A two‐stage searching method for continuous time‐delay systems identification

This paper presents a novel method to estimate the unknown parameters of continuous‐time systems with time delay. In the proposed method, the time delay and plant parameters are estimated separately. To estimate the time delay, a one‐dimensional searching method with variable step size is proposed to improve computational efficiency. The searching method consists of two stages: the coarse stage and the refined searching stage. To analyze the convergence of the searching method, the concept of significant interval is proposed. By defining the significant interval, a sufficient condition for global convergence of the searching method is provided. Based on the two‐stage searching method, a novel identification algorithm is developed in which the simplified refined instrumental variable for continuous‐time models algorithm is used to estimate the plant parameters. Simulation results demonstrate that the proposed identification method can estimate the unknown parameters of continuous‐time system with time delay efficiently. The estimation results under different noisy conditions verify the reliability and robustness of the proposed method. The applicability of the developed identification method is demonstrated by a practical example.     

具有不确定性时滞及仿射结构不确定性过程的简易自适应控制

讨论了具有不确定性时滞及仿射结构不确定系统的简易自适应控制问题.给出了对系统再建模方法,所提出的方法可更精确评价不确定性时滞.通过对受控对象附加鲁棒并行补偿器补偿,设计了简易自适应控制器.     

Identification of continuous-time systems with multiple unknown time delays by global nonlinear least-squares and instrumental variable methods

This paper considers the identification problem of multiple input single output (MISO) continuous-time systems with unknown time delays of the inputs, from sampled input-output data. An iterative global separable nonlinear least-squares (GSEPNLS) method which estimates the time delays and transfer function parameters separably is derived to significantly reduce the possibility of convergence to a local minimum, by using the stochastic global-optimization techniques. Furthermore, the GSEPNLS method is modified to a novel global separable nonlinear instrumental variable (GSEPNIV) method to remove the biases of the estimates in the presence of high measurement noise. Simulation results show that the proposed algorithms work quite well.     

Non-iterative optimal min-max instrumental variable method for system identification

An optimal min-max instrumental variable (IV) method for estimating the parameters in difference equation models is presented. The method gives the smallest estimation error variance in the ‘worst noise’ case from a prespecified class of noises. Implementation of this new method does not require knowledge of system or noise parameters and therefore can be done without iteration. This is an attractive feature since other min-max or generally optimal IV methods previously introduced require at least a knowledge of system parameters, and cannot be implemented directly. Results of simulations demonstrate the applicability of the method to both artificial and real data.     

Identification of discrete-time output error model for industrial processes with time delay subject to load disturbance

In this paper, a bias-eliminated output error model identification method is proposed for industrial processes with time delay subject to unknown load disturbance with deterministic dynamics. By viewing the output response arising from such load disturbance as a dynamic parameter for estimation, a recursive least-squares identification algorithm is developed in the discrete-time domain to estimate the linear model parameters together with the load disturbance response, while the integer delay parameter is derived by using a one-dimensional searching approach to minimize the output fitting error. An auxiliary model is constructed to realize consistent estimation of the model parameters against stochastic noise. Moreover, dual adaptive forgetting factors are introduced with tuning guidelines to improve the convergence rates of estimating the model parameters and the load disturbance response, respectively. The convergence of model parameter estimation is analyzed with a rigorous proof. Illustrative examples for open- and closed-loop identification are shown to demonstrate the effectiveness and merit of the proposed identification method.     

Passive Control for Stochastic Interval Systems with Interval Time‐Varying Delay

This paper is concerned with the problem of delay‐dependent passive analysis and control for stochastic interval systems with interval time‐varying delay. The system matrices are assumed to be uncertain within given intervals, and the time delay is a time‐varying continuous function belonging to a given range. By the transformation of the interval uncertainty into the norm‐bounded uncertainty, partitioning the delay into two segments of equal length, and constructing an appropriate Lyapunov–Krasovskii functional in each segment of the delay interval, delay‐dependent stochastic passive control criteria are proposed without ignoring any useful terms by considering the information of the lower bound and upper bound for the time delay. The main contribution of this paper is that a tighter upper bound of the stochastic differential of Lyapunov–Krasovskii functional is obtained via a newly‐proposed bounding condition. Based on the criteria obtained, a delay‐dependent passive controller is presented. The results are formulated in terms of linear matrix inequalities. Numerical examples are given to demonstrate the effectiveness of the method.     

Adaptive robust control of uncertain nonlinear systems with nonlinear delayed state perturbations

The problem of robust stabilization of uncertain nonlinear dynamical systems with multiple time delays is considered. In the paper, the upper bound of the nonlinearity and uncertainty, including delayed states, is assumed to be a linear function of some parameters which are still assumed to be unknown. Here, we do not require that the nonlinear terms including delayed states are linear norm-bounded in the states. An improved adaptation law with σ-modification is employed to estimate the unknown parameters, and a class of memoryless adaptive robust state feedback controllers is proposed. It is also shown that the proposed adaptive robust controllers can guarantee the uniform asymptotic stability of uncertain nonlinear time-delay systems. Finally, as a numerical example, an uncertain time-delay ecosystem with two competing species is given to demonstrate the validity of the results.     

过程控制常用连续模型的直接辨识法及应用

针对工业过程中最常用的一阶加滞后、二阶加滞后、二阶加零点、二阶加零点及滞后、积分惯性加滞后等环节,给出了基于阶跃响应的连续模型参数直接辨识算法。由传递函数的拉普拉斯逆变换式和对象阶跃响应的采样数据构成模型参数回归表达式,用最小二乘法或辅助变量法直接辨识对象的连续时间传递函数模型参数。仿真与实际应用结果表明,该算法提高了模型辨识精度,减小了对过程的扰动,并且对输出测量噪声不敏感,鲁棒性强,容易编程实现,可提高实际PID控制器参数整定质量。     

Robust stabilization for uncertain time-delay systems containingsaturating actuators

A class of uncertain time-delay systems containing a saturating actuator is considered. These systems are characterized by delayed state equations (including a saturating actuator) with norm-bounded parameter uncertainty (possibly time varying) in the state and input matrices. The delay is assumed to be constant bounded but unknown. Using a Razumikhin approach for the stability of functional differential equations, upper bounds on the time delay are given such that the considered uncertain system is robustly stabilizable, in the case of constrained input, via memoryless state feedback control laws. These bounds are given in terms of solutions of appropriate finite dimensional Riccati equations     

BIBO stability and stabilization of networked control systems with short time‐varying delays

This paper presents a robust control approach to solve the stability and stabilization problems for networked control systems (NCSs) with short time‐varying delays. A new discrete‐time linear uncertain system model is proposed to describe the NCS, and the uncertainty of the network‐induced delay is transformed into the uncertainty of the system matrix. Based on the obtained uncertain system model, a sufficient BIBO stability condition for the closed‐loop NCS is derived by applying the small gain theorem. The obtained stability condition establishes a quantitative relation between the BIBO stability of the closed‐loop NCS and two delay parameters, namely, the delay upper bound and the delay variation range bound. Moreover, design procedures for the state feedback stabilizing controllers are also presented. An illustrative example is provided to demonstrate the effectiveness of the proposed method. Copyright © 2010 John Wiley & Sons, Ltd.     

Parameter identification of distributed parameter systems in the presence of measurement noise

A new approach to recursive parameter identification of second-order distributed parameter systems in the presence of measurement noise under unknown initial and boundary conditions is proposed. A two-dimensional low-pass filter is introduced to pre-filter the observed data corrupted by measurement noise. The low-pass filter is designed in the continuous time-space domain and discretized by bilinear transformation. Thus a discrete estimation model of the system under study is easily constructed with filtered input-output data for recursive identification algorithms. The recursive least squares method is still efficient in the presence of low measurement noise if the filter parameters are designed so that the noise effects are reduced sufficiently. Using filtered input data as instrumental variables, a recursive instrumental variable method is also presented to obtain consistent estimates when the digital low-pass filters are not designed successfully or when the output data is corrupted by high measurement noise. Illustrative examples are given to demonstrate the applicability of the proposed methods.     

ROBUST CONTROL FOR A CLASS OF UNCERTAIN STATE‐DELAYED SINGULARLY PERTURBED SYSTEMS

This paper considers the problem of robust control for a class of uncertain state‐delayed singularly perturbed systems with norm‐bounded nonlinear uncertainties. The system under consideration involves state time‐delay and norm‐bounded nonlinear uncertainties in the slow state variable. It is shown that the state feedback gain matrices can be determined to guarantee the stability of the closed‐loop system for all ∞ ∞ (0, ∞00) and independently of the time‐delay. Based on this key result and some standard Riccati inequality approaches for robust control of singularly perturbed systems, a constructive design procedure is developed. We present an illustrative example to demonstrate the applicability of the proposed design approach.     

Real-time optimization under parametric uncertainty: a probability constrained approach

Uncertainty is an inherent characteristic in most industrial processes, and a variety of approaches including sensitivity analysis, robust optimization and stochastic programming have been proposed to deal with such uncertainty. Uncertainty in a steady state nonlinear real-time optimization (RTO) system and particularly making robust decisions under uncertainty in real-time has received little attention. This paper discusses various sources of uncertainty within such closed loop RTO systems and a method, based on stochastic programming, that explicitly incorporates uncertainty into the RTO problem is presented. The proposed method is limited to situations where uncertain parameters enter the constraints nonlinearly and uncertain economics enter the objective function linearly. Our approach is shown to significantly improve the probability of a feasible solution in comparison to more conventional RTO techniques. A gasoline blending example is used to demonstrate the proposed robust RTO approach.     

Refined instrumental variable methods for identification of LPV Box-Jenkins models

The identification of linear parameter-varying systems in an input-output setting is investigated, focusing on the case when the noise part of the data generating system is an additive colored noise. In the Box-Jenkins and output-error cases, it is shown that the currently available linear regression and instrumental variable methods from the literature are far from being optimal in terms of bias and variance of the estimates. To overcome the underlying problems, a refined instrumental variable method is introduced. The proposed approach is compared to the existing methods via a representative simulation example.     

Robust stability of uncertain time-delay systems

This paper presents several sufficient conditions, delay-independent or delay-dependent, that guarantee the robust stability of uncertain time-delay systems subjected to parametric perturbations. Both single and composite uncertain systems with one delayed state are considered and each of these results, expressed by a succinct scalar inequality, permits the assessment of the transient behaviour of uncertain systems. The robustness of the time-delay system with respect to delay uncertainty is also discussed. Furthermore, these results are extended to the perturbed systems with multiple non-commensurate time delays. It is shown that the parameter perturbations may destabilize the system; hence the nominal system should be sufficiently stable to ensure robust stability.     

Robust PID tuning for Smith predictor in the presence of model uncertainty

This paper presents robust PID tuning for the Smith predictor in the presence of model uncertainty. The concept of the equivalent gain plus time delay (EGPTD) is introduced to incorporate robust stability in PID tuning of the Smith predictor. In particular, an application is developed for the robust tuning of the first order plus time delay (FOPTD) system and the second order plus time delay (SOPTD) system because the systems have been used extensively to describe chemical processes. The proposed tuning method can cope with simultaneous uncertainties in all parameters of the model in an efficient manner. Another important and attractive feature of the method is that it can utilize many currently available PID tuning rules. Simulation results are provided to demonstrate the availability of the method.     

Structure identification of uncertain general complex dynamical networks with time delay

It is well known that many real-world complex networks have various uncertain information, such as unknown or uncertain topological structure and node dynamics. The structure identification problem has theoretical and practical importance for uncertain complex dynamical networks. At the same time, time delay often appears in the state variables or coupling coefficients of various practical complex networks. This paper initiates a novel approach for simultaneously identifying the topological structure and unknown parameters of uncertain general complex networks with time delay. In particular, this method is also effective for uncertain delayed complex dynamical networks with different node dynamics. Moreover, the proposed method can be easily extended to monitor the on-line evolution of network topological structure. Finally, three representative examples are then given to verify the effectiveness of the proposed approach.     

Robust consensus for networked mechanical systems with coupling time delay

This paper studies the state consensus for a class of networked nonlinear mechanical systems with coupling time delay. In particular, robust consensus protocols for both deterministic and uncertain systems with time delay are investigated. For deterministic systems, we develop a P-like protocol which allows for variable coupling time delay. We show that it is sufficient to have only the relative position information together with a damping control term, whereas the relative velocity information is not needed for state consensus. Then, an adaptive robust control protocol is proposed for uncertain systems with unknown parameters in the system dynamics and arbitrary constant coupling time delays. By introducing the passivity-based framework, we demonstrate that state consensus is still reachable in this case. Finally, a numerical example is included to illustrate the obtained results.