled-data systems

In this paper, the continuous-time deadbeat control problem for the sampled-data systems is considered. We derived the class of all controllers that achieve the continuous-time deadbeat control     

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.     

Parametrization of all ripple-free deadbeat controllers

This paper is concerned with deadbeat control in sampled-data systems. Deadbeat control achieves finite-time settling (deadbeat settling) at sampling instants, but there may exist error called ripple “between” sampling instants even after the response is settled “at” sampling instants. The objective of this paper is to give a parametrization of all ripple-free deadbeat controllers (controllers which achieve deadbeat settling without ripple) in sampled-data systems. It is also shown that the following holds in general: minimum-time deadbeat control causes ripple when the pulse transfer function to be controlled has stable zeros.     

Robust ripple-free regulation and tracking for parameter-dependentsampled-data systems

The robust ripple-free asymptotic tracking and disturbance rejection problem is studied for sampled-data systems whose matrices are assumed to depend on some “physical” parameters, each of which possibly affects all the elements of the matrices describing the system, and for the case when only a subset of the scalar outputs must track corresponding exogenous reference signals; ripple-free dead-beat regulation and tracking is also required at the nominal parameters. The necessary and sufficient conditions are given for the existence of a solution which may exist even when no solution exists for wholly independent variations of the entries of the matrices describing the system. A design procedure of both the continuous-time internal model and the discrete-time controller is also outlined     

石英挠性加速度计数字闭环控制研究

数字化石英挠性加速度计因其可靠性高、易于集成等优点而成为石英挠性加速度计发展的一个新趋势。现有的石英挠性加速度计数字闭环控制多采用PID算法,但是该算法存在系统超调大、调节时间长、控制精度低的问题。针对这一问题,提出了基于最少拍无纹波的数字闭环控制算法。仿真证明：在相同的带宽和采样频率下,该算法的系统超调远小于5%,调节时间只需3个采样周期,稳态误差远小于0.001%,这些性能均优于PID算法。     

Design of ripple-free multivariable robust servomechanisms

The application of standard robust servomechanism theory to sampled data systems guarantees asymptotic tracking at sampling instances and between sampling instants, the output will normally contain ripple. In this note, the robust servomechanism theory is extended to sampled-data systems and a technique is proposed for ripple-free tracking of sinusoids and polynomials. It is shown that a continuous internal model is necessary and sufficient to provide ripple-free response.     

Finite-settling-time control of continuous-time plants

A design method of ripple-free finite-settling-time control of continuous-time plants is presented in this paper. The method is applicable to a vast kind of plants including nonminimum phase plants. It is shown that deadbeat tracking design in the discrete-time domain yields a ripple-free finite-settling-time control for a step input. The design method relies on frequency-domain pole-assignment techniques.     

Optimal ripple-free deadbeat control using an integral of time squared error (ITSE) index

This paper describes an optimal ripple-free deadbeat control strategy for single-input–single-output (SISO) linear sampled data plants. The cost function to be minimized is a linear combination of a time-weighted cumulative term that penalizes the tracking error, that is, an integral of time squared error (ITSE) cost term, and a cumulative term which penalizes the control signal deviations from its steady-state value. The optimization problem turns out to be convex, and closed-form solutions are obtained. An example is included to illustrate our results.     

Double objective optimal multivariable ripple-free deadbeat control

This paper presents novel results on optimal multivariable deadbeat control. Given a discrete-time, stable, linear, time invariant plant model, we give a simple parameterization of all stabilizing ripple-free deadbeat controllers of a given order. The free parameter is then optimized in the sense that a quadratic index is kept minimal. The optimality criterion has the advantage of accounting for both tracking performance and magnitude of the control effort. The proposed design procedure is simple to use and allows the tuning of the controller with a scalar weighting factor. Simulation results are included to illustrate the effectiveness of the proposed design algorithm.     

Optimum design of linear multivariate sampled-data control systems†

This paper deals with the optimum design of linear multivariate sampled-data control systems,

Section 2 is concerned with the design of such control systems which are optimum on the basis of deadbeat performance. This design procedure is general and can be applied similarly to any deterministic inputs such as step, ramp, etc.

Section 3 is concerned with such control systems with respect to an integral form performance criterion. It is desired that the performance index takes the form of an integral, especially when the state variables of a control system are continuous with respect to time. For this reason, the minimum integral control is considered here.

The performance limits for such systems optimized for a deterministic input are considered in §4, and some interesting theorems are proved by using the w-transform.     

Robust guaranteed cost control of uncertain fuzzy systems under time-varying sampling

In practice, the system is often modeled as a continuous-time fuzzy system, while the control input is applied only at discrete instants. This system is called a sampled-data control system. In this paper, robust guaranteed cost control for uncertain sampled-data fuzzy systems is discussed. A guaranteed cost control where a quadratic cost function is bounded by a certain scalar, not only stabilizes a system but also considers a control performance. A typical sampled-data control is the zero-order input, which can be represented as a piecewise-continuous delay. Here we take a delay system approach to the sampled-data guaranteed cost control problem. The closed-loop system with a sampled-data state feedback controller becomes a system with time-varying delay. First, guaranteed cost control performance conditions for the closed-loop system are given in terms of linear matrix inequalities (LMIs). Such conditions are derived by using Leibniz–Newton formula and free weighting matrix method for fuzzy systems under the assumption that sampling time is not greater than some prescribed scalar. Then, a design method of robust guaranteed cost state feedback controller for uncertain sampled-data fuzzy systems is proposed. Examples are given to illustrate our robust sampled-data guaranteed cost control design.     

Performance recovery under output feedback sampled-data stabilization of a class of nonlinear systems

This paper studies sampled-data output feedback control of a class of nonlinear systems. It is shown that the performance of a stabilizing continuous-time state feedback controller can be recovered by a sampled-data output feedback controller when the sampling period is sufficiently small. The output feedback controller uses a deadbeat discrete-time observer to estimate the unmeasured states. Two schemes are proposed to overcome large initial transients when the controller is switched on.     

Comments on `Ripple-free deadbeat control of SISO discrete systems'by H.R. Sirisena

The commenter argues that the necessary and sufficient conditions given by M.R. Sirisena (ibid., vol.AC-30, p.168-170, Feb. 1985) for solving the ripple-free deadbeat problem are incorrect     

An output delay approach to fault estimation for sampled-data systems

The problem of fault estimation for a class of non-uniformly sampled-data systems is investigated from the time delay point of view in this paper.Firstly,the output delay approach is employed to model the sampled-data system as a continuous-time one with time-varying delay output.Then,based on the analysis of the inapplicability of the adaptive fault diagnosis observer in such class of time-delay systems,a novel augmented fault estimation observer design method is proposed to guarantee the exponential convergence of the estimation errors.Furthermore,an extension to the case of time varying fault estimation for the noisy sampled-data systems is studied.Finally,simulation results of a flight control system are presented to demonstrate the effectiveness of the proposed method.     

2 optimal control for sampled-data systems

This paper considers an ₂ optimal control problem for sampled-data systems. After defining a new ₂ norm for sampled-data systems, we give a state space solution to the optimal controller synthesis problem. We show that the ₂ optimal control problem for a sampled-data system is equivalent to a standard ₂ optimal control problem for a related discrete-time system.     

切换非线性系统采样控制的研究现状与进展

切换非线性系统由于其广泛的工程应用背景以及重要的理论研究价值引起各行业学者的广泛关注.近年来,随着计算机技术的快速发展,切换非线性系统采样控制问题成为研究热点.对目前切换非线性系统采样控制领域的研究现状进行综述.首先介绍了切换非线性系统的基本问题,并梳理了切换非线性系统几个常用控制方法的基本思想.然后从时间触发采样控制和事件触发采样控制两个方面对切换非线性系统采样控制的国内外研究现状进行了论述.最后进行了总结并提出切换非线性系统采样控制领域未来值得关注的研究方向.     

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.     

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.     

On the Discrete-Time Integral Sliding-Mode Control

A new discrete-time integral sliding-mode control (DISMC) scheme is proposed for sampled-data systems. The new control scheme is characterized by a discrete-time integral sliding manifold which inherits the desired properties of the continuous-time integral sliding manifold, such as full order sliding manifold with pole assignment, and elimination of the reaching phase. In particular, comparing with existing discrete-time sliding-mode control, the new scheme is able to achieve more precise tracking performance. It will be shown in this work that, the new control scheme achieves O(T²) steady-state error for state regulation with the widely adopted delay-based disturbance estimation. Another desirable feature is, the proposed DISMC prevents the generation of overlarge control actions due to deadbeat response, which is usually inevitable due to the existence of poles at the origin for a reduced order sliding manifold designed for sampled-data systems. Both the theoretical analysis and illustrative example demonstrate the validity of the proposed scheme     

Deadbeat control of linear multivariable generalized state-spacesystems

The classic idea of deadbeat control is extended to linear multivariable discrete-time generalized state-space systems using algebraic methods. The asymptotic properties of the linear quadratic regulator theory are used to obtain the classes of deadbeat controllers using stabilizing full semistate feedback. The solution is constructed from a `cheap control' problem. Both semistate and output deadbeat control laws are considered. The main design criteria are to drive the semistate and/or outputs of the system to zero in minimum time and that the closed-loop system be internally stable. Unique properties of these types of control laws are discussed. For semistate deadbeat control, all the (dynamic) poles including the ones at infinity are moved to the origin, whereas for output deadbeat, some of the finite transmission zeros are canceled. Numerically reliable algorithms are developed to solve both problems