A bias-eliminated least-squares method for continuous-time model identification of closed-loop systems

Schemes for system identification based on closed-loop experiments have attracted considerable interest lately. However, most of the existing approaches have been developed for discrete-time models. In this paper, the problem of continuoustime model identification is considered. A bias correction method without noise modelling associated with the Poisson moment functionals approach is presented for indirect identification of closed-loop systems. To illustrate the performances of the proposed method, the bias-eliminated least-squares algorithm is applied to the parameter estimation of a simulated system via Monte Carlo simulations.     

Identification of closed-loop systems with low-order controllers

A bias correction method without noise modelling was recently proposed for indirect identification of closed-loop systems. A key assumption used in deriving this method required that the order of the controller is not less than that of the open-loop plant. A significant feature of the results presented in this paper is the removal of this assumption to enable the method to be applicable to unbiased identification of closed-loop systems with low order controllers.     

Closed-loop identification: a two step approach

The accuracy aspects of identification (with respect to both variance and bias of estimates) and the role of filtering in closed-loop identification is discussed in this paper. It is shown that the key difference between closed-loop and open-loop identification is the existence of the sensitivity function. A closed-loop identification algorithm which asymptotically yields the same expressions as open-loop identification, in both variance and bias errors, is proposed. The proposed algorithm is evaluated by simulated examples as well as experiments performed on a computer-interfaced pilot-scale process.     

An energy-gain bounding approach to robust fuzzy identification

A novel method for the robust identification of interpretable fuzzy models, based on the criterion that identification errors are least sensitive to data uncertainties and modelling errors, is suggested. The robustness of identification errors towards unknown disturbances (data uncertainties, modelling errors, etc.) is achieved by bounding (i.e. minimizing) the maximum possible value of energy-gain from disturbances to the identification errors. The solution of energy-gain bounding problem, being robust, shows an improved performance of the identification method. The flexibility of the proposed framework is shown by designing the variable learning rate identification algorithms in both deterministic and stochastic frameworks.     

High-performance decentralized control design for general interconnected systems with applications in cooperative control

This paper deals with the decentralized control of an interconnected system, where each subsystem has models of all other subsystems (subject to uncertainty). A decentralized controller is constructed based on a reference centralized controller. It is shown that when a priori knowledge of each subsystem about the other subsystems’ models is exact, then the decentralized closed-loop system can perform exactly the same as its centralized counterpart. An easy-to-check necessary and sufficient condition for the internal stability of the decentralized closed-loop system is obtained. Moreover, the stability of the closed-loop system in the presence of the perturbation in the parameters of the system is investigated, and it is shown that the decentralized control system is probably more robust than its centralized counterpart. A proper cost function is then defined to evaluate the closeness of the decentralized closed-loop system to the corresponding centralized control system. This enables the designer to obtain the maximum allowable standard deviation for the modelling errors of the subsystems to achieve a satisfactorily small relative performance deviation with a sufficiently high probability. Finally, the proposed method is exploited to design a near-optimal decentralized control law with respect to a quadratic cost function, whose performance can, under certain conditions, be equal to the minimum achievable performance index corresponding to the centralized LQR control law. The effectiveness of the proposed method is demonstrated in three numerical examples.     

Time-domain fixed-structure closed-loop model identification of an unstable multivariable maglev nanopositioning system

This paper presents improved empirical representations of a general class of open-loop unstable systems using closed-loop system identification. A multi-axis magnetic-levitation (maglev) nanopositioning system with an extended translational travel range is used as a test model to verify the closed-loop system-identification method presented in this paper. A closed-loop identification technique employing a known controller structure is used for model identification and validation. Direct and coupling transfer functions (TFs) are then derived from the experimental input-output time sequences and the knowledge of controller dynamics. A persistently excited signal with a bandwidth in the frequency range of interest is used as a reference input. An order-reduction algorithm is developed to obtain TFs with predefined orders, which gives the closest match in the frequency range of interest without missing any significant plant dynamics. The entire analysis is performed in the discrete-time domain in order to avoid any errors due to continuous-to-discrete-time conversion and vice versa. Continuous-time TFs are used only for order-reduction and performance analysis of the identified TFs. Experimental results are presented in the time as well as frequency domains to verify the accuracy of the identified plant TFs. These results also demonstrate the effectiveness of the developed closed-loop identification method in meeting all of the three core objectives—(i) reduction in cross-axial coupling from 9.213 μm to 0.911 μm in translation and from 22.03 μrad to 1.353 μrad in rotation, (ii) large range motion capability with a travel range of ±2.9 mm, and (iii) improved robust stability.     

A methodology for control-relevant nonlinear system identification using restricted complexity models

A broadly-applicable, control-relevant system identification methodology for nonlinear restricted complexity models (RCMs) is presented. Control design based on RCMs often leads to controllers which are easy to interpret and implement in real-time. A control-relevant identification method is developed to minimize the degradation in closed-loop performance as a result of RCM approximation error. A two-stage identification procedure is presented. First, a nonlinear ARX model is estimated from plant data using an orthogonal least squares algorithm; a Volterra series model is then generated from the nonlinear ARX model. In the second stage, a RCM with the desired structure is estimated from the Volterra series model through a model reduction algorithm that takes into account closed-loop performance requirements. The effectiveness of the proposed method is illustrated using two chemical reactor examples.     

Closed-loop subspace identification using the parity space

It is known that many subspace algorithms give biased estimates for closed-loop data due to the existence of feedback. In this paper we present a new subspace identification method using the parity space employed in fault detection in the past. The basic algorithm, known as subspace identification method via principal component analysis (SIMPCA), gives consistent estimation of the deterministic part and stochastic part of the system under closed loop. Column weighting for SIMPCA is introduced which shows improved efficiency/accuracy. A simulation example is given to illustrate the performance of the proposed algorithm in closed-loop identification and the effect of column weighting.     

闭环系统的输出过采样辨识方法及其估计精度分析

传统闭环系统辨识方法的可辨识性受到参考设定信号和控制器结构的限制．提出了一种通过对输出过采样实现线性离散时间闭环系统辨识的方法，输出过采样提供了更多的系统结构信息，在传统辨识方法的可辨识条件不满足的情况下，仍能正确辨识系统参数，针对有色噪声干扰，分析其在不同过采样率下的估计精度，得出最优估计的过采样率计算方法．辨识方法实现简单、运算量小、估计精度高．仿真试验验证了其有效性．     

基于逼近误差调节的直接自适应模糊控制

对含未知参数的一类非线性系统给出一种新的直接自适应模糊控制方案．利用在线自适应调节估计逼近误差,用此估计值设计补偿器减小逼近误差对跟踪精度的影响．该方法不仅能够保证闭环系统的稳定性,而且可以使跟踪误差收敛到0或0的小邻域．     

Indirect closed-loop identification by optimal instrumental variable method

Recently, a new bias-compensating least-squares (BCLS) method was proposed for the identification of a closed-loop system with high-order controller. The major feature of this method is that it can achieve consistent parameter estimation without modelling the coloured noises acting on the system. This paper studies the connection between the BCLS method and the instrumental variable (IV) family. It is shown that the BCLS method is a kind of weighted instrumental variable (WIV) method whose results do not depend upon the order of the controller.     

基于单位分解的一类非线性系统的变结构控制设计

采用单位分解概念和技术,结合交结构控制方法和LMI方法,讨论一类非线性系统的控制设计问题．首先利用单位分解在紧致域上能够以任意给定精度逼近连续函数的性质,将一类非线性系统表示为带有误差的近似模形式;然后在误差满足某些条件的情况下,利用交结构控制设计了渐近稳定控制器;最后以仿真实例说明了该方法的有效性。     

基于正交分解的递推子空间闭环辨识方法

为实现闭环系统在线辨识,提出递推正交分解闭环子空间辨识方法(RORT)。首先,根据闭环系统状态空间模型和数据间投影关系,构建确定-随机模型,并利用GIVENS变换实现投影向量的递推QR分解;然后,引入带遗忘因子的辨识算法,构建广义能观测矩阵的递推更新形式,以减少子空间辨识算法中QR分解和SVD分解的计算量;最后,针对某型号陀螺仪闭环系统进行实验。实验结果表明, RORT法的辨识拟合度高于91%,能够对陀螺仪闭环系统模型参数进行在线监测。     

基于末端转角误差的并联机器人零点标定方法

针对一种4自由度高速并联机器人（Cross-IV机器人）的零点标定问题,提出了一种基于末端转角误差信息的快速零点标定方法．基于机器人的单支链闭环矢量方程,建立了零点误差全集与末端误差之间的映射模型．通过对误差传递矩阵的分解,在仅利用旋转编码器对末端转角误差进行测量的基础上,构建了该机器人的快速零点误差辨识模型．为进一步最大化测量效率及提高辨识矩阵的鲁棒性,提出了一种优化的测量点选择方案．通过仿真详细验证了该零点标定方法的鲁棒性与准确性．基于激光跟踪仪的验证实验表明,经标定后机器人末端位置误差降低至1.312 mm,转角误差降低至0.202°,标定结果表明该零点标定方法简单、有效．     

A measurement-based approach for designing reduced-order controllers with guaranteed bounded error

The objective of this paper is to present a measurement-based control-design approach for single-input single-output linear systems with guaranteed bounded error. A wide range of control-design approaches available in the literature are based on parametric models. These models can be obtained analytically using physical laws or via system identification using a set of measured data. However, due to the complex properties of real systems, an identified model is only an approximation of the plant based on simplifying assumptions. Thus, the controller designed based on a simplified model can seriously degrade the closed-loop performance of the system. In this paper, an alternative approach is proposed to develop fixed-order controllers based on measured data without the need for model identification. The proposed control technique is based on computing a suitable set of fixed-order controller parameters for which the closed-loop frequency response fits a desired frequency response that meets the desired closed-loop performance specifications. The control-design problem is formulated as a nonlinear programming problem using the concept of bounded error. The main advantages of our proposed approach are: (1) it guarantees that the error between the computed and the desired frequency responses is less than a small value; (2) the difficulty of finding the globally optimal solution in the error minimisation problem is avoided; (3) the controller can be designed without the use of any analytical model to avoid errors associated with the identification process; and (4) low-order controllers can be designed by selecting a fixed low-order controller structure. To experimentally validate and illustrate the efficacy of the proposed approach, proportional-integral measurement-based controllers are designed for a DC (direct current) servomotor.     

Robust predictor feedback for discrete-time systems with input delays

This work studies the design problem of feedback stabilisers for discrete-time systems with input delays. A backstepping procedure is proposed for disturbance-free discrete-time systems. The feedback law designed by using backstepping coincides with the predictor-based feedback law used in continuous-time systems with input delays. However, simple examples demonstrate that the sensitivity of the closed-loop system with respect to modelling errors increases as the value of the delay increases. The paper proposes a Lyapunov redesign procedure that can minimise the effect of the uncertainty. Specific results are provided for linear single-input discrete-time systems with multiplicative uncertainty. The feedback law that guarantees robust global exponential stability is a nonlinear, homogeneous of degree 1 feedback law.     

Integral sliding mode controller for precise manoeuvring of autonomous underwater vehicle in the presence of unknown environmental disturbances

We propose an integral sliding mode controller (ISMC) to stabilse an autonomous underwater vehicle (AUV) which is subject to modelling errors and often suffers from unknown environmental disturbances. The ISMC is effective in compensating for the uncertainties in the hydrodynamic and hydrostatic parameters of the vehicle and rejecting the unpredictable disturbance effects due to ocean waves, tides and currents. The ISMC is comprised of an equivalent controller and a switching controller to suppress the parameter uncertainties and external disturbances, and its closed-loop system is exponentially stable. Numerical simulations were performed to validate the proposed control approach, and experimental tests using Cyclops AUV were carried out to demonstrate its practical feasibility.     

Further results on input-to-state stability for nonlinear systems with delayed feedbacks

We consider a class of nonlinear control systems for which stabilizing feedbacks and corresponding Lyapunov functions for the closed-loop systems are available. In the presence of feedback delays and actuator errors, we explicitly construct input-to-state stability (ISS) Lyapunov-Krasovskii functionals for the resulting feedback delayed dynamics, in terms of the available Lyapunov functions for the original undelayed dynamics, which establishes that the closed-loop systems are input-to-state stable (ISS) with respect to actuator errors. We illustrate our results using a generalized system from identification theory and other examples.     

伺服系统弹性负载的闭环辨识方法EI北大核心CSCD

为有效解决机械谐振问题,伺服系统弹性负载的辨识是非常关键的步骤.本文以工业中最常见的双惯量系统作为辨识对象设计闭环辨识方法,使用伪随机二进制序列作为激励并采集电机电流转速信号.在此基础上,使用最小二乘法拟合系统的自回归移动平均模型,并提高模型阶次以保证拟合精度.为抑制采样噪声的影响,提出基于平衡截断的模型降阶方法,根据Hankel奇异值大小判断系统阶次并提取主要模态.最后,通过仿真和实验进行验证,结果表明:相比于传统辨识方法,本文所提出的辨识方法能够有效抑制噪声干扰,具有更高的精度.     

Sufficient condition for stable control of discrete-time systems with statistical process model

A method for investigating the stability of discrete-time control systems with statistical uncertainties in model parameters is presented. These uncertainties are due to estimation errors arising in the identification of the process model. A mutually independent representation of these errors is applied. The process model and a controller algorithm are investigated in a state-space form. The closed-loop system is considered to be an autonomous one, with some mutually independent statistics affecting the system coefficients. Sufficient conditions for stability of these systems are derived. The example of a second-order non-minimal-phase system with state-space linear quadratic-problem controller and pole-placement controller is discussed.