On sampled data approach to parameter identification of continuous linear systems

It is generally preferable to estimate unknown parameters in analog transfer functions by sampled data techniques. This approach calls for the derivation of an appropriate discrete modelD(z)for a given analog systemH(s)with undetermined parameters, and then the fitting of the sampled input-output data byD(z)to estimate these parameters. This correspondence presents a method for obtaining such discrete models. It also provides a more effective procedure for calculating the parameter estimates from the identified discrete transfer functionhat{D}(z).     

A state-space approach to optimum postfiltering of sampled data

In this paper, we apply state-space techniques to the problem of reconstructing a random continuous-time waveform from its discrete-time samples. The optimal zero-lag filter that accomplishes this is well known, but to our knowledge the smoothing problem has not been previously considered in this context. We develop smoothing algorithms in the mixed-time framework appropriate to the interpolation problem, and then compare our results with those obtained previously in discrete time. Our results are related to those previously obtained in a simple and intuitive way, and the required computations are straightforward modifications of those described previously for purely discrete and purely continuous time.     

H ∞ sampled data control of systems with time-delays

Sampled-data H _∞ control of linear systems with constant state, control and measurement delays is considered. The sampling of the controlled input and of the measured output is not assumed to be uniform. The system is modelled as a continuous-time one, where the controlled input and the measurement output have piecewise-continuous delays. The input–output approach to stability and L ₂-gain analysis is applied to the resulting system. The discretised Lyapunov functional method is extended to the case of multiple delays, where the Lyapunov functional is complete in one of the delays (in the state) and is simple in the other delays (those in the input and in the output), which are constant. Solutions to the state-feedback and the output-feedback H _∞ control problems are derived in terms of linear matrix inequalities (LMIs).     

Generalized sampled data feedback control of distributed parameter systems

In the sampled-data control literature there are necessary conditions and sufficient conditions for stabilizability of distributed parameter systems by generalized sampled-data control. For finite-dimensional systems the necessary conditions are also known to be sufficient. We show that this equivalence extends to the infinite-dimensional case if the underlying semigroup is analytic. However, for general systems, the necessary conditions are not sufficient, nor are the sufficient conditions necessary. We prove this by a single example with a free parameter – one choice of parameter shows that the necessary conditions are too weak, and another choice shows that the sufficient conditions are too strong.     

Polynomial modal control for sampled data systems with delay

The problem of modal sampled-data control for continuous-time linear time-invariant plant with delay is considered. The characteristic matrix of the system is constructed. An algorithm is given for generating the set of causal discrete-time controllers that place eigenvalues of the characteristic matrix at specified points of the complex plane.     

Optimal control of sampled data systems by geometric programming

The optimal control problem with constrained control and fixed terminal bounds has been the subject of extensive study by several investigators. This paper presents a simple method of determining the control sequence of a discrete data system by applying the Geometric Programming Technique. For purposes of illustration, a simple nonlinear second order sampled data system has been analysed by applying the Geometric Programming Technique. The analysis presented in this paper brings out the considerable flexibility of use which Geometric Programming has, and which in the authors' opinion makes this method one of immense future potential in the realm of optimal control.     

A relation between overshoot and sampling period in sampled data feedback control systems

This correspondence shows that the overshoot of response of a sampled data feedback control system sometimes tends to infinity as the sampling period tends to zero provided that the assigned poles are constant. This suggests that an optimal sampling period exists in designing, deadbeat controllers.     

A normal form augmentation approach to adaptive control of space robot systems

In this paper, we model a free-floating space robot system as anextended robot which is composed of a pseudo-arm representing the base motion resulting from six hyperthetic passive joints, and a real robot arm. The model allows us to categorize the space robot as an under-actuated system, and reveal fundamental properties of the system. Through input-output linearization of the model, we demonstrate a non-trivial internal dynamics, and propose an adaptive control scheme based on a normal form augmentation approach. This approach overcomes two fundamental difficulties in adaptive control design of space robot systems, i.e., nonlinear parameterization of the dynamic equation, and uncertainty of kinematic mapping from Cartesian space to joint space.     

A new computer graphics approach to parameter space design of control systems

This paper presents a new approach to parameter space design of linear multivariable control systems. The complete solution of a pole region assignment problem for single-input systems is obtained as an admissible region in then-dimensional parameter space of state feedback gains. We develop a new modeling technique for these admissible parameter space regions which is superior to previous ones because it permits unambiguous and efficient graphical display of slices in 2D and 3D subspaces. In an interactive computer graphics implementation, this method provides an environment where the influence of stability, performance, robustness, integrity, and control constraints on design parameters can be directly visualized and complex tradeoffs are resolved in an interactive way. By judicious combination of overlays, color, and/ or animation, admissible ranges of up to five or six design parameters can be displayed simultaneously. A sequential decomposition technique which selects slices for full parameter space design of lower dimensional subsystems such that the remaining eigenvalues are invariant is used for systems of arbitrarily high order. Parameter space design of unity rank feedback for multiinput systems is done in exactly the same fashion, while systematic sequential design of full rank feedback is achieved as the sum of dyadic stages to which the single-input modeling techniques apply. Examples are given for all presented methods to show the flexibility and potential as a computer-aided control system design framework with a novel integration of computer graphics technology.     

解系统控制问题的递推方法

本文对系统控制及其他领域中的一大类问题,介绍一种递推解法,使当数据增加时,递推解以概率1收敛到真解.这方法主要以3个步骤来实现:首先,把欲解的问题参数化;然后,选择适用的递推参数估计算法;最后,证明递推估计收敛到笔者想要的值.文中列举了具体的系统控制问题,展示如何把它们参数化.作为递推估计算法,文中介绍了扩展截尾的随机逼近算法(SAAWET),给出了它的一般收敛定理.随后,以两个系统控制问题,展示该方法的具体实现,所附模拟计算实例证实了该方法.实际上,这种方法已成功地解决了系统控制及其他相关领域中的一系列问题.     

A multiple Lyapunov function approach to stabilization of fuzzy control systems

This paper addresses stability analysis and stabilization for Takagi-Sugeno fuzzy systems via a so-called fuzzy Lyapunov function which is a multiple Lyapunov function. The fuzzy Lyapunov function is defined by fuzzily blending quadratic Lyapunov functions. Based on the fuzzy Lyapunov function approach, we give stability conditions for open-loop fuzzy systems and stabilization conditions for closed-loop fuzzy systems. To take full advantage of a fuzzy Lyapunov function, we propose a new parallel distributed compensation (PDC) scheme that feedbacks the time derivatives of premise membership functions. The new PDC contains the ordinary PDC as a special case. A design example illustrates the utility of the fuzzy Lyapunov function approach and the new PDC stabilization method.     

Spatial periodic adaptive control approach for rotary systems in sampled time

A periodic adaptive control approach is proposed for a class of nonlinear sampled‐time systems with varying parametric uncertainties that are periodic with respect to angular displacement, and the only prior knowledge is the periodicity. The new adaptive controller updates the parameters and the control signal periodically in a pointwise manner between two consecutive spatial cycles and in the sequel achieves the asymptotic tracking convergence. Rigorous analysis are presented along with a numerical example to show the effectiveness of the proposed controller. Copyright © 2012 John Wiley & Sons, Ltd.     

Simplification of the characteristic equation of multirate sampled data control systems

A method of simplifying the characteristic equation of two classes of linear time invariant multirate sampled data systems to a form similar to that of the analogous single-rate system is developed. The resulting equations are useful for multirate system design.     

Formation-containment control of second-order multi-agent systems with only sampled position data

This paper studies the formation-containment control problem of second-order multi-agent systems with only sampled position data. It is assumed that there exist interactions among leaders and the leaders’ neighbours are only leaders. Two different control protocols with only sampled position information are proposed for followers and leaders, respectively. By the algebraic graph theory and matrix theory, sufficient conditions are given to guarantee that the leaders achieve a desired formation and the followers asymptotically converge into the convex hull formed by the corresponding states of the leaders, i.e. the multi-agent systems achieve formation-containment. Moreover, an explicit expression of the formation position function is given for each leader. Finally, a numerical simulation is provided to illustrate the effectiveness of theoretical results.     

Control of asynchronous sampled data systems

This paper is concerned with the problem of controller design in the case of asynchronous sampled data systems. Optimal LQG controllers are obtained for the class of two-rate systems where all the control inputs are held at a rate which is asynchronously related to the rate with which all of the outputs are sampled. Furthermore for this class, a parameterization of all stabilizing controllers is provided     

A hierarchical approach to state space constrained optimization problems

A class of hierarchical prediction-type methods for solving state space constrained optimization problems is studied. The approach is a generalization of the balance-type methods suggested by the authors in earlier papers, where the state space constrained optimization problem was converted into a two-level problem with control constrained first-level problems by using the multiplier method of Hestenes. The use of a prediction-type approach allows simpler first-level optimization problems via decomposition and/or simplification of the constraints.     

A fuzzy-logic approach to industrial control problems

Increasing demands for improved profitability and product quality, together with a growing awareness of the effects of industrial wastage on the environment, is forcing manufacturers to closely examine their process operations. As a consequence there is currently significant research and development activity aimed at improving control system strategies in a variety of industrial sectors. Recent years have witnessed renewed interest in fuzzy logic and rule-based control strategies and, by considering two illustrative industrial case studies, this paper highlights some of the potential advantages. This work was presented, in part, at the International Symposium on Artificial Life and Robotics, Oita, Japan, February 18–20, 1996     

The design of stochastic sampled data control systems containing a discrete actuator

A numerical method is outlined for synthesizing optimum impulse compensators in the mean-square error sense for feedback systems containing a coarse quantization actuator element where thesigma/qratio must be specified not only to ensure a valid estimate of the quantization error but also to limit the delay errors caused by the finite rate of actuator operation.